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All right, good morning.

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This is good morning.

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Sorry.

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How dare you say good morning back to me when I'm not finished introducing this podcast.

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We've been, were you like on Noster all morning and you're just good morning.

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Good morning.

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Yeah, I'm just, I'm locked in.

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I'm locked in for my morning.

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Good morning.

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This is the magic internet math podcast.

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Episode three title unknown.

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um what's up man how you been doing well how are you i'm great dude i'm excited like every time i

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get to do this i'm excited really like i'm excited for what we're gonna do today i feel like we're

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you know we spent the last two episodes setting up you and i kind of just shooting the shit

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right it's been good yeah and i think now we're gonna get into a little bit of meat

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We've lulled the subscriber base

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Into a full sense of security

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And now we're going to bring them into the actual math stuff

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This is why I brought you on, man

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To explain to me what the hell we have been doing

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Thank you

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That is exactly what we've done

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Do you think it's okay

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To motivate why we're about to have this discussion today?

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Yeah

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Um, so I think today what we're going to start talking about is how Bitcoin actually secures money, right?

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There's a lot of very helpful abstractions we give to people so that the first time they hear about Bitcoin, they're not learning about a bunch of finite field math and a bunch of electric curves and all this stuff.

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We say, hey, you have a secret.

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Here are your secret words.

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You do not share these with anyone.

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And that is an abstraction on top of an abstraction on top of an abstraction.

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What do I mean by that?

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Your 12 or 24 seed words is from BIP39.

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And it's a way of generating a BIP32 extended private key.

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And that extended private key is basically your map to the elliptic curve on how Bitcoin operates.

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At the most foundational level, you just need entropy.

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You need a random thing.

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Those 12 and 24 words, you can reasonably discern if you generated, like if you didn't just, you know, pick them yourself.

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or if you didn't, you know, if you had a good trusted setup in how to generate that.

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It's the first time those 12 or 24 English words have ever been assembled in that order.

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Yeah.

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So there's, yeah.

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When you get a key, unless it's like in alphabetical order, it's going to look pretty random to you.

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Right.

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Or unless they all start with the same letter or something like that.

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It's going to, the thing I was like, when you first, the second you started talking,

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The image that came to my mind with people.

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Have you ever seen the picture of, I don't know if it's a frog or a beaver, but it's drinking out of a fire hose?

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I'm not sure if I've seen that one.

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So this used to, in my last company, I had a boss who had this picture right outside his office.

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And it was like a frog drinking out of a fire hose.

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And that's basically because that's kind of like what we are all doing when we get into Bitcoin, especially when it comes to the math.

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and we don't even really know it.

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At some point, you don't even realize you just opened wide,

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jammed a fire plug, and turned it on.

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And I think that's why a lot of people just,

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like I think it's like a reflex reaction to be like,

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all right, dude, like what?

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Everything over 21 million, okay?

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That's the math, okay?

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And there's just so much, like everything you just said,

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and it wasn't that much,

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but it's like it implies so much uh math behind it yes and some of it's actually i think it's like

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you know you get a 12 word key from a wallet that you make and trust or you make it yourself and you

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tell me if i'm wrong when i say everyone has probably asked themselves the question how do

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i know this is this key is like safe and no one can yeah no one can act even accidentally collide

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with it or intentionally like people are worried about back doors and wallet providers rightfully

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so because there's no way like i said so when you visually inspect your key right unless it's like

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unless it's absolutely ordered for human sight you're not going to have too many clues that it

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is either random or not random or you know so you have to kind of like this is one of those exercises

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that it would be nice if you can just if we can do it yourself you know i always love the dice

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role thing. Because otherwise, there's really no way for you to just trust God so much that that

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key is that no one can recreate it. Nobody could accidentally stumble on it. Those kinds of

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questions. I feel like no matter whether you care about math or not, every Bitcoiner is asked that

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question when they made a key. Right. Because it's the math that you have to fundamentally,

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it's one part of the map that's in your control.

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Everything else just works as software

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within the Bitcoin protocol.

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But like it start,

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there's a genesis somewhere of something you did,

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which is getting those keys.

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And from those words,

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you generate your addresses

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and your ability to sign your signatures

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and everything else, right?

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So it is incredibly foundational.

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Now, when you're,

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you mentioned dice rolls.

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Humans are really bad at perceiving

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if things are random or not.

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So even if like, like I wouldn't even trust an eyeball heuristic of a something random or not, because you could easily have like the number one, 100 hashed and turned into a C phrase.

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Right.

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Sure.

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So like you, you actually, there is no human heuristic eyeballing that can go about it.

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But that's my point, right?

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It's like, unless you get 12 of the same word, your brain's not going to say something's wrong here.

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And this is a funny thing too.

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Like, so in the BIP39 spec, you're allowed to repeat words.

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It can happen.

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And as someone who has generated hundreds.

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And that's a feature of pseudo-randomness, right?

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Not in a certain way, right?

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Well, right.

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Oh, you would perceive that like, oh, right.

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That you shouldn't get repeat words.

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You could repeat it.

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Well, but you can like repeat instances or maybe you don't.

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This is like the classic, like, is it a shuffle?

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is like your iPad shuffle, a random number.

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Right.

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And it's not totally random because you, you know,

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if it were random, truly random,

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you could get six in a row.

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Exactly.

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Right.

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Yeah.

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Exactly.

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Right.

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And so you have this element where I've,

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I've generated hundreds of seed phrases with testing,

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spinning up wallets, looking at stuff.

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And one time I was walking someone through a wallet setup,

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like for a test account, just to like, see how it works.

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And they're like, wait, I think something's broken.

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I just got the same word twice in a row.

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And I was like, that could happen.

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So there's 2,048 words in the bit 39 words, and they each correspond to a portion of bits.

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And when you take 12 or 24 of them together, when you take 12 of them together, you get 2 to the 128, which is a pretty large number.

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And if you do 24, you get 2 to the 256.

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And just before we even start to talk about like the expanded possible universe, 2 to the 256 is the total amount of valid numbers that fit on what we're going to talk about today, this, you know, elliptical, elliptic curve.

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2 to the 256, there are more possible Bitcoin private keys that exist than atoms in the observable universe.

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Just to talk about, because another thing humans are bad at, not just like detecting randomness, but being able to truly appreciate the size and scale of numbers.

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2 to the 256 is incredibly, incredibly, incredibly massive in the scale that is beyond things on even like a universe.

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level of observing. If every single atom in the observable universe was a Bitcoin private key,

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there would be plenty more Bitcoin private keys that were available.

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Right? Yeah. So real quick, I'm going to recommend a book. People should read this book.

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Okay. It's actually incredible and really important. It was written by my probability

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professor in college. His name is John Alan Paulos. I will probably bring his name up a lot.

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and I did it a lot and motivate the math.

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And this guy was one of the most important people I ever encountered in my life.

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It turned out he was a bestselling author of books.

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He was like on David Letterman talking about a book he wrote called Math and Humor.

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But the real bestseller that he wrote was called Innumeracy,

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subtitled Mathematical Illiteracy and Its Consequences.

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And in the prologue of the book, he really spends four or five pages trying to get you to understand how do you know how big something actually is?

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And like, how do you even imagine?

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How do you just imagine magnitudes of size?

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You know, I don't think it's not cryptography based.

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This book was written in like 1992.

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But like, which doesn't mean it could be.

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But basically it's like – just imagine like a million grains of sand.

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What happens in your mind when you even try to visualize or imagine something so unimaginable?

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And I think this is why like all the cheesy interview questions were like, tell me how you would count all the manhole covers in New York City or things like that.

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They're all really just getting at this question of how do you think about things that are sort of unthinkable?

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And when, you know, knowing the size of things, I mean, it's true, even to me, two to the 128th versus two to the 256. Like, there's clearly a universe of difference between those two numbers. But in my mind, it's hard to really discern between those two, right?

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Absolutely. Yeah. And so basically, as we're starting this off and kind of hitting at the touchpoint where most Bitcoiners interact with this, your C phrase, which maps to an extended private key, which we don't have to get exactly into, it's BIP32 of basically your big, big keychain.

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it is the genesis point of how you pick random numbers to be securing your money.

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And this is important because while your seed phrase, your words are the gateway to your money,

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it's not just one number. You have one genesis number, which then generates children numbers.

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And the reason is, is because every time you use a Bitcoin wallet, if you give me a new address,

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That's a new number. And basically your seed phrase acts as a deterministic treasure map. If you start with this, you can generate many children for any other address that you need that your wallet can control.

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Now, to tie this –

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to be on the curve. And so when you multiply the generator, you multiply that private key.

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Private key is a point on the curve. Nobody knows what it is. And then you multiply it by some

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number. That's going to be on the curve. That's really important. I have to stop using the word

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key to note importance. But that is the translation in mathematical structure. And what we'll be

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talking about today will be sort of how to understand, how do we build towards understanding

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that mathematical structure? Absolutely. Right. Yep. Absolutely. That's a good thing. Moving away

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from the concept of a key and turning this into a mathematical language of this is a point on a

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curve and all of the transformations you do on the curve, any of the, like you said, the field

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that addition is contained within the set of the data points that exist on the curve.

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for our ultra premium subscribers at home who have the video feed.

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You can see I'm wearing my LibSecP shirt today.

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You joke, but we are going to have it.

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Yeah.

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The curve exists.

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It's something that you probably would have seen in like 10th, 11th grade math.

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It's not super complicated.

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but

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this jump off point

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the last thing just to say on entropy

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is just the reason why

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you need to keep that secret because if someone else

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has that same exact starting point you have

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they can trivially

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figure out everything else which maybe goes into

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just as an initial point of

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why is this principle important

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is there is an asymmetry

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between

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knowing a private key and proving you

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own it and someone looking at that proof

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and being able to understand where your private key came from.

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So that asymmetry is critically important

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when it comes to the function of how this works,

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because you're able to essentially have the ability

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to prove that you own something

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without revealing what it actually is.

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And that is the entire basis of how Bitcoin works.

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the rest of the network sees the end result of this mathematical transformation, which is the

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point on the curve, which is mapped then to a public key. But only you have the requisite ability

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to prove that you have the private key tied to that public key. Very last point is I used to

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kind of make this metaphor, explaining to non-technical people, going to Lloyd's of London

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and explaining the concept of a public and a private key. And I would say you would walk into

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a post office and you have a wall of plexi class boxes, like your PO boxes, but instead

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of metal, they're like pure plastic.

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Like so you can, they're transparent.

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You can see through them.

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Yeah.

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And basically that is the Bitcoin blockchain, the entire UTXO set of all the addresses.

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And you can count how many envelopes are in each one.

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And anyone can look at any time at those public keys, but to necessarily move them, you have

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to publish a proof, which is a Bitcoin transaction that you control the underlying private key.

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And that's what your mailbox key is.

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That allows you to open up the box, take the envelopes out, and you can move the envelope somewhere else by putting it back in the mail sheet.

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So I think we've done a good amount of high-level easing into the water so we can kind of just jump right in.

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And I think the most important place to start, if we're going to talk about the first mathematical concept and how this field addition works, is modulo arithmetic.

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Mod.

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Yep.

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Right.

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So let's quickly – okay, if you're like brand new here, this is going to sound like – this is going to sound weird and strange.

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But if you've even like looked at this, if you're like intelligent enough to have found the podcast and hit play, this is something you'll realize you probably should have learned in third grade.

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and um maybe you even did but you didn't you know let's you know look these were around this

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modulo concept was around for a really long time it was gauss who just basically put it all into

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this type of framework and made it easy for everybody to grok it's right and it's modulo

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means remainder and i don't know about you but like i've been around math my whole life and when

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I first heard this concept, I was like, oh, that is remainders suck. I hate remainders. I like when

228
00:16:25,040 --> 00:16:29,980
there's no remainder. I remember, I would even push back to say that I think everyone has learned

229
00:16:29,980 --> 00:16:33,680
the concept of modulo, even if they didn't realize it, because the first thing you do when you learn

230
00:16:33,680 --> 00:16:38,560
long division is learn about what the heck a remainder is. That's right. And it's like the

231
00:16:38,560 --> 00:16:44,220
most disappointing and painful thing to deal with. It's like, oh, what? Why can't it just divide

232
00:16:44,220 --> 00:16:48,300
evenly. What the heck? I hate the number seven. That doesn't divide anything.

233
00:16:48,820 --> 00:16:54,900
And let's start with the easiest example, right? So three divided by two doesn't go into it evenly.

234
00:16:55,040 --> 00:17:00,300
If it was two divided by two, it'd be one. If it was two divided by four, it'd be two. So if you do

235
00:17:00,300 --> 00:17:09,080
three divided by two, your remainder is one because two goes into three one time. It can't do it twice.

236
00:17:09,080 --> 00:17:16,080
it's too many then so it three divided by two is one remainder one so there's one left over and

237
00:17:16,080 --> 00:17:21,360
that would be like the simplest initial place to start is you're and you could take any number

238
00:17:21,360 --> 00:17:27,800
and you were able to derive divided by two you can get some number in there the you know it's

239
00:17:27,800 --> 00:17:32,580
either one or zero um i'm assuming using whole integers you're not using fractions and stuff

240
00:17:32,580 --> 00:17:35,420
right but like if you're using whole numbers you're either going to have a remainder of zero

241
00:17:35,420 --> 00:17:36,760
or you have a remainder of one.

242
00:17:37,080 --> 00:17:37,940
It's going to be a remainder of zero

243
00:17:37,940 --> 00:17:39,260
for every single even number

244
00:17:39,260 --> 00:17:40,840
because it goes in evenly and perfect.

245
00:17:41,060 --> 00:17:43,300
And you're going to have a remainder of one for odd

246
00:17:43,300 --> 00:17:44,640
because it's always going to be one away

247
00:17:44,640 --> 00:17:45,380
from an even number.

248
00:17:45,580 --> 00:17:47,220
That's the simplest place to start.

249
00:17:47,560 --> 00:17:47,740
Right.

250
00:17:47,820 --> 00:17:49,820
And so the key point here is that

251
00:17:49,820 --> 00:17:53,360
we are really, you know,

252
00:17:53,660 --> 00:17:55,000
in the world we came from,

253
00:17:55,540 --> 00:17:57,400
we basically divided things

254
00:17:57,400 --> 00:17:59,320
and we eliminated the remainder.

255
00:17:59,440 --> 00:18:00,340
We didn't care about the remainder.

256
00:18:00,440 --> 00:18:01,560
We only cared about how many times

257
00:18:01,560 --> 00:18:02,780
that, you know, things divide.

258
00:18:03,100 --> 00:18:04,100
In this world,

259
00:18:04,100 --> 00:18:08,220
we only care about the remainder and we toss everything else out the window.

260
00:18:08,560 --> 00:18:13,060
So in this world, any number that has a remainder of one,

261
00:18:13,400 --> 00:18:17,040
in other words, any operation that results in a remainder of one is the same thing.

262
00:18:17,140 --> 00:18:22,960
And like you can call, there's a name for that in what you just described called the odd numbers, right?

263
00:18:23,040 --> 00:18:23,860
We just name it.

264
00:18:24,360 --> 00:18:29,160
Or where you say there's this world where there's two types of numbers, right?

265
00:18:29,160 --> 00:18:33,400
There's this two types of numbers modulo two, right?

266
00:18:33,400 --> 00:18:41,040
Right. Which is those that have a remainder of zero, i.e. the even numbers, or those that have the remainder of one, i.e. the odd numbers.

267
00:18:41,120 --> 00:18:43,260
But what we're abstracting is off the remainder.

268
00:18:44,720 --> 00:18:50,500
And, you know, like Bitcoin, the modulo, we're not divided by two or divided by two to the 256.

269
00:18:51,900 --> 00:18:52,340
Right.

270
00:18:52,340 --> 00:18:55,940
In certain ways, like in a hash function, that's what we're dividing by.

271
00:18:56,120 --> 00:18:57,520
That's the mod, right?

272
00:18:57,520 --> 00:19:08,440
But basically, the key is all of those remainders now, anything with the remainder of one or two is going to be the same.

273
00:19:08,580 --> 00:19:16,500
So in other words, if you're dividing by three, then the number four has a remainder of one.

274
00:19:16,800 --> 00:19:18,360
Number seven has the remainder of one.

275
00:19:18,400 --> 00:19:19,240
Number 10, right?

276
00:19:19,280 --> 00:19:22,660
So all those numbers are basically the same in this construct.

277
00:19:22,660 --> 00:19:29,020
All numbers that have the same remainder now are considered the same.

278
00:19:29,820 --> 00:19:32,100
And when dividing by three, there's three types of numbers.

279
00:19:32,240 --> 00:19:35,820
Those with the remainder of zero, remainder of one, and those with the remainder of two.

280
00:19:36,920 --> 00:19:39,740
And this is how we kind of build what is called the finite field.

281
00:19:39,920 --> 00:19:44,620
But this text we're going through starts with – they call it clock math.

282
00:19:45,340 --> 00:19:46,280
And then we build.

283
00:19:46,940 --> 00:19:50,940
And we're actually going to build – so when I asked you about motivating this thing, right?

284
00:19:50,940 --> 00:19:54,640
It was more of like, well, what are we actually, are we building to?

285
00:19:54,720 --> 00:19:57,580
We're building to potentially a conversation with a particular person.

286
00:19:58,080 --> 00:20:09,060
And that is like where we want to build from the most simple building block to LibSec, LibSec 256.

287
00:20:09,400 --> 00:20:12,380
And I think we've created a document that can do that.

288
00:20:12,480 --> 00:20:13,620
And that will link that.

289
00:20:13,720 --> 00:20:13,940
Yeah.

290
00:20:13,940 --> 00:20:17,020
Link that to the website, magicinternetmath.com.

291
00:20:17,020 --> 00:20:26,260
um so is that like i guess we've we've motivated it enough yeah so yeah i think we've motivated

292
00:20:26,260 --> 00:20:31,760
enough one last very simple example because we talked about clock arithmetic so we have divided

293
00:20:31,760 --> 00:20:36,580
by like the two one divisor where the remainder zero or one is like the simplest abstraction you

294
00:20:36,580 --> 00:20:43,600
can go to one that people use all of the time is that a clock you basically do modulo arithmetic

295
00:20:43,600 --> 00:21:04,520
You divide it by 12. So if you're not using military time, I'm going to put that aside for a second. If it's 1 a.m. and if it's 1 o'clock and 1 a.m., 1 o'clock in the morning and you say 15 hours from now, it's not 16 o'clock.

296
00:21:04,520 --> 00:21:09,200
it's 4 o'clock, sorry, it's 5 p.m.

297
00:21:09,520 --> 00:21:09,760
Right?

298
00:21:09,840 --> 00:21:13,220
So you're doing a modulo 12, a.m. and p.m., a.m. and p.m.

299
00:21:13,220 --> 00:21:15,880
Every 12 hours, you could take whatever number

300
00:21:15,880 --> 00:21:18,320
and you just flip it from a.m. to p.m.

301
00:21:18,340 --> 00:21:18,600
Right?

302
00:21:18,700 --> 00:21:20,800
And you're basically looking at it that way

303
00:21:20,800 --> 00:21:21,720
as like a modulo 12.

304
00:21:22,140 --> 00:21:25,240
Now, what we actually do in Bitcoin,

305
00:21:25,580 --> 00:21:28,400
which you mentioned, is we take a prime number,

306
00:21:28,500 --> 00:21:30,160
which is one of the other things that mathematic,

307
00:21:30,160 --> 00:21:33,360
like things that mathematicians are most obsessed about

308
00:21:33,360 --> 00:21:34,200
is prime numbers.

309
00:21:34,520 --> 00:21:38,140
Um, the actual, yes.

310
00:21:38,280 --> 00:21:50,100
And the actual point that we're going to do all of our modulo arithmetic from is two to the 256 minus two to the 232 minus 977.

311
00:21:51,600 --> 00:21:52,200
Yeah.

312
00:21:52,340 --> 00:22:01,280
That's probably worth like just memorizing that, that, that those three numbers, two to the 256 minus two to the 32nd power minus 977.

313
00:22:01,800 --> 00:22:02,280
Yeah.

314
00:22:02,280 --> 00:22:06,460
and you can actually expand factor that out and it becomes two to the 256

315
00:22:06,460 --> 00:22:11,460
minus two to the 232 minus two to the nine minus two to the eight minus two to

316
00:22:11,460 --> 00:22:14,360
the seven minus two to the six minus two to the four minus one

317
00:22:14,360 --> 00:22:18,420
and there's a binary representation of this too and that you know like there's

318
00:22:18,420 --> 00:22:22,600
a there's actually a reason um you know it'll be fun when we get there but

319
00:22:22,600 --> 00:22:27,360
that's a reason why that is the space that's the number right

320
00:22:27,360 --> 00:22:28,840
yeah

321
00:22:28,840 --> 00:22:33,660
there's a special

322
00:22:33,660 --> 00:22:38,320
name for these kind of prime numbers

323
00:22:38,320 --> 00:22:40,420
where you basically take 2 to the n

324
00:22:40,420 --> 00:22:41,400
of some number

325
00:22:41,400 --> 00:22:44,020
and then child factorizations of those

326
00:22:44,020 --> 00:22:44,700
minus 1

327
00:22:44,700 --> 00:22:46,500
it's actually a very common heuristic

328
00:22:46,500 --> 00:22:47,340
of what you're able to do

329
00:22:47,340 --> 00:22:48,720
it's called a Mersenne prime

330
00:22:48,720 --> 00:22:49,780
right

331
00:22:49,780 --> 00:22:53,220
so this is something that has been proven

332
00:22:53,220 --> 00:22:54,260
to be a prime number

333
00:22:54,260 --> 00:22:57,660
and an important thing to ask is

334
00:22:57,660 --> 00:23:04,380
why modulo a prime number with elliptic curve cryptography, right?

335
00:23:04,380 --> 00:23:05,380
You could pick any number.

336
00:23:05,520 --> 00:23:06,400
You're doing this curve.

337
00:23:06,820 --> 00:23:11,540
Why does it matter that you're doing modulo arithmetic with a prime number?

338
00:23:12,200 --> 00:23:12,320
Yeah.

339
00:23:12,480 --> 00:23:19,260
And before you answer, we just want to remember the fact that, you know, primes can't be divided.

340
00:23:20,160 --> 00:23:24,680
They don't have, like, primes are unable to be divided by anything other than itself in one, right?

341
00:23:25,300 --> 00:23:25,480
Yeah.

342
00:23:25,480 --> 00:23:39,240
But this is actually going to tee up into our next concept, though, is that the reason why you pick a prime number and do modular arithmetic, it proves that every non-zero number you put into this modular arithmetic.

343
00:23:39,240 --> 00:23:48,840
Now, again, remember, you could take any number and throw it into this operation, and you will get some modular remainder.

344
00:23:48,840 --> 00:23:59,820
And what's really important is when you have a prime number as the unit in which you do modulo arithmetic, you will always have a multiplicative inverse.

345
00:24:00,760 --> 00:24:04,000
You always will have a multiplicative inverse, which is very important.

346
00:24:04,000 --> 00:24:16,640
A translation for the non-technicals, because this is multiplicative inverse is a terminology that probably you learn somewhere in high school or college, right?

347
00:24:16,640 --> 00:24:21,400
But all it means is that you can divide it by something other than zero.

348
00:24:21,620 --> 00:24:24,640
You can understand that you're never allowed to divide by zero.

349
00:24:25,760 --> 00:24:32,500
So if a number has an inverse, it means that it can be divided validly.

350
00:24:33,360 --> 00:24:33,460
Yeah.

351
00:24:35,940 --> 00:24:39,260
So we just need to know.

352
00:24:39,420 --> 00:24:42,600
When we're dealing with massive numbers that we can't see and verify,

353
00:24:42,940 --> 00:24:46,080
we just need a way to know that it's all legit.

354
00:24:46,640 --> 00:24:57,340
Yes. And that's the point is that you're not going to have a number that you generate a point on the curve that's going to break.

355
00:24:58,340 --> 00:25:04,880
The example of not using a prime number, by the way, is say like if you're doing modulo four, right?

356
00:25:05,220 --> 00:25:05,460
Yep.

357
00:25:05,460 --> 00:25:12,800
Two times two is zero. So two doesn't have an inverse if you're using mod four.

358
00:25:12,800 --> 00:25:22,700
To the number two, there's nothing you can multiply it by to actually give it a modulo, to give it a remainder of one.

359
00:25:23,120 --> 00:25:23,680
Right.

360
00:25:23,920 --> 00:25:33,500
And since the remainder is what ultimately matters for this ability to find points on the curve, you need to have a non-zero number.

361
00:25:33,760 --> 00:25:40,260
Because if it's zero, then you don't have enough requisite information to do all of the field addition that we're talking about.

362
00:25:40,260 --> 00:25:58,480
And like you said, with two, like even if we go back to the clock example, why don't we just do modulo 12? Remember, we said that like the remainder is the thing we care about, which means you need to have a robust, like you need to be able to take many, many different numbers and ultimately make sure that you don't get a remainder of zero.

363
00:25:58,480 --> 00:26:02,580
And three times four on that is 12.

364
00:26:02,780 --> 00:26:04,480
And 12 modulo 12 is zero.

365
00:26:04,800 --> 00:26:12,080
And now you're back at the start where you have a zero, but you can't actually derive any information to be able to do that field addition.

366
00:26:12,540 --> 00:26:16,660
So just know zero is an unacceptable result for us.

367
00:26:16,660 --> 00:26:28,480
And, you know, like you could imagine building a system of money without actually knowing that every potential number on this curve can be transformed into another number on the curve.

368
00:26:28,600 --> 00:26:38,700
If you don't know that, the only way to know that is to actually, well, right now for humans on Earth right now, the only way we know that is that every number has an inverse.

369
00:26:38,700 --> 00:26:40,540
In other words, every number has a number.

370
00:26:40,760 --> 00:26:44,340
It could be multiplied to equal the number one.

371
00:26:44,560 --> 00:26:46,340
And that's what we say is an inverse.

372
00:26:46,660 --> 00:26:54,020
In the real numbers, we say 5, the inverse of 5 is 1 fifth because 5 times 1 fifth equals 1.

373
00:26:54,640 --> 00:27:01,120
But in the number system of what we call a finite field, which is like we described before,

374
00:27:01,220 --> 00:27:05,260
the field of remainders modulo some number prime, right?

375
00:27:06,480 --> 00:27:11,420
The way we divide is by multiplying by the inverse, but we don't have fractions.

376
00:27:11,680 --> 00:27:13,900
We just have other numbers in the system, right?

377
00:27:13,900 --> 00:27:22,060
And so we just need to make sure, but we still need to make sure we can take any two numbers and get the number one modulo, the prime.

378
00:27:22,920 --> 00:27:23,060
Yeah.

379
00:27:23,260 --> 00:27:33,920
And so I think as the point to tie this together, to explain why this matters, this field addition that we do is the mapping from the private key to the public key.

380
00:27:34,140 --> 00:27:35,840
That is ultimately what we're doing.

381
00:27:35,840 --> 00:27:38,040
and we need to be able to take,

382
00:27:38,320 --> 00:27:40,120
and this is also just an important concept of

383
00:27:40,120 --> 00:27:42,040
someone did not go through

384
00:27:42,040 --> 00:27:44,780
and look at all numbers between 0 and 2 to the 256

385
00:27:44,780 --> 00:27:49,700
and figure out, okay, like, does this number work?

386
00:27:49,800 --> 00:27:50,480
Does this number work?

387
00:27:50,540 --> 00:27:51,200
Does this number work?

388
00:27:51,400 --> 00:27:54,180
This is proven on a higher mathematical abstraction

389
00:27:54,180 --> 00:27:57,260
that you will be able to find this inverse.

390
00:27:57,680 --> 00:28:00,420
And the reason why the numbers are between 0 and 2 to the 256,

391
00:28:01,240 --> 00:28:04,200
you can pick a number bigger than 2 to the 256

392
00:28:04,200 --> 00:28:06,400
when you do this operation.

393
00:28:06,760 --> 00:28:07,860
But if you remember,

394
00:28:08,680 --> 00:28:11,200
the field in which we're doing this modular arithmetic

395
00:28:11,200 --> 00:28:15,020
is two to the 256 minus two to the 232.

396
00:28:15,400 --> 00:28:17,380
So if you take a number even bigger

397
00:28:17,380 --> 00:28:19,880
than two to the 256, it will work.

398
00:28:20,160 --> 00:28:22,280
Like it's not like you're gonna break Bitcoin

399
00:28:22,280 --> 00:28:24,240
if you find a bigger number to put into this thing.

400
00:28:24,380 --> 00:28:26,580
It is just going to get compressed down

401
00:28:26,580 --> 00:28:28,700
into the field of remainders

402
00:28:28,700 --> 00:28:31,080
where the largest number is two to the 256.

403
00:28:31,440 --> 00:28:33,000
It's like asking for 50 o'clock.

404
00:28:33,000 --> 00:28:34,700
It's like you're looping around.

405
00:28:34,980 --> 00:28:35,100
Exactly.

406
00:28:35,100 --> 00:28:36,100
That's two hours.

407
00:28:36,220 --> 00:28:37,320
That's two hours from now.

408
00:28:37,760 --> 00:28:37,960
Right.

409
00:28:38,160 --> 00:28:38,520
Exactly.

410
00:28:39,080 --> 00:28:39,480
Right.

411
00:28:39,660 --> 00:28:42,120
And so that's exactly right.

412
00:28:42,920 --> 00:29:00,837
This all comes down to the basically the really remarkable elegant simple proofs that Gauss did that showed that all of the math we know works in this space like you don really have to think that much about it but we go through the dot like

413
00:29:00,837 --> 00:29:07,437
it just works adding works in this space multiplying works in this space um adding

414
00:29:07,437 --> 00:29:13,057
multiplying are basically the operations of rings and fields so adding and multiplying is what you

415
00:29:13,057 --> 00:29:18,177
need to worry about. And that's why when we don't divide, we multiply by an inverse to divide.

416
00:29:18,177 --> 00:29:26,537
And that's like a big concept. So, yeah. So basically what we're talking about now

417
00:29:26,537 --> 00:29:36,137
is the concept of congruence. Okay. Right. So like we, we talked, we're talking about congruence

418
00:29:36,137 --> 00:29:42,337
modulo a number, which is like in, in the world we came from, we talked about the two things,

419
00:29:42,337 --> 00:29:46,077
two numbers being equal to each other, five equaling five.

420
00:29:46,197 --> 00:29:51,397
But now in the world of congruence, we're just saying that actually five could be equal

421
00:29:51,397 --> 00:29:58,157
to an infinite amount of numbers that when divided by your modulus, the remainder is

422
00:29:58,157 --> 00:29:59,677
five, right?

423
00:29:59,817 --> 00:29:59,977
Right.

424
00:29:59,977 --> 00:30:06,657
When we talked about the number one in a mod three concept, we said one, four, seven,

425
00:30:07,217 --> 00:30:10,737
10, et cetera, are all congruent.

426
00:30:10,977 --> 00:30:11,917
They're not equal.

427
00:30:12,337 --> 00:30:13,377
They're congruent.

428
00:30:13,797 --> 00:30:14,237
Right.

429
00:30:15,337 --> 00:30:17,477
Because as that final emphasis,

430
00:30:17,637 --> 00:30:18,937
all we care about is the remainder.

431
00:30:19,457 --> 00:30:20,557
That's all we care about.

432
00:30:20,957 --> 00:30:22,457
So that's why if you pick a number bigger,

433
00:30:22,917 --> 00:30:23,737
you can loop around.

434
00:30:23,877 --> 00:30:24,337
You're just going to,

435
00:30:24,717 --> 00:30:26,077
what you're going to do is

436
00:30:26,077 --> 00:30:27,857
if you pick a number larger than 2 to 256,

437
00:30:28,397 --> 00:30:29,937
you're just going to get a number

438
00:30:29,937 --> 00:30:31,997
that is going to map to another number

439
00:30:31,997 --> 00:30:34,557
within this modulo operation.

440
00:30:34,757 --> 00:30:37,537
Just like two o'clock and, you know,

441
00:30:37,997 --> 00:30:39,677
if you're doing modulo 12,

442
00:30:39,817 --> 00:30:42,237
2 a.m. and 2 p.m. are the same remainder.

443
00:30:42,337 --> 00:30:47,757
so like you're gonna get to the same thing yeah so real quick i want to read out of the document

444
00:30:47,757 --> 00:30:55,197
um please a snippet um and it's another thinker i think you're gonna hear a lot from from me is

445
00:30:55,197 --> 00:31:02,597
rudolf steiner who's the uh um renaissance man from the late 18th sorry the late 19th century

446
00:31:02,597 --> 00:31:07,897
early 20th century who created the waldorf schools where my children went were educated

447
00:31:07,897 --> 00:31:14,797
but really had a lot to say about thinking knowledge and really lines up with, it's probably

448
00:31:14,797 --> 00:31:18,537
the reason I think this way is because I've studied his work also for the last 15 years.

449
00:31:20,097 --> 00:31:27,177
So anyway, these documents include his thinking. And I just want to read this real quick. It says,

450
00:31:27,177 --> 00:31:33,197
what is the number three? Not three apples, not three tally marks, not the symbol three,

451
00:31:33,197 --> 00:31:39,957
The number itself, you cannot see it, hear it, or touch it. Yet, you can think it with perfect

452
00:31:39,957 --> 00:31:44,117
clarity, and your thinking of it is identical to every other person's thinking of it.

453
00:31:44,957 --> 00:31:51,537
Steiner argues that mathematical objects are the paradigm of thought content realities that

454
00:31:51,537 --> 00:31:57,297
exist for thinking alone, independent of any sensory medium. The number three is the same,

455
00:31:57,397 --> 00:32:01,537
whether represented by Roman numerals, binary digits, or Babylonian wedge marks.

456
00:32:01,537 --> 00:32:03,757
The representations change

457
00:32:03,757 --> 00:32:05,857
The thought content does not

458
00:32:05,857 --> 00:32:09,557
The modular arithmetic makes this vivid

459
00:32:09,557 --> 00:32:12,937
So in Z7

460
00:32:12,937 --> 00:32:16,777
Z7 means like that's when the modulus is 7

461
00:32:16,777 --> 00:32:18,057
We're dividing everything by 7

462
00:32:18,057 --> 00:32:20,717
So in Z7 the number 10 is 3

463
00:32:20,717 --> 00:32:22,257
It doesn't represent 3

464
00:32:22,257 --> 00:32:23,877
It's not equivalent to 3

465
00:32:23,877 --> 00:32:24,857
But it is 3

466
00:32:24,857 --> 00:32:27,137
What we call the residue class

467
00:32:27,137 --> 00:32:30,397
Which would be 3, 10, 17, 24, etc

468
00:32:30,937 --> 00:32:35,757
That's a single mathematical object perceived by thinking as a unity,

469
00:32:36,097 --> 00:32:38,317
despite having infinitely many representatives.

470
00:32:39,037 --> 00:32:44,217
So when you compute 5 plus 6, and remember in this mod 7, that equals 4.

471
00:32:44,837 --> 00:32:46,937
So 5 plus 6 equals 4 mod 7.

472
00:32:47,397 --> 00:32:48,997
You're not manipulating symbols.

473
00:32:49,557 --> 00:32:52,857
You are perceiving a relationship among thought contents,

474
00:32:52,857 --> 00:32:57,077
a relationship that holds necessarily, universally, and eternally.

475
00:32:57,077 --> 00:33:04,877
and as one last um extended line out for people who may be lost the reason why six plus five

476
00:33:04,877 --> 00:33:12,957
equals three in this context is six plus five equals eleven sorry equals four because six plus

477
00:33:12,957 --> 00:33:17,097
five equals eleven you're killing these guys i'm killing it i'm killing it i'm killing them

478
00:33:17,097 --> 00:33:22,437
i'm still waking up here so six plus five equals eleven and when you divide eleven by seven

479
00:33:22,437 --> 00:33:24,177
it goes into it once

480
00:33:24,177 --> 00:33:25,557
and you have a remainder of four.

481
00:33:25,937 --> 00:33:27,017
So that's why in this context,

482
00:33:27,137 --> 00:33:28,077
six plus five,

483
00:33:28,857 --> 00:33:30,637
modulo seven equals four.

484
00:33:31,077 --> 00:33:32,397
And now we're going to...

485
00:33:32,397 --> 00:33:33,857
Yeah, we may be taking for granted

486
00:33:33,857 --> 00:33:36,157
our own speed of like those types

487
00:33:36,157 --> 00:33:37,437
of addition and subtraction.

488
00:33:37,737 --> 00:33:38,557
So if you guys are like,

489
00:33:38,977 --> 00:33:40,577
if you need to pause and just be like,

490
00:33:40,637 --> 00:33:43,117
all right, do I need to pull a pen and paper out?

491
00:33:43,177 --> 00:33:43,957
Don't be ashamed.

492
00:33:44,097 --> 00:33:44,477
It's okay.

493
00:33:44,917 --> 00:33:46,677
I think this point right here

494
00:33:46,677 --> 00:33:49,957
is a good checkpoint of if you're,

495
00:33:50,297 --> 00:33:52,257
if what I just explained does not make sense...

496
00:33:52,437 --> 00:33:56,057
And you want to learn, rewind and give it a listen the second time.

497
00:33:56,497 --> 00:34:05,817
And from here now, we're going to take a step forward and talk about in the, like, the domain is this very large prime number and all of its remainders.

498
00:34:06,057 --> 00:34:12,277
And they map onto an elliptic curve, which is kind of the next point.

499
00:34:12,377 --> 00:34:12,957
So we have this.

500
00:34:13,157 --> 00:34:14,117
Oh, sorry, real quick.

501
00:34:14,457 --> 00:34:15,997
I want to just interject one thing.

502
00:34:18,657 --> 00:34:22,417
We're not going to get that deeply into it, but I have covered it on prior podcasts.

503
00:34:22,437 --> 00:34:32,677
that you can go look up. The way that we can know that what we're doing in our minds around

504
00:34:32,677 --> 00:34:39,717
numbers we understand, like 10 and 11 and 7, the way we know that all that math applies in the 2

505
00:34:39,717 --> 00:34:48,717
to the 256 realm, in a realm we can't possibly visualize or understand, is the way we know is

506
00:34:48,717 --> 00:34:52,297
through something. Usually it's through something called mathematical induction, but there are many

507
00:34:52,297 --> 00:34:55,957
There are many ways that we prove things.

508
00:34:56,257 --> 00:35:01,037
That is going to be a topic that we do get into, which is like, how do we really know?

509
00:35:01,277 --> 00:35:03,477
That's always the big thing I talk about.

510
00:35:03,497 --> 00:35:04,377
How do you really know?

511
00:35:05,037 --> 00:35:11,837
And so usually the way we extrapolate knowledge from the sort of knowable, observable world

512
00:35:11,837 --> 00:35:19,657
we live in to the unobservable, almost infinite, but we say it's not, is this concept of mathematical

513
00:35:19,657 --> 00:35:26,917
induction, meaning if you can prove it at a very basic level, and then you can prove that every

514
00:35:26,917 --> 00:35:34,157
increment, every next increment is true, then eventually you can just extrapolate mentally.

515
00:35:34,337 --> 00:35:38,117
And there is a rigorous construct for that that we're not going to get into. But I just want to

516
00:35:38,117 --> 00:35:45,497
build that bridge that there needs to be that bridge that we know that one plus one equals two.

517
00:35:45,497 --> 00:35:50,577
We can sort of extrapolate these operations into numbers we can't understand.

518
00:35:51,137 --> 00:35:51,217
Yeah.

519
00:35:51,257 --> 00:35:54,157
And I think there's some interesting visual points.

520
00:35:54,377 --> 00:35:59,277
I know this is primarily an audio podcast, but if you're sitting here, if you're listening

521
00:35:59,277 --> 00:36:04,957
to this, what we're about to start talking about is this curve, the LibSecP256K1 curve.

522
00:36:05,037 --> 00:36:06,537
We'll get into exactly what that means.

523
00:36:06,877 --> 00:36:14,397
But if you type in LibSecP256K1, enter, and Google images, you'll see it.

524
00:36:14,397 --> 00:36:22,537
And it's a graph, it's a curve that you would have easily seen some point in your high school math education, for sure.

525
00:36:22,797 --> 00:36:24,337
You wouldn't have realized it was that important.

526
00:36:24,857 --> 00:36:26,377
But the elliptic curve...

527
00:36:26,377 --> 00:36:27,997
I've seen it in Bitcoin a lot.

528
00:36:28,297 --> 00:36:30,517
I mean, you see it in Rob's shirt right now.

529
00:36:30,757 --> 00:36:33,997
Yeah, the shirt I'm wearing, it gets thrown around here and there.

530
00:36:34,897 --> 00:36:37,657
It's almost the logo of a magic internet math, but it's not.

531
00:36:37,737 --> 00:36:41,397
I kind of like transformed it into an infinity kind of.

532
00:36:41,397 --> 00:36:42,117
Yeah, yeah.

533
00:36:42,217 --> 00:36:43,437
More of an alpha symbol.

534
00:36:43,677 --> 00:36:44,117
Yeah.

535
00:36:44,397 --> 00:36:53,897
But it's basically, and I'll do one quick, it's basically a curve that loops on itself across the X and Y axis.

536
00:36:54,097 --> 00:37:02,137
So across the X axis, any point on the X axis, there's actually two points on the Y axis that you can go to.

537
00:37:03,397 --> 00:37:05,657
Let's say the bell curve flipped on it, turned it on the side.

538
00:37:05,877 --> 00:37:06,217
Oh, yeah.

539
00:37:06,257 --> 00:37:10,337
So if you took a bell curve and you've rotated it 90 degrees, if you're a shape rotator.

540
00:37:10,717 --> 00:37:11,017
It just looks like that.

541
00:37:11,017 --> 00:37:11,657
It looks like that.

542
00:37:11,657 --> 00:37:13,657
It's not that, but it looks like that.

543
00:37:13,657 --> 00:37:16,537
No, like we're not saying it has the same tails.

544
00:37:16,797 --> 00:37:20,117
We're just saying visually it kind of looks like a bell curve.

545
00:37:20,237 --> 00:37:20,597
Absolutely.

546
00:37:20,597 --> 00:37:22,437
90 degree rotation.

547
00:37:23,297 --> 00:37:26,537
And so I'm going to explain what the equation is.

548
00:37:26,577 --> 00:37:28,497
We're going to talk about why this is helpful.

549
00:37:28,677 --> 00:37:29,677
Like we're going to build on this.

550
00:37:29,677 --> 00:37:39,137
But I'm just going to make the jump and say the curve that Bitcoin specifically uses is Y squared equals X cubed plus seven.

551
00:37:40,757 --> 00:37:42,697
And we're going to talk about why that is.

552
00:37:42,697 --> 00:37:46,157
And if you can see on my shirt or if you look up online, it's slightly pushed up a little bit.

553
00:37:46,217 --> 00:37:47,377
And that's when that plus seven comes in.

554
00:37:48,357 --> 00:37:49,477
Why the hell does this matter?

555
00:37:49,937 --> 00:37:59,457
If you take any two points on the curve and you drew a straight line so that they touched, it's always going to hit one additional point.

556
00:38:01,477 --> 00:38:05,137
And that one additional point is because it's a cubic operation, X cube.

557
00:38:05,377 --> 00:38:07,897
So you're always going to have a given point.

558
00:38:07,957 --> 00:38:09,037
You're going to have the three intersections.

559
00:38:09,037 --> 00:38:15,397
and if you reflect that x point across if you reflect that that third point across the x-axe

560
00:38:15,397 --> 00:38:21,957
that's the sum of the two original points and this is kind of like the whole magic of how this works

561
00:38:21,957 --> 00:38:27,857
and this works for any curve that follows the general y squared equals x cubed plus ax plus b

562
00:38:27,857 --> 00:38:33,637
like the general function of these libraries and we're going to get into like why that if you take

563
00:38:33,637 --> 00:38:38,037
two points you connect them you can take the third and flip it over the x-axe and you get the sum of

564
00:38:38,037 --> 00:38:47,157
the two, like why that's really important. But to start, like even the Y squared equals X cubed

565
00:38:47,157 --> 00:38:59,257
plus seven was a choice. Why that? And that is the libsec P256k1 curve. Um, SEC, the SEC,

566
00:38:59,397 --> 00:39:03,977
standards for efficient cryptography, P, it's because it's using a prime field. We already

567
00:39:03,977 --> 00:39:06,857
talked about the prime field, right? You already, you already understand why there's a prime field

568
00:39:06,857 --> 00:39:07,777
in any of this at all.

569
00:39:08,397 --> 00:39:08,997
The 256,

570
00:39:09,477 --> 00:39:11,137
is it because it's 256 bit prime?

571
00:39:11,597 --> 00:39:11,757
All right.

572
00:39:11,797 --> 00:39:12,777
So that seems like we're,

573
00:39:13,217 --> 00:39:14,257
we've already done a lot

574
00:39:14,257 --> 00:39:16,977
to demystify what libsecp256k1 means.

575
00:39:17,737 --> 00:39:18,337
What's lib?

576
00:39:18,657 --> 00:39:20,177
Sorry, is lib for,

577
00:39:20,677 --> 00:39:22,857
is this a political statement?

578
00:39:22,857 --> 00:39:23,777
Is this a political statement?

579
00:39:23,777 --> 00:39:24,277
Is this a library you import?

580
00:39:24,597 --> 00:39:25,177
Yeah, yeah, yeah.

581
00:39:25,257 --> 00:39:26,397
I don't want to get you going,

582
00:39:26,517 --> 00:39:27,357
but a lot of people think

583
00:39:27,357 --> 00:39:28,697
that there's political statements.

584
00:39:28,697 --> 00:39:29,797
Yeah, it's all these libs,

585
00:39:29,997 --> 00:39:31,097
all these damn libs.

586
00:39:31,297 --> 00:39:33,437
No, lib is the library, right?

587
00:39:33,477 --> 00:39:34,997
Because you're pulling from this library

588
00:39:34,997 --> 00:39:46,757
of sec p256k1 uh so we got through sec p256k is um a koblet uh a koblet's curve um yeah

589
00:39:46,757 --> 00:39:52,577
and we've talked i've talked about those in the past um and i have there's a course on magic

590
00:39:52,577 --> 00:39:59,137
internet math.com on koblet's book number theory and cryptography and then one is that it's the

591
00:39:59,137 --> 00:40:04,197
first and only such of its curve now the koblet's part is actually really important and i actually

592
00:40:04,197 --> 00:40:08,837
tweeted this out last night um probably two days ago by the time this gets out the door for everyone

593
00:40:08,837 --> 00:40:17,697
to listen to how finney in 2011 opens a thread on bitcoin talk and says like why this curve right

594
00:40:17,697 --> 00:40:23,597
and like a bunch of like greg maxwell christian decker uh gavin andreason mike hearn like all of

595
00:40:23,597 --> 00:40:31,157
the original like big bitcoin developers time yeah of course of course that's there yeah um

596
00:40:31,157 --> 00:40:34,377
The curve was actually invented on Little St. James, for sure.

597
00:40:35,657 --> 00:40:44,777
And so the ultimate point that gets talked about and somewhat inferred is that this curve doesn't have anything weird going on about it.

598
00:40:44,857 --> 00:40:46,597
You could be like, oh, why is it plus seven?

599
00:40:46,777 --> 00:40:52,677
But that's not meaningfully a big transformation in the context of what we're about to talk about,

600
00:40:52,977 --> 00:40:57,237
is that there's no weird constant that just doesn't make any sense whatsoever.

601
00:40:57,997 --> 00:41:01,377
I would more ask why the middle coefficient is zero.

602
00:41:01,657 --> 00:41:02,597
Why do you go right?

603
00:41:03,257 --> 00:41:03,997
That's a good point.

604
00:41:04,177 --> 00:41:05,937
That's like the one of the things I've always wondered.

605
00:41:06,377 --> 00:41:06,657
Yeah.

606
00:41:06,777 --> 00:41:11,837
Well, if you actually make the A zero, it allows you to do simpler mathematical transformations

607
00:41:11,837 --> 00:41:14,777
and it makes it 30% faster than other standard NIST curves.

608
00:41:15,877 --> 00:41:19,657
Because you're just taking something to zero that's less transformation and less computational

609
00:41:19,657 --> 00:41:20,057
overhead.

610
00:41:20,197 --> 00:41:21,737
So it actually makes the curve more efficient.

611
00:41:21,737 --> 00:41:24,137
and further talking about...

612
00:41:24,137 --> 00:41:27,377
Can you circle roughly when in history

613
00:41:27,377 --> 00:41:28,617
was this being determined?

614
00:41:30,217 --> 00:41:33,637
Not for Bitcoin, but when was this curve?

615
00:41:33,757 --> 00:41:37,037
When was SecP 256K1 created?

616
00:41:37,037 --> 00:41:40,457
I don't want to get into the whole history right now,

617
00:41:40,677 --> 00:41:41,877
but you know what I mean?

618
00:41:41,997 --> 00:41:44,037
Just so people don't realize,

619
00:41:44,197 --> 00:41:45,617
Satoshi didn't invent this.

620
00:41:46,297 --> 00:41:48,757
It wasn't part of...

621
00:41:48,757 --> 00:41:52,157
It was invented prior to 2008.

622
00:41:53,157 --> 00:41:57,597
Well, so it was invited prior to the cobblitz curve.

623
00:41:57,997 --> 00:41:59,097
The cobblitz curve itself.

624
00:41:59,217 --> 00:41:59,417
Yeah.

625
00:41:59,417 --> 00:42:02,237
In other words, this X cubed plus seven was sorry.

626
00:42:02,657 --> 00:42:05,517
This is Y squared equals X cubed plus seven.

627
00:42:06,237 --> 00:42:06,797
Yeah.

628
00:42:06,917 --> 00:42:14,537
Y squared equals X cubed plus seven was a known curve that was used for things.

629
00:42:15,177 --> 00:42:15,497
Potentially.

630
00:42:15,657 --> 00:42:15,937
Yes.

631
00:42:16,137 --> 00:42:16,637
That was a no.

632
00:42:16,637 --> 00:42:20,157
It wasn't like Satoshi said, I understand this library.

633
00:42:20,877 --> 00:42:24,537
I am going to just conjure.

634
00:42:25,317 --> 00:42:26,937
It wasn't like conjured.

635
00:42:27,017 --> 00:42:29,517
It was like selected from things that had been played around with.

636
00:42:30,077 --> 00:42:30,297
Correct?

637
00:42:30,917 --> 00:42:31,337
Correct.

638
00:42:31,677 --> 00:42:32,057
Yes.

639
00:42:32,717 --> 00:42:34,977
And I'm pulling up the exact year right now.

640
00:42:35,197 --> 00:42:35,557
So I'm trying to-

641
00:42:35,557 --> 00:42:36,557
It had some known properties.

642
00:42:37,557 --> 00:42:37,897
Yes.

643
00:42:38,097 --> 00:42:39,117
It had some known properties.

644
00:42:39,537 --> 00:42:43,417
It wasn't really used at any large scale anywhere outside.

645
00:42:43,417 --> 00:42:47,417
like there wasn't like a bunch of applications that were running this curve specifically

646
00:42:47,417 --> 00:42:55,177
um but you locked in and said that's a candidate yes and i'm what i'm doing right now is i'm trying

647
00:42:55,177 --> 00:43:00,757
to find i was actually looking into this last night and i'm trying to find my original uh

648
00:43:00,757 --> 00:43:07,657
conversation that i was having with this um if you give me a moment it would be pre-deeded 2008

649
00:43:07,657 --> 00:43:21,137
And I think as I'm pulling this up, just the thing to sprinkle through, what we're going to be mainly talking about today is ECDSA, elliptive curve, digital signing algorithm, which is what Satoshi originally started with.

650
00:43:21,517 --> 00:43:24,537
This did not use Schnorr signing algorithm.

651
00:43:24,997 --> 00:43:28,557
That was something that was actually patented through 2008.

652
00:43:28,677 --> 00:43:32,457
So when Satoshi originally came out with this, he couldn't use Schnorr, which was known to be more efficient.

653
00:43:32,457 --> 00:43:39,457
um the um what was i going to say the uh

654
00:43:41,077 --> 00:43:48,277
schnorr's slightly different group structure characteristics and they're more designed we've

655
00:43:48,277 --> 00:43:53,937
talked about it a little bit when in the i did this with gary in one of those episodes i'll try

656
00:43:53,937 --> 00:43:57,917
to remember it and link it but like we talked a little bit about there it has slightly different

657
00:43:57,917 --> 00:44:03,797
group characteristics, which allows, there's like additional closure that allows you to

658
00:44:03,797 --> 00:44:06,677
abstract maybe more of the information.

659
00:44:06,677 --> 00:44:14,237
So it's not all, you know, you can kind of abstract a couple of the variables into single

660
00:44:14,237 --> 00:44:17,997
objects so that you're showing less.

661
00:44:18,217 --> 00:44:21,297
And like the thing with Schnorr was like, you can, everything looks like one address.

662
00:44:21,557 --> 00:44:26,137
So you don't, you can't easily diagnose a two of two multi-sig and say, oh, that's

663
00:44:26,137 --> 00:44:27,357
clearly a two of two multi-sig.

664
00:44:27,357 --> 00:44:28,177
That's a lightning channel.

665
00:44:28,657 --> 00:44:29,017
Absolutely.

666
00:44:29,337 --> 00:44:29,577
Yeah.

667
00:44:29,797 --> 00:44:37,577
And so basically the biggest upside you get with Schnorr is that you're able to effectively add keys together in a very efficient way.

668
00:44:37,797 --> 00:44:44,917
That allows you to, as a result, since you can add the keys together, you can take individual shards and you can aggregate the signature.

669
00:44:45,117 --> 00:44:45,697
So you can have a two of two.

670
00:44:45,697 --> 00:44:48,537
And that's a result of the group structure.

671
00:44:49,017 --> 00:44:49,557
That's correct.

672
00:44:49,817 --> 00:44:50,037
Of Schnorr.

673
00:44:50,337 --> 00:44:50,457
Yeah.

674
00:44:50,617 --> 00:44:52,497
I just need to emphasize that here, right?

675
00:44:52,497 --> 00:44:55,977
Because that's really what we're talking about and why we learn about the structures.

676
00:44:55,977 --> 00:45:15,957
Yeah, so the curve SecP predated Bitcoin roughly the year 2000 was when it was invented. So it had been around for almost a decade when Satoshi picked it. And the point I'm getting to is why that matters is because the curve you pick is kind of like, this is the entire field in which you're doing all of your public private key mapping.

677
00:45:15,957 --> 00:45:23,837
and going taking it back to this Hal Finney post um he basically everyone starts inferring that

678
00:45:23,837 --> 00:45:30,017
it's the one curve in that general family and library that doesn't have any really weird traits

679
00:45:30,017 --> 00:45:36,037
about it and you would be like well Rob you know like this all of this stuff is weird like what do

680
00:45:36,037 --> 00:45:42,917
you what like this is all weird like why why does that matter um basically what's a weird what's an

681
00:45:42,917 --> 00:45:49,137
example than in this world of something weird that they declined they rejected yeah so other curves

682
00:45:49,137 --> 00:45:56,677
hold constants within the curve that don't immediately make sense and it's very popular

683
00:45:56,677 --> 00:46:03,117
um in what does that mean real quick what does that mean so what that means is that

684
00:46:03,117 --> 00:46:08,637
when you are setting up this equation they'll tack something onto the end

685
00:46:08,637 --> 00:46:14,757
like some extra little thing and typically like a constant number you meaning so in other words

686
00:46:14,757 --> 00:46:22,837
yeah or it's an object a constant object or like so for example okay slightly you have to know

687
00:46:22,837 --> 00:46:28,677
calculus to answer this question but like when you integrate a number of sorry you integrate a

688
00:46:28,677 --> 00:46:36,217
function like x and you get one half x squared you have to say plus c because you don't really know

689
00:46:36,217 --> 00:46:40,397
So unless you define the limits of the integration, I'm sorry if I just derailed.

690
00:46:40,457 --> 00:46:42,397
No, no, no, no, no, no, no, no.

691
00:46:42,397 --> 00:46:52,817
So like there's another, there's a NIST, you know, and NIST, NIST is like the National Institute for Standards and Technology.

692
00:46:53,217 --> 00:46:54,137
It's a government.

693
00:46:54,317 --> 00:46:55,237
I should put that.

694
00:46:55,257 --> 00:46:56,457
I should put those on my website.

695
00:46:56,597 --> 00:46:57,177
I got the BIPS.

696
00:46:57,377 --> 00:46:58,237
I got the BOLTs.

697
00:46:58,377 --> 00:46:58,777
I got the NIST.

698
00:46:58,777 --> 00:47:01,077
I should get the NIST standards in there.

699
00:47:01,077 --> 00:47:09,657
Here's the thing. Unlike BIPs, the NIST comes from the government, which means even the mathematicians in Bitcoin don't trust the government.

700
00:47:10,317 --> 00:47:15,357
And the reason why this matters is that there was another curve. There was a NIST P256 curve that could have been used.

701
00:47:16,677 --> 00:47:23,777
It has a coefficient from a mysterious SHA-1 hash that no one really knows where it came from.

702
00:47:23,777 --> 00:47:29,237
and basically there was a scandal in 2013

703
00:47:29,237 --> 00:47:32,197
where the NSA was caught trying to backdoor

704
00:47:32,197 --> 00:47:33,297
elliptic curve standards

705
00:47:33,297 --> 00:47:38,217
and this is why Satoshi

706
00:47:38,217 --> 00:47:41,217
picked the curve he did is it didn't have a mysterious NSA backdoor

707
00:47:41,217 --> 00:47:44,117
whereas if he picked if he was like

708
00:47:44,117 --> 00:47:47,257
well I want to be taken seriously so I'm going to use the credential

709
00:47:47,257 --> 00:47:50,057
the elliptic curve library to make sure that like other cryptographers

710
00:47:50,057 --> 00:47:53,117
it's like instantly the domain in which we're operating in

711
00:47:53,117 --> 00:47:57,137
is not an academic one where we're trying to get peer review and get accolades and kind of like

712
00:47:57,137 --> 00:48:02,637
work our way up through a corporate structure or political pseudo corporate political structure

713
00:48:02,637 --> 00:48:09,277
like a university. Yeah. We are trying to make unfuckable money, which means that you have to

714
00:48:09,277 --> 00:48:14,477
really go foundational level primitives to understand why things work. And if Satoshi

715
00:48:14,477 --> 00:48:18,657
had picked the accredited curve, Bitcoin would have been dead by now. Absolutely.

716
00:48:18,657 --> 00:48:22,357
It would have been entirely backdoored and destroyed. Maybe they'd still be waiting.

717
00:48:23,117 --> 00:48:44,517
Maybe. Well, that's true. They could just be waiting for something to happen, right? And so Satoshi picking this curve that was invented in 2000 that was seldomly used was actually very intelligent because it was the curve that fit all the properties we've talked to up to this point that would be good for elliptic curve cryptography to secure Bitcoin and secure money in a trustless way that didn't have these back doors, right?

718
00:48:44,517 --> 00:48:47,977
And so I think that kind of just lays out the highest level.

719
00:48:48,077 --> 00:48:51,477
Now, now we're going to take two things and we're going to combine them together.

720
00:48:51,617 --> 00:48:54,477
We have this curve, this curvy object on a graph.

721
00:48:54,757 --> 00:48:56,957
And we have this field of finite points.

722
00:48:57,337 --> 00:48:58,137
Sideways bell curve.

723
00:48:58,777 --> 00:49:00,897
We have the sideways bell curve graph.

724
00:49:01,137 --> 00:49:01,577
It's sleeping.

725
00:49:01,577 --> 00:49:04,817
And we have this modulo arithmetic, right?

726
00:49:04,837 --> 00:49:05,937
We have all of these little dots.

727
00:49:05,937 --> 00:49:12,417
So what you do to casually draw it is you draw a series of connected numbers.

728
00:49:12,417 --> 00:49:18,937
like one continuous line for this entire sideways bell curve in reality if you interrupt you real

729
00:49:18,937 --> 00:49:23,357
quick like just as an example for lay people imagine drawing you would draw a circle with

730
00:49:23,357 --> 00:49:28,497
a radius of one you would take this function called x squared plus y squared equals one

731
00:49:28,497 --> 00:49:34,317
and then you would start taking combinations every combination of x and y you can basically

732
00:49:34,317 --> 00:49:42,317
imagine and that that make that equation work and plot right you'd plot every one of those

733
00:49:42,317 --> 00:49:45,797
X, Y's and Cartesian, you know, and Cartesian coordinates.

734
00:49:46,077 --> 00:49:50,277
And what you would, if you had, if you asked Python to do it, you would see a circle getting

735
00:49:50,277 --> 00:49:50,997
drawn very quickly.

736
00:49:52,177 --> 00:49:52,777
That's right.

737
00:49:53,237 --> 00:49:57,177
And so that's, that's essentially like, so it's just like what we're natively used to

738
00:49:57,177 --> 00:50:00,317
doing is the number, like the real number system that we grew up with.

739
00:50:00,757 --> 00:50:07,237
Whereas you're doing the same thing in something called an elliptic curve, but your plot, the

740
00:50:07,237 --> 00:50:09,997
equation is now the, is a remainder.

741
00:50:10,657 --> 00:50:10,897
Yeah.

742
00:50:10,897 --> 00:50:18,837
Yeah, and so rather than drawing, and the reason like this Cartesian plot with x squared plus y squared equals one to draw a circle with a radius one, right?

743
00:50:19,177 --> 00:50:28,657
You're taking, when you're drawing a continuous line, you're basically, in shorthand, you're taking all possible x values and filling them in for all possible y values, and it's continuous.

744
00:50:28,657 --> 00:50:30,637
Like, there is no break in the curve.

745
00:50:31,137 --> 00:50:40,457
For this elliptic field, to combine these two concepts of the sideways bell curve, this elliptic curve, and this field of finite numbers, super zoomed out, it looks like it's all connected.

746
00:50:40,457 --> 00:50:45,357
like one continuous line but if you zoom in and you zoom in and you zoom in it's actually a series

747
00:50:45,357 --> 00:50:50,837
of dots so there's not actually really a continuous line it's a bunch of little points

748
00:50:50,837 --> 00:50:59,377
that map out all of the remainders as it relates to this very large mersane prime of two to the 256

749
00:50:59,377 --> 00:51:05,717
minus two to the 232 you know well but we what you're trying to say is it's discrete too right

750
00:51:05,717 --> 00:51:12,157
Yes, that too. And so we now at this point have been able to stumble.

751
00:51:12,497 --> 00:51:24,317
Sorry, the book Mastering Bitcoin, the Antonopoulos book, has a very, I think, a good illustration of this where he just shows it at a larger and larger moduli drawing this curve.

752
00:51:24,497 --> 00:51:31,117
If you recall, I think, chapter four. So if you have that book, it's a good visual cue for this right now.

753
00:51:31,117 --> 00:51:37,957
yeah mastering bitcoin by intelophilus and also programming bitcoin by jimmy's song we're

754
00:51:37,957 --> 00:51:41,837
basically we're going through the initial introductory chapters of how this all works

755
00:51:41,837 --> 00:51:49,517
um and so we now have the foundation to actually talk about how we use this stuff so we have this

756
00:51:49,517 --> 00:51:53,037
sideways bell curve that's what we're just going to call the lipsec p curve because that's what it

757
00:51:53,037 --> 00:51:59,057
visually looks like so you have this curve you take all of the modulo possible remainders from

758
00:51:59,057 --> 00:52:04,217
this very large prime number and you connect them into this function and you're able to get

759
00:52:04,217 --> 00:52:11,157
this curve that gets drawn out and you're able to see all these little dots so from here

760
00:52:11,157 --> 00:52:19,417
we are now at the point where we're actually going to do some actual math equations what we've done

761
00:52:19,417 --> 00:52:23,937
like visualized like some basic math equations but now we're going to start smashing things

762
00:52:23,937 --> 00:52:26,137
together. We have this field of

763
00:52:26,137 --> 00:52:27,597
modulo prime

764
00:52:27,597 --> 00:52:29,277
numbers,

765
00:52:29,817 --> 00:52:31,837
so it's not continuous, but you have this

766
00:52:31,837 --> 00:52:33,477
curve that the math gets transformed on.

767
00:52:33,977 --> 00:52:35,617
And we're going to start talking about now

768
00:52:35,617 --> 00:52:37,917
what the hell this has to do with Bitcoin.

769
00:52:42,697 --> 00:52:44,077
So your starting

770
00:52:44,077 --> 00:52:44,597
place

771
00:52:44,597 --> 00:52:47,477
is this

772
00:52:47,477 --> 00:52:48,617
random number.

773
00:52:49,637 --> 00:52:51,777
Now, whether that random number is

774
00:52:51,777 --> 00:52:58,157
literally your seed phrase encoded into a number or like in your own abstraction.

775
00:52:58,377 --> 00:53:03,017
The way it actually works though, as I mentioned earlier, is you have your master extended private

776
00:53:03,017 --> 00:53:05,977
key and that to generate child keys.

777
00:53:06,057 --> 00:53:11,837
And those child keys are just numbers between zero and two to the 256 that then get placed

778
00:53:11,837 --> 00:53:12,557
on this curve.

779
00:53:12,917 --> 00:53:14,437
You take that private key.

780
00:53:14,437 --> 00:53:14,677
Yeah.

781
00:53:16,257 --> 00:53:21,997
And if we start just, if we just start in a small place, right.

782
00:53:21,997 --> 00:53:27,917
And we just say, what's the, if we look at a finite field modulo five.

783
00:53:28,857 --> 00:53:29,297
Okay.

784
00:53:29,717 --> 00:53:31,477
And you start with this number two.

785
00:53:31,857 --> 00:53:33,017
I did this last week.

786
00:53:33,097 --> 00:53:34,097
So do it again.

787
00:53:34,177 --> 00:53:34,437
Right.

788
00:53:34,677 --> 00:53:36,237
Let's start with, start with the number two.

789
00:53:36,597 --> 00:53:40,577
You can generate every point on the curve with this number.

790
00:53:40,797 --> 00:53:43,397
So when you double it, you get four.

791
00:53:44,017 --> 00:53:44,417
Right.

792
00:53:44,437 --> 00:53:50,677
So like in other words, in modulo 5, we're looking for the points 0, 1, 2, 3, 4, right?

793
00:53:50,797 --> 00:53:54,077
And we can do this with the number 2 because 2 times 2 is 4.

794
00:53:54,897 --> 00:54:00,517
And then you multiply by 2 again, and you get 8, but mod 5 is 3.

795
00:54:00,617 --> 00:54:03,397
So you go 2, 4, 3, right?

796
00:54:03,537 --> 00:54:04,757
Because 4 times 2 is 3.

797
00:54:05,237 --> 00:54:08,337
3 times 2 is 1, right?

798
00:54:08,857 --> 00:54:11,717
So now you've got, what would we say?

799
00:54:11,777 --> 00:54:13,057
2, 4, 3, 1.

800
00:54:13,057 --> 00:54:16,997
and then multiply that by two again.

801
00:54:17,297 --> 00:54:18,657
Basically, you've done it, right?

802
00:54:19,657 --> 00:54:21,157
You've completed the loop.

803
00:54:21,337 --> 00:54:22,297
You've completed the loop.

804
00:54:22,377 --> 00:54:26,897
You've generated every point with this operation of addition.

805
00:54:27,617 --> 00:54:30,017
Multiplying by two is basically adding a number to itself.

806
00:54:30,997 --> 00:54:31,217
Yeah.

807
00:54:33,117 --> 00:54:36,177
So you've generated every point.

808
00:54:36,337 --> 00:54:39,857
So I'm just trying to get a tangible thing you can do.

809
00:54:39,857 --> 00:54:52,597
And then now we're going to move to the tableau of this curve that is based on things we can't as easily determine, but we can abstract the concept and the functionality.

810
00:54:54,357 --> 00:54:54,957
Yeah.

811
00:54:55,397 --> 00:54:55,657
Right?

812
00:54:56,517 --> 00:55:01,177
You can generate every point in that curve with this massive prime number.

813
00:55:02,317 --> 00:55:04,937
You're able to generate every single point in that curve.

814
00:55:05,437 --> 00:55:06,137
That's right.

815
00:55:06,897 --> 00:55:11,277
And that's why the, and again, just to really hammer it home, that's why we pick a very large

816
00:55:11,277 --> 00:55:16,277
modulo base is that you're not going to really be able to get that closure where you can quickly

817
00:55:16,277 --> 00:55:21,317
loop through and get all possible options. The space in which you're doing this module

818
00:55:21,317 --> 00:55:27,037
arithmetic on is so large, you're not going to be able to trivially close that loop and get back to

819
00:55:27,037 --> 00:55:31,457
where you started. And you can't check it with pen and paper. And knowing it's a group, part of

820
00:55:31,457 --> 00:55:34,157
is also how you know it preserves these operations.

821
00:55:35,197 --> 00:55:36,397
It's almost all you know.

822
00:55:36,917 --> 00:55:36,977
Yeah.

823
00:55:37,257 --> 00:55:39,857
All you really know and all we care about.

824
00:55:39,957 --> 00:55:41,777
That's why I love groups.

825
00:55:41,837 --> 00:55:45,597
I love structures because all we really care about in this instance

826
00:55:45,597 --> 00:55:49,997
is that we have the closure and the operations are preserved.

827
00:55:50,397 --> 00:55:51,977
That's literally all we care about.

828
00:55:51,977 --> 00:55:56,817
That's why the mathematicians invented this thing called group.

829
00:55:57,417 --> 00:55:57,717
Yeah.

830
00:55:57,717 --> 00:56:03,017
is so that we know this and we can move into this space of maybe not being able to check with a pen

831
00:56:03,017 --> 00:56:08,917
and paper. Yes. But we know, we know for a fact, and you can, you know, you can study it and go

832
00:56:08,917 --> 00:56:13,417
through the proofs and know for a fact that these operations are preserved and you maintain closure.

833
00:56:14,197 --> 00:56:21,117
Yep, exactly. And so from, from this context, we're going to get into the next like thing that

834
00:56:21,117 --> 00:56:24,657
we may take a second to pause just to fully connect it together is you take this private

835
00:56:24,657 --> 00:56:29,177
number that only no one else knows. This is your private key. This is not your seed phrase. This is

836
00:56:29,177 --> 00:56:34,277
your seed phrase is literally the seed in which all of your child private keys can derive from.

837
00:56:34,577 --> 00:56:37,977
So you're taking your first child private key, which is just a number between zero and two to

838
00:56:37,977 --> 00:56:44,097
the 256. That's the starting point. You put it on the curve. Your private key is the grain of sand

839
00:56:44,097 --> 00:56:49,177
on that curve that you just happen to know that's the point and no one else does. No one else knows

840
00:56:49,177 --> 00:56:53,637
that point. And the ability, the asymmetry is because there's so many possible points on the

841
00:56:53,637 --> 00:56:58,557
curve, the only way someone would be able to reverse engineer that is if they guessed

842
00:56:58,557 --> 00:57:01,877
all of the possible grains of sand combinations to see if they could find your key.

843
00:57:02,057 --> 00:57:02,317
That's right.

844
00:57:02,357 --> 00:57:05,957
Which, from a game theory of Bitcoin, which is actually just interesting in general, you're

845
00:57:05,957 --> 00:57:11,037
economically more incentivized to just, if you have spare compute cycles, to just try

846
00:57:11,037 --> 00:57:11,937
and find a block.

847
00:57:12,537 --> 00:57:12,777
Yes.

848
00:57:12,777 --> 00:57:13,257
It is.

849
00:57:13,637 --> 00:57:19,377
You have, as infinitesimally unlikely it is that your computer would be able to solo mine

850
00:57:19,377 --> 00:57:20,997
a Bitcoin block.

851
00:57:20,997 --> 00:57:29,057
it is still infinitely more likely that you will find a block mining on your computer with like

852
00:57:29,057 --> 00:57:35,697
half a giga hash of hash rate yeah then it would be for you to randomly stumble upon someone else's

853
00:57:35,697 --> 00:57:40,017
private key and that's like the really important thing to go into here is that like even like

854
00:57:40,017 --> 00:57:54,194
outside of the math for a second just thinking about from a game theory perspective if you have spare compute cycles like i think many people when they first get into Bitcoin is like I just going to build a script It just going to guess all of the numbers If you have spare compute cycles you are infinitely better off just trying to mine a block

855
00:57:54,834 --> 00:58:06,314
Even though it's like a little bit more heavy of an operation, it's greatly offset by the possibility and probabilistic likelihood that you're going to find a block could technically happen before the heat death of the universe.

856
00:58:06,314 --> 00:58:13,734
Whereas you're waiting for the heat death of the universe to go through the entire index of all two to the 256 numbers to try and get a reverse engineer of a key at random chance.

857
00:58:14,254 --> 00:58:14,374
Yes.

858
00:58:14,434 --> 00:58:14,994
I want to ask.

859
00:58:15,114 --> 00:58:15,794
So we have this.

860
00:58:16,054 --> 00:58:18,874
I want to ask a quick question just because it's the elephant in the room.

861
00:58:18,914 --> 00:58:23,174
And I want to know if we're capable of handling it in 60 seconds or less.

862
00:58:23,174 --> 00:58:23,894
But like.

863
00:58:24,214 --> 00:58:24,414
Yes.

864
00:58:25,254 --> 00:58:28,054
What about what about when we have quantum computers?

865
00:58:29,514 --> 00:58:29,754
Yeah.

866
00:58:30,954 --> 00:58:32,834
So a quantum computer.

867
00:58:33,034 --> 00:58:33,434
Yeah.

868
00:58:33,594 --> 00:58:35,514
So I think this was going to be a legit question.

869
00:58:35,514 --> 00:58:40,574
It's just, yeah, this was going to be like the culminating thing we're going to end on is like the discrete log problem.

870
00:58:41,674 --> 00:58:54,694
So a quantum computer essentially breaks down the space in which the computer necessarily has to compute to be able to get an answer.

871
00:58:54,914 --> 00:58:56,614
It's like, how does it affect the game theory?

872
00:58:56,754 --> 00:58:57,394
I guess you're right.

873
00:58:57,474 --> 00:59:00,494
How does, without having to explain what it is, right?

874
00:59:00,494 --> 00:59:08,334
It greatly reduces the doors in which you need to randomly guess through to be able to get to an answer.

875
00:59:08,554 --> 00:59:15,354
It's an efficiency, an ability to find the inverse with a public key, the private key.

876
00:59:15,754 --> 00:59:20,834
We're talking about how you have this private key, you do some mathematical transformations, you get a public key.

877
00:59:21,254 --> 00:59:26,754
And the asymmetry is such that to be able to find that public key, your best option is to randomly guess everything.

878
00:59:26,854 --> 00:59:30,254
A quantum computer breaks this heuristic, so it's no longer a random guess.

879
00:59:30,494 --> 00:59:35,334
and you are essentially able to use that generator point

880
00:59:35,334 --> 00:59:36,554
that we're about to talk about

881
00:59:36,554 --> 00:59:38,554
and very quickly find the...

882
00:59:38,554 --> 00:59:41,934
Very quickly in a timescale and sense

883
00:59:41,934 --> 00:59:43,974
compared to what we currently have available

884
00:59:43,974 --> 00:59:44,894
of guessing everything.

885
00:59:45,334 --> 00:59:48,134
It could still take like a day, a week, right?

886
00:59:48,214 --> 00:59:50,174
But like it is no longer talking about

887
00:59:50,174 --> 00:59:50,894
heat death of the universe.

888
00:59:50,894 --> 00:59:52,634
You're talking about in some measurable,

889
00:59:53,154 --> 00:59:54,314
realistic human timeframe.

890
00:59:55,094 --> 00:59:57,714
If you had a cryptographically relevant quantum computer,

891
00:59:57,934 --> 01:00:00,314
you could take a public key and find the private key.

892
01:00:00,494 --> 01:00:04,154
It becomes a pretty good idea for some time.

893
01:00:04,374 --> 01:00:06,634
It becomes a good idea to try to find Satoshi's coins.

894
01:00:07,754 --> 01:00:08,034
Right?

895
01:00:08,454 --> 01:00:11,854
But then the question is, in the game theory, what's the response?

896
01:00:13,374 --> 01:00:17,834
Is there a fairly easy response in the game theory?

897
01:00:17,834 --> 01:00:17,894
Yeah.

898
01:00:19,514 --> 01:00:21,034
We're not going to sit there and be like,

899
01:00:21,134 --> 01:00:23,014
we're not going to sit and watch it eat all the Bitcoin.

900
01:00:23,294 --> 01:00:23,634
Right.

901
01:00:23,814 --> 01:00:25,254
And so this is funny.

902
01:00:25,354 --> 01:00:28,934
As someone who loves deep Bitcoin nuance and lore,

903
01:00:28,934 --> 01:00:32,314
this was one of my favorite nuggets of things like four years ago.

904
01:00:32,314 --> 01:00:34,374
And now it's like the most common talking point,

905
01:00:34,474 --> 01:00:36,174
which is fine because it's a real point.

906
01:00:36,174 --> 01:00:37,094
Like it's a legitimate thing.

907
01:00:37,094 --> 01:00:37,434
It's just,

908
01:00:37,834 --> 01:00:40,234
it's funny because like I've been thinking of this lens for years.

909
01:00:40,794 --> 01:00:43,014
When Bitcoin was first originally created,

910
01:00:43,254 --> 01:00:47,854
there was not like the main default way that you would receive funds was

911
01:00:47,854 --> 01:00:49,934
through a public key,

912
01:00:50,094 --> 01:00:53,054
pay to public key where you just put the raw public key on the Bitcoin

913
01:00:53,054 --> 01:00:53,454
blockchain.

914
01:00:54,014 --> 01:00:56,714
So Satoshi's coin specifically use this very,

915
01:00:56,794 --> 01:00:58,194
very old legacy address.

916
01:00:58,194 --> 01:01:04,154
and those are prime uh those are for the picking basically when it comes to a quantum computer

917
01:01:04,154 --> 01:01:08,734
because those public keys have been publicly available for anyone to look at since 2009

918
01:01:08,734 --> 01:01:14,594
when the genesis which really goes to show you how secure that is right now right right millions

919
01:01:14,594 --> 01:01:20,234
of coins right and and to get into the bitcoin level a little bit the thing is is that it's not

920
01:01:20,234 --> 01:01:26,894
like if i get one cracked i get a million bitcoin all of satoshi's bitcoin each address that satoshi

921
01:01:26,894 --> 01:01:28,594
has has a different public key.

922
01:01:29,114 --> 01:01:37,554
So you have 200,050 Bitcoin lotto tickets that a, in theory, a quantum computer could

923
01:01:37,554 --> 01:01:38,194
go try and attack.

924
01:01:38,594 --> 01:01:41,954
Now, this is definitely outside the scope of the conversation today.

925
01:01:42,034 --> 01:01:46,294
But just to put a small point on this, a quantum computer's ability to reverse engineer a public

926
01:01:46,294 --> 01:01:49,574
key to a private key is different than being able to undo a one-way hash function.

927
01:01:50,434 --> 01:01:51,794
And why does that matter?

928
01:01:51,794 --> 01:01:54,754
is that very early in Bitcoin,

929
01:01:54,974 --> 01:01:55,914
like by 20,

930
01:01:57,234 --> 01:01:58,614
even like actually,

931
01:01:58,734 --> 01:02:00,294
even in the first couple thousand blocks,

932
01:02:00,374 --> 01:02:01,074
there were a couple of these,

933
01:02:01,194 --> 01:02:04,414
but you can hash your public key

934
01:02:04,414 --> 01:02:06,354
and put the hash on chain,

935
01:02:06,534 --> 01:02:08,754
which gives you a certain level of protection

936
01:02:08,754 --> 01:02:10,494
because to be able to reverse engineer

937
01:02:10,494 --> 01:02:11,494
the hashing function

938
01:02:11,494 --> 01:02:13,774
uses its Grover's algorithm

939
01:02:13,774 --> 01:02:16,834
versus reversing a public private key

940
01:02:16,834 --> 01:02:17,954
is Shor's algorithm.

941
01:02:18,594 --> 01:02:19,794
And quantum computers handle this

942
01:02:19,794 --> 01:02:21,014
with different levels of efficiency.

943
01:02:21,014 --> 01:02:31,674
There are efficiencies, but it's not the complete catastrophic breakdown of the ability to find the inverse or find the pre-image as it relates to hashes.

944
01:02:32,954 --> 01:02:39,474
So that's kind of what we're talking about now is definitely entering that realm of when people start talking about quantum computers.

945
01:02:39,754 --> 01:02:42,314
Like this is the foundational math we're talking about that would be broken apart.

946
01:02:42,314 --> 01:02:56,754
And what I really want people to just be able to do, and you're not going to do it in this conversation, but I think as we go on the podcast, I want us to be able to say, okay, if there's a risk, let's say it's quantum computers or whatever it is, there's a risk.

947
01:02:56,854 --> 01:02:59,214
It's not like a all or nothing risk.

948
01:02:59,494 --> 01:03:01,674
It's like certain things are exposed.

949
01:03:02,574 --> 01:03:03,294
Certain things are not.

950
01:03:03,554 --> 01:03:05,194
Certain things have easy answers.

951
01:03:05,354 --> 01:03:06,054
Certain things don't.

952
01:03:06,454 --> 01:03:07,594
And that's like the kind of thinking.

953
01:03:07,594 --> 01:03:26,954
And when we start bringing the experts on here to talk about these things, it's like this is what we are building right now is sort of the we're prying apart the nylon threading of the all piece, the all or nothing piece, prying apart a little bit, just then, you know, maybe mixing the glue, breaking up that glue so that we can start to see that there's more.

954
01:03:26,954 --> 01:03:30,634
it's more than all or nothing. And it takes some brainpower and thought and discussion

955
01:03:30,634 --> 01:03:36,034
and a little bit of rigor to pull these things apart so that we can, when we finally have

956
01:03:36,034 --> 01:03:39,494
like the real conversation about this stuff, it can really land.

957
01:03:39,794 --> 01:03:43,294
That's exactly right. We want, we want to be able to serve the audience in a way where

958
01:03:43,294 --> 01:03:49,154
if you listen to like the prerequisite material, which is the podcast, having it somewhat self

959
01:03:49,154 --> 01:03:54,514
contained that when we were, when we have guests on or we have subject matter experts on, um,

960
01:03:54,514 --> 01:04:00,614
you're not starting at a cold start you will have the foundational requisite pieces of the

961
01:04:00,614 --> 01:04:06,074
underlying math to where and to be clear we're also going to be struggling when we get deep into

962
01:04:06,074 --> 01:04:10,594
the technical nuances of the implementation of all this stuff but you'll at least have a life raft

963
01:04:10,594 --> 01:04:16,594
and like a a lifesaver get thrown out to you so that you can if you want to go through the journey

964
01:04:16,594 --> 01:04:24,334
with us you have the foundational pieces laid out um so we have this curve we have this field

965
01:04:24,334 --> 01:04:29,454
of finite math, the way this ultimately works as a starting point, you pick that private key.

966
01:04:30,654 --> 01:04:35,334
That private key is then computed to find the public key. And how do you do that?

967
01:04:35,854 --> 01:04:41,554
This is where we get something called a generator point. And this is kind of what you were just

968
01:04:41,554 --> 01:04:47,174
talking about as it related to finding and completing the loop of the circuit, right?

969
01:04:47,174 --> 01:04:53,614
You take this generator. Basically, if you take a number and throw it into this modular arithmetic,

970
01:04:53,614 --> 01:04:55,934
you can generate children

971
01:04:55,934 --> 01:04:58,014
like you get like a family

972
01:04:58,014 --> 01:05:00,134
of generations of like what you get

973
01:05:00,134 --> 01:05:01,974
and so

974
01:05:01,974 --> 01:05:03,534
you take your private number

975
01:05:03,534 --> 01:05:04,854
you throw it through this function

976
01:05:04,854 --> 01:05:07,934
and you get a new number when you get there

977
01:05:07,934 --> 01:05:09,294
when you put it through

978
01:05:09,294 --> 01:05:10,874
and putting it through there

979
01:05:10,874 --> 01:05:14,014
essentially gives you

980
01:05:14,014 --> 01:05:16,474
a public key that you can go talk about

981
01:05:16,474 --> 01:05:18,274
and I'm going to pause there for a second

982
01:05:18,274 --> 01:05:20,054
because I know in my own standards

983
01:05:20,054 --> 01:05:22,454
that that was not done as cleanly as possible

984
01:05:22,454 --> 01:05:26,234
if you want to take a throw at the generator point and how that works.

985
01:05:26,454 --> 01:05:30,394
I just think the grounding is we're just plotting points in a curve.

986
01:05:30,514 --> 01:05:33,714
We may not be doing it in Euclidean XY coordinates also.

987
01:05:33,994 --> 01:05:42,574
So it's just a – if I go back to the circle analogy, I mean I'm kind of deathly afraid to talk about something called polar coordinates.

988
01:05:42,574 --> 01:05:49,374
But like if you can draw a circle by plotting all the XY points, that gives you X squared plus Y squared equals one.

989
01:05:49,374 --> 01:05:55,354
But there's also another way to view it, which is you can say, I already know the radius is one, right?

990
01:05:55,374 --> 01:06:00,974
And I can pick any point and I can just keep rotating the angle on the x-axis.

991
01:06:00,974 --> 01:06:03,534
I can just rotate that angle, right?

992
01:06:04,154 --> 01:06:08,834
And eventually I'm going to rotate it 360 degrees and have my circle.

993
01:06:09,034 --> 01:06:13,674
I'm going to plot every point just by rotating the angle like a little bit until I have the whole circle.

994
01:06:13,674 --> 01:06:22,914
and then the reason why that is um like sort of relevant is that that gives you the repeatable

995
01:06:22,914 --> 01:06:27,854
that's like the clock math okay eventually you repeat and you just end up plotting the same

996
01:06:27,854 --> 01:06:35,634
points in the same curve and because an eletric curve you're not it's not xy it's not exactly xy

997
01:06:35,634 --> 01:06:41,074
well i guess it is right y cubed equals x yeah it's x squared plus seven so it is xy but but

998
01:06:41,074 --> 01:06:46,674
But the domain is a finite field so that it will keep eventually repeating.

999
01:06:47,874 --> 01:06:51,854
You'll keep cycling through not in order necessarily, right?

1000
01:06:52,034 --> 01:06:52,194
Yep.

1001
01:06:52,854 --> 01:06:55,674
So you have – the generator point is just a point on the curve.

1002
01:06:55,814 --> 01:06:56,234
It's a point.

1003
01:06:56,334 --> 01:06:58,594
It's literally some – we call it G.

1004
01:06:58,594 --> 01:07:00,054
So why is it confusing then?

1005
01:07:00,174 --> 01:07:02,194
This G is an X and a Y.

1006
01:07:02,534 --> 01:07:08,354
G is an XY point that makes Y squared equaled Y cubed plus 7.

1007
01:07:08,354 --> 01:07:13,934
So the G is just a name that contains the X and the Y, right?

1008
01:07:14,034 --> 01:07:22,994
And if you go on any of the Bitcoin GitHub, you can see those massive numbers, the X and Y that give you the public, this G, this big capital G, right?

1009
01:07:23,534 --> 01:07:23,934
That's right.

1010
01:07:24,354 --> 01:07:24,834
That's right.

1011
01:07:25,234 --> 01:07:28,214
And so it's a publicly known point that everyone agrees upon in the network.

1012
01:07:30,914 --> 01:07:32,274
Everything traces back to it.

1013
01:07:32,274 --> 01:07:41,274
If you have a private key, your public key is your private key and adding, taking the

1014
01:07:41,274 --> 01:07:46,274
generator point and adding it to itself, the number of times that number is that your private

1015
01:07:46,274 --> 01:07:46,514
key.

1016
01:07:47,274 --> 01:07:51,674
So just to make it simple, if your private key was one, which would not be secure because

1017
01:07:51,674 --> 01:07:54,634
it's something that is not random and someone would be able to reasonably guess, you take

1018
01:07:54,634 --> 01:07:59,054
the generator point against itself and you get a public key.

1019
01:07:59,054 --> 01:08:09,914
And when you sign and you produce that signature, what you're doing is you're taking the generator point and you're adding to it K times.

1020
01:08:10,174 --> 01:08:11,814
And we'll talk about this too.

1021
01:08:11,894 --> 01:08:14,934
I'm realizing that we may be getting a little bit into nonces.

1022
01:08:14,934 --> 01:08:22,374
I just had another kind of thought here on just what is the significance of a generator point?

1023
01:08:22,374 --> 01:08:31,855
And if you've studied number theory, you've suffered enough to know that not every number generates the whole curve.

1024
01:08:32,434 --> 01:08:32,634
Yes.

1025
01:08:32,734 --> 01:08:39,334
And it's actually – it's a lot of work sometimes to find – like I went through modulo 5.

1026
01:08:39,474 --> 01:08:41,895
I showed you that 2 does generate the whole curve.

1027
01:08:42,334 --> 01:08:44,534
It turns out 3 does too, but 4 doesn't.

1028
01:08:44,634 --> 01:08:49,454
So like if we just go through the exercise, 4 plus 4 is 3.

1029
01:08:50,214 --> 01:08:52,374
Well, maybe I might have just stepped into shit again.

1030
01:08:52,934 --> 01:08:53,474
Maybe it does.

1031
01:08:53,794 --> 01:08:55,355
Four plus four is three, right?

1032
01:08:55,434 --> 01:08:56,214
Three plus four.

1033
01:08:56,294 --> 01:08:56,895
I guess it does.

1034
01:08:57,074 --> 01:08:57,714
Not every number.

1035
01:08:57,934 --> 01:08:59,714
The point is not every number does.

1036
01:08:59,794 --> 01:09:01,654
And it's actually not that easy.

1037
01:09:01,874 --> 01:09:04,254
It's not that easy to find the generator point.

1038
01:09:04,355 --> 01:09:07,134
So it was really important that that's set for everybody.

1039
01:09:07,134 --> 01:09:07,454
Yeah.

1040
01:09:07,674 --> 01:09:11,494
And so the reason why the generator point that was selected is there,

1041
01:09:11,494 --> 01:09:19,534
It is, it was the smallest X coordinate that generates a group of the correct order prime

1042
01:09:19,534 --> 01:09:19,754
N.

1043
01:09:20,734 --> 01:09:26,154
And it's what we call in like the general form of cryptography, nothing up my sleeve numbs.

1044
01:09:26,514 --> 01:09:28,754
And it's deterministic and verifiable.

1045
01:09:29,134 --> 01:09:34,834
It was not cherry picked to hold a random value that was arbitrary that maybe inadvertently

1046
01:09:34,834 --> 01:09:35,754
has a backdoor somewhere.

1047
01:09:36,194 --> 01:09:36,395
Right.

1048
01:09:36,395 --> 01:09:40,614
this is compared to the

1049
01:09:40,614 --> 01:09:42,954
what we talked about earlier with the NIST-P curve

1050
01:09:42,954 --> 01:09:45,054
the generator was derived from an

1051
01:09:45,054 --> 01:09:47,054
unrevealed seed and

1052
01:09:47,054 --> 01:09:49,174
with the reason

1053
01:09:49,174 --> 01:09:51,174
why they picked that number was like hey if we pick this generator

1054
01:09:51,174 --> 01:09:53,074
number and you do this backdoor

1055
01:09:53,074 --> 01:09:55,034
operation you can actually reverse engineer every

1056
01:09:55,034 --> 01:09:57,154
public-private key pair through this generator point

1057
01:09:57,154 --> 01:09:59,114
so the picking and not just of the

1058
01:09:59,114 --> 01:09:59,974
curve and of

1059
01:09:59,974 --> 01:10:03,094
the finite field but the generator point you use

1060
01:10:03,094 --> 01:10:04,374
on the curve is also

1061
01:10:04,374 --> 01:10:07,914
foundational to the security of the entire operation.

1062
01:10:08,634 --> 01:10:13,714
And so what's important about this is that

1063
01:10:13,714 --> 01:10:16,234
with this generator point,

1064
01:10:16,954 --> 01:10:21,494
the entire group that generates it,

1065
01:10:21,614 --> 01:10:23,254
you can get every single point on the curve,

1066
01:10:23,254 --> 01:10:26,414
which means that the full field of all possible outcomes is available.

1067
01:10:27,574 --> 01:10:29,794
And when you keep adding the generator to itself,

1068
01:10:30,054 --> 01:10:33,634
you could just go out to infinity and you will get all of the points.

1069
01:10:34,374 --> 01:10:40,895
And it's important to know it's also like, and I guess everyone should know, I step in shit all the time because I'm not like a, I'm not the mathematician.

1070
01:10:40,895 --> 01:10:41,774
I just engage.

1071
01:10:41,954 --> 01:10:43,214
That's why we got Rob here.

1072
01:10:43,714 --> 01:10:55,094
But, you know, it's, it's important not just to know it generates the whole curve, but like, but you just said, I didn't realize that, that the generator point was the smallest X coordinate.

1073
01:10:55,614 --> 01:11:00,034
So that's like actually also pretty important thing as well.

1074
01:11:00,034 --> 01:11:11,954
And as you wade and slog a little bit more through number theory and abstract algebra, that will, I think, become pretty clear as to why it's important that you know the smallest point.

1075
01:11:12,114 --> 01:11:22,294
That's remarkable that that could be known that we can have a cryptographically secure system and we know the generator point, right?

1076
01:11:22,694 --> 01:11:24,154
We don't have to guess at that.

1077
01:11:24,154 --> 01:11:28,494
And the fact that it really is remarkable.

1078
01:11:28,634 --> 01:11:29,634
I'm sorry for this aside.

1079
01:11:29,634 --> 01:11:41,634
It's not mathematical, but it's remarkable to be able to abstract all of this for, you know, anybody in the Nigerian jungle can use this thing, you know, like it's also abstracted.

1080
01:11:41,694 --> 01:11:51,154
And I think that like we I almost think that human beings have figured out it's abstracted enough for human beings to use much faster than like the Internet was.

1081
01:11:51,254 --> 01:11:51,674
Yep.

1082
01:11:51,674 --> 01:11:58,114
which is partly why we're in this state of like so many people know how well it works and we're

1083
01:11:58,114 --> 01:12:03,134
like what the hell waiting for the world to figure it out right it's because of how freaking

1084
01:12:03,134 --> 01:12:10,855
daftly the math has been extracted for use yes incredibly uh as a force multiplier being able

1085
01:12:10,855 --> 01:12:14,634
to leverage this stuff without knowing all the nuance think about it like you get to have

1086
01:12:14,634 --> 01:12:19,514
ownership because you have something that no one else knows about like you could just literally

1087
01:12:19,514 --> 01:12:25,454
like people say, you could just know 12 words in your head and you have a unique ability to

1088
01:12:25,454 --> 01:12:28,395
leverage all of this cryptography in a way that allows you to touch money.

1089
01:12:30,234 --> 01:12:34,754
And so at the highest level, again, let's say you have a private key.

1090
01:12:35,754 --> 01:12:41,374
You then take the generator point and you add the generator to itself

1091
01:12:41,374 --> 01:12:46,634
the number of times the size of your private key.

1092
01:12:46,634 --> 01:12:53,094
yeah you just keep adding to it just keep adding and in the document there in the document there's a

1093
01:12:53,094 --> 01:12:58,094
there's a function so i think it's called square multiply but it's like there's a method out the

1094
01:12:58,094 --> 01:13:02,154
methodology you've had to do that for really big numbers as you know we've extracted a lot out of

1095
01:13:02,154 --> 01:13:06,254
the document but kind of i would say i would expect motivated people to really go through it and just

1096
01:13:06,254 --> 01:13:12,154
try to learn math and um the arithmetic and do the exercises and stuff absolutely uh for sure

1097
01:13:12,154 --> 01:13:16,514
I definitely recommend as a follow along for this podcast,

1098
01:13:16,614 --> 01:13:19,754
this is more of like a director's cut commentary of the study guide

1099
01:13:19,754 --> 01:13:21,134
is what we're talking about right now.

1100
01:13:22,534 --> 01:13:25,454
So you take this number, your private key,

1101
01:13:25,674 --> 01:13:27,794
you add the generator point to itself that many times.

1102
01:13:27,855 --> 01:13:29,254
The reason why the generator point matters again

1103
01:13:29,254 --> 01:13:32,054
is because it can generate all of the possible values on the curve.

1104
01:13:32,534 --> 01:13:34,594
And remember, the curve, the sideways bell curve,

1105
01:13:34,634 --> 01:13:37,834
is actually a series of points that are just dotted along,

1106
01:13:37,994 --> 01:13:39,054
mapping across this function.

1107
01:13:39,054 --> 01:13:43,895
and you are able to ultimately get a point,

1108
01:13:43,974 --> 01:13:44,934
another point on the curve.

1109
01:13:44,994 --> 01:13:48,134
And that point on the curve is your public key.

1110
01:13:48,254 --> 01:13:49,414
So you almost have this machine

1111
01:13:49,414 --> 01:13:50,794
where you put in a number,

1112
01:13:51,434 --> 01:13:53,174
you add the number to itself,

1113
01:13:53,594 --> 01:13:55,114
the generator point number to itself,

1114
01:13:55,294 --> 01:13:57,774
the number of times that is the number of your private key.

1115
01:13:57,954 --> 01:13:59,794
You get a new point on the curve

1116
01:13:59,794 --> 01:14:00,855
that is not deterministic

1117
01:14:00,855 --> 01:14:02,654
or it's not like the point next to it.

1118
01:14:02,654 --> 01:14:05,614
And you can't apply an easy mathematical concept

1119
01:14:05,614 --> 01:14:08,334
to be able to reverse engineer where that came from.

1120
01:14:08,334 --> 01:14:10,994
But you have a now point on the curve, which is the public key.

1121
01:14:12,034 --> 01:14:15,214
And that public key is where people can send you money, right?

1122
01:14:15,274 --> 01:14:18,714
That public key maps to a hash, which maps to an address.

1123
01:14:19,355 --> 01:14:25,274
Now, the beautiful thing now is if you send me money to this public key that I give you,

1124
01:14:25,334 --> 01:14:28,794
which gets abstracted into an address, how do I prove my ownership?

1125
01:14:29,874 --> 01:14:33,534
And you can do this without ever revealing your original private key.

1126
01:14:34,395 --> 01:14:37,014
You know a secret, which is your private key.

1127
01:14:37,014 --> 01:14:39,574
and you know where it lands on the curve.

1128
01:14:39,874 --> 01:14:41,474
And you need to convince everyone

1129
01:14:41,474 --> 01:14:43,395
that you know the secret without giving the secret.

1130
01:14:44,395 --> 01:14:45,855
And then this is what you do.

1131
01:14:46,514 --> 01:14:48,634
You provide a second secret.

1132
01:14:49,034 --> 01:14:54,414
This is called a nonce, number only used once, a nonce.

1133
01:14:54,935 --> 01:14:56,194
And with that nonce-

1134
01:14:56,194 --> 01:14:57,534
I like to think it's almost nonsense.

1135
01:14:58,214 --> 01:14:58,855
That's right.

1136
01:14:59,154 --> 01:15:00,794
But you have to pick an additional,

1137
01:15:01,034 --> 01:15:02,834
you bring a one-time secret.

1138
01:15:03,214 --> 01:15:05,594
A nonce is a only used once, it's a one-time secret.

1139
01:15:05,674 --> 01:15:06,594
So you have your permanent secret,

1140
01:15:06,594 --> 01:15:07,414
which is the private key.

1141
01:15:07,694 --> 01:15:09,094
And then you have this nonce.

1142
01:15:09,614 --> 01:15:11,514
And what you do is you pick a fresh nonce.

1143
01:15:11,554 --> 01:15:12,315
And I'll get to it in a second.

1144
01:15:12,374 --> 01:15:13,174
This is actually really important.

1145
01:15:13,935 --> 01:15:15,054
You pick a fresh nonce

1146
01:15:15,054 --> 01:15:21,114
and you bounce into the generator that many times.

1147
01:15:22,114 --> 01:15:22,474
Yeah.

1148
01:15:23,114 --> 01:15:24,594
It's like a test multiplier.

1149
01:15:24,895 --> 01:15:25,074
Yeah.

1150
01:15:25,834 --> 01:15:26,154
Yep.

1151
01:15:26,294 --> 01:15:27,234
And then what you do,

1152
01:15:27,514 --> 01:15:30,174
yeah, so you pick a random number as a one-time use.

1153
01:15:30,414 --> 01:15:32,634
And I'll get into how that gets actually picked in a second.

1154
01:15:32,694 --> 01:15:33,234
It's really important.

1155
01:15:33,234 --> 01:15:35,234
you then

1156
01:15:35,234 --> 01:15:37,574
you take this random number

1157
01:15:37,574 --> 01:15:38,514
this nonce

1158
01:15:38,514 --> 01:15:40,815
you put it to the generator point

1159
01:15:40,815 --> 01:15:43,634
and you create a challenge by hashing

1160
01:15:43,634 --> 01:15:45,494
together your

1161
01:15:45,494 --> 01:15:47,654
signature and the original public key

1162
01:15:47,654 --> 01:15:49,014
and the transaction message

1163
01:15:49,014 --> 01:15:51,594
and you can combine these

1164
01:15:51,594 --> 01:15:53,214
together and show that the secret

1165
01:15:53,214 --> 01:15:55,634
equals this

1166
01:15:55,634 --> 01:15:57,534
combination of the transaction

1167
01:15:57,534 --> 01:15:59,774
message and your public key and the nonce

1168
01:15:59,774 --> 01:16:01,654
now there are

1169
01:16:01,654 --> 01:16:09,574
like five things that I just want to very quickly explain here. One, the nonce, just like your

1170
01:16:09,574 --> 01:16:17,154
private key has to be random. Now, there is a beautiful deterministic way that is standard

1171
01:16:17,154 --> 01:16:23,554
for how you actually derive this deterministic nonce. You basically pick a number that is related

1172
01:16:23,554 --> 01:16:28,974
to the transaction message itself. And what do I mean by that? So now we're going to take a half

1173
01:16:28,974 --> 01:16:35,054
step away from math and just explain how Bitcoin works. When you provide a signature, what you're

1174
01:16:35,054 --> 01:16:43,594
doing is you're actually signing a hash. Now, what is that hash? What does that mean? What does that

1175
01:16:43,594 --> 01:16:50,855
mean, signing a hash? I actually really do feel like there are people that with this Nod's thing

1176
01:16:50,855 --> 01:16:56,574
are lost to see already. Let's start at the basic thing. I want to send you Bitcoin.

1177
01:16:56,574 --> 01:17:01,694
I have my transaction data for my UTXOs and I want to send a Bitcoin to you.

1178
01:17:02,734 --> 01:17:05,594
That is like, I view this as like you're writing a check.

1179
01:17:05,815 --> 01:17:12,774
I'm going to the bank of Bitcoin and I'm saying, hey, I want to send fundamentals, one Bitcoin to this address.

1180
01:17:14,474 --> 01:17:19,034
And now the question is, is what you can do is you can take that check that hasn't been signed yet.

1181
01:17:20,895 --> 01:17:24,674
All of the encoding transaction data and you can hash it.

1182
01:17:24,674 --> 01:17:31,094
so rather like you don't sign like you can hash anything you can literally hash anything you can

1183
01:17:31,094 --> 01:17:36,574
literally hash anything and you will always get some ramp pseudo right like you will get a random

1184
01:17:36,574 --> 01:17:40,895
what you'll get a random functions are called cryptographic one-way hash functions the reason

1185
01:17:40,895 --> 01:17:45,234
why they're one-way hash functions is i could take the word dog and it'll look like a bunch

1186
01:17:45,234 --> 01:17:49,954
of gobbledygook but anyone else in the world can take the word dog and get the same exact

1187
01:17:49,954 --> 01:17:56,194
gobbledygook. And from that gobbledygook output, you cannot infer what the original pre-image is

1188
01:17:56,194 --> 01:18:02,274
by just looking at it. The interjection here is that hashes are just as useful

1189
01:18:02,274 --> 01:18:09,514
just operationally as they are cryptographically. Because you can take literally anything in the

1190
01:18:09,514 --> 01:18:15,214
world, throw it into a hash function, and it'll look the same. It'll look like the same object.

1191
01:18:15,214 --> 01:18:23,514
And so that's extremely useful for indexing if you think about databases and we get into that.

1192
01:18:23,714 --> 01:18:38,674
So like just hash as a tool is as much for obfuscation as it is for staging the next operation because you're getting a very standard input into the next thing.

1193
01:18:39,294 --> 01:18:39,654
Absolutely.

1194
01:18:40,315 --> 01:18:40,594
Right.

1195
01:18:40,674 --> 01:18:45,114
And so, and just one quick example of why hashes are useful is if you're, they're often

1196
01:18:45,114 --> 01:18:47,054
used in the background, you don't even realize it for security.

1197
01:18:47,054 --> 01:18:52,234
If I'm writing software, I write my software and I say, hit compile, and then I can take

1198
01:18:52,234 --> 01:18:54,494
the binary of my code and I can hash it.

1199
01:18:54,734 --> 01:18:57,974
And then I can say like, Hey, this is the official hash for my software.

1200
01:18:58,114 --> 01:19:02,054
So if you download my software and it doesn't match this hash, someone messed with your

1201
01:19:02,054 --> 01:19:02,794
system, right?

1202
01:19:02,794 --> 01:19:05,174
Like that's a very simple example because it's a hash.

1203
01:19:05,274 --> 01:19:06,554
I also look at it as like a fingerprint.

1204
01:19:06,554 --> 01:19:12,794
it is a unique fingerprint for some bit of data so i like to think of it as a you're holding the

1205
01:19:12,794 --> 01:19:20,194
needle in the haystack yeah yeah now you're like this specific hash means something to me and you

1206
01:19:20,194 --> 01:19:24,654
could prove by revealing the pre-image which is what you put into the hash function is a pre-image

1207
01:19:24,654 --> 01:19:29,974
before you do the hash that um what that data is so i have this transit bitcoin transaction

1208
01:19:29,974 --> 01:19:34,834
think of it like a check i rob in sending one bitcoin from this utxo to fundamentals

1209
01:19:34,834 --> 01:19:36,914
and I haven't signed it yet,

1210
01:19:36,974 --> 01:19:38,494
but I now have this data.

1211
01:19:38,494 --> 01:19:39,214
Go ahead and sign it, please.

1212
01:19:39,315 --> 01:19:39,654
Thank you.

1213
01:19:40,034 --> 01:19:41,094
And then when I sign it,

1214
01:19:41,435 --> 01:19:44,094
what I do is I don't sign that big blob of data.

1215
01:19:44,694 --> 01:19:47,274
I take the entire check of the metadata

1216
01:19:47,274 --> 01:19:51,094
of the transaction and I hash it.

1217
01:19:52,094 --> 01:19:52,574
So now I'm,

1218
01:19:52,754 --> 01:19:55,395
and rather than signing a very large bit of data

1219
01:19:55,395 --> 01:19:56,774
that could be really, really big,

1220
01:19:56,974 --> 01:19:58,754
like Bitcoin transaction could be up to four megabytes,

1221
01:19:58,834 --> 01:20:00,494
rather than doing a signing operation

1222
01:20:00,494 --> 01:20:01,494
across four megabytes,

1223
01:20:02,134 --> 01:20:02,935
I do a hash

1224
01:20:02,935 --> 01:20:05,054
and now it's a 256 bit number.

1225
01:20:06,454 --> 01:20:07,074
SHA-256.

1226
01:20:07,234 --> 01:20:08,194
Which now is small.

1227
01:20:08,315 --> 01:20:09,534
Which now is a small number.

1228
01:20:09,774 --> 01:20:10,634
Which is a small number

1229
01:20:10,634 --> 01:20:13,294
in the context of doing this multiplication

1230
01:20:13,294 --> 01:20:16,154
because that's ultimately what a signature is.

1231
01:20:16,194 --> 01:20:17,435
It's a multiplication operation

1232
01:20:17,435 --> 01:20:19,714
of adding itself to the field generator

1233
01:20:19,714 --> 01:20:21,014
because if you...

1234
01:20:21,014 --> 01:20:22,435
And again, we're talking about addition.

1235
01:20:22,554 --> 01:20:23,194
What do you mean multiplication?

1236
01:20:23,474 --> 01:20:24,435
Well, if you're taking a number

1237
01:20:24,435 --> 01:20:26,654
and then you're multiplying it,

1238
01:20:27,574 --> 01:20:29,774
you're adding to itself a certain amount of times.

1239
01:20:30,454 --> 01:20:31,694
Like if my generator point is five,

1240
01:20:31,694 --> 01:20:34,794
if G plus G plus G plus G plus G five times,

1241
01:20:34,874 --> 01:20:36,954
that's just G times five, right?

1242
01:20:36,954 --> 01:20:38,254
So that's what we're talking about here

1243
01:20:38,254 --> 01:20:38,935
with multiplication.

1244
01:20:39,494 --> 01:20:40,355
This is the beauty.

1245
01:20:40,574 --> 01:20:42,435
If I know a number, right?

1246
01:20:42,994 --> 01:20:43,895
That's my private key.

1247
01:20:44,214 --> 01:20:45,395
I map it to this public key

1248
01:20:45,395 --> 01:20:46,594
by going through the generator point.

1249
01:20:47,194 --> 01:20:48,234
I now have a Bitcoin address.

1250
01:20:48,374 --> 01:20:49,734
You send me Bitcoin to that address.

1251
01:20:49,935 --> 01:20:52,014
It's now time for me to prove that I own it.

1252
01:20:52,395 --> 01:20:54,214
What I do is I write a Bitcoin transaction

1253
01:20:54,214 --> 01:20:56,614
with all of the requisite metadata

1254
01:20:56,614 --> 01:20:57,855
making sure it informs consensus.

1255
01:20:58,355 --> 01:20:59,274
I then hash it.

1256
01:20:59,574 --> 01:21:01,395
So I collapse all of that data into a number.

1257
01:21:01,694 --> 01:21:06,355
So now I have this message that I'm signing, which is the Bitcoin transaction.

1258
01:21:06,994 --> 01:21:27,674
You then take a new random number, and I'm about to get right to, and then what you do is you throw that through the generator point, and you can take an output, and you can show that, hey, this signature, which is the multiplication through the generator point with my nonce, maps to my signed message to this public key.

1259
01:21:27,674 --> 01:21:35,954
and how the hell do you even pick what your nonce is because you could pick the number three but

1260
01:21:35,954 --> 01:21:40,994
then if someone's able to kind of if you you have problems if someone can actually find out what your

1261
01:21:40,994 --> 01:21:51,694
nonce is and ultimately this is where it gets into deterministic nonces uh but like you know

1262
01:21:51,694 --> 01:21:53,094
just to land the plane though,

1263
01:21:53,714 --> 01:21:58,395
it's that one multiple of your private key

1264
01:21:58,395 --> 01:22:01,074
and another multiple of your private key

1265
01:22:01,074 --> 01:22:04,355
are going to be able to sort of reconcile.

1266
01:22:04,994 --> 01:22:05,474
Yes.

1267
01:22:05,474 --> 01:22:05,634
Right.

1268
01:22:06,054 --> 01:22:07,014
To the public key.

1269
01:22:07,395 --> 01:22:07,974
You're able to do a little...

1270
01:22:07,974 --> 01:22:09,034
For the public key, right.

1271
01:22:09,514 --> 01:22:12,014
You're able to do a bunch of private key operations

1272
01:22:12,014 --> 01:22:14,514
and show that they relate to the public key

1273
01:22:14,514 --> 01:22:16,034
without revealing the private key itself.

1274
01:22:16,435 --> 01:22:16,774
Yeah.

1275
01:22:16,834 --> 01:22:18,974
It's kind of like if you remember in seventh grade

1276
01:22:18,974 --> 01:22:20,834
when you learned Y equals MX plus B.

1277
01:22:20,834 --> 01:22:27,554
right you say oh if i know the slope and i know a point on the curve i can draw the whole line

1278
01:22:27,554 --> 01:22:33,174
or if i know two points in the curve i could draw the whole line and it's like um

1279
01:22:33,174 --> 01:22:39,714
that it's it feels to me like that type of that that just like that type of abstraction

1280
01:22:39,714 --> 01:22:46,414
yeah right where at least on the public line i can verify right i can sort of verify that i can

1281
01:22:46,414 --> 01:22:52,174
we can all generate, you know, we can generate the public line with this, with this information.

1282
01:22:52,435 --> 01:22:59,355
Yeah. So now for the nonce specifically, how do you pick one? There is a spec called RFC request

1283
01:22:59,355 --> 01:23:05,454
for comment 6979. And it's how you can deterministically, whenever you're doing

1284
01:23:05,454 --> 01:23:11,794
elliptic curve math operations, you can get a true, like basically a random nonce that an attacker

1285
01:23:11,794 --> 01:23:12,734
would not be able to derive.

1286
01:23:12,874 --> 01:23:14,194
And what it ultimately is,

1287
01:23:14,734 --> 01:23:18,334
your nonce is basically a hash

1288
01:23:18,334 --> 01:23:22,274
of your private key and the message.

1289
01:23:22,514 --> 01:23:24,435
So you're taking information no one else has.

1290
01:23:24,494 --> 01:23:25,815
You're the only one with the private key.

1291
01:23:26,454 --> 01:23:27,974
And you take that private key

1292
01:23:27,974 --> 01:23:30,094
and you smush it together with the message

1293
01:23:30,094 --> 01:23:31,714
that you're signing, the Bitcoin transaction.

1294
01:23:32,054 --> 01:23:34,474
You smash those together and then you hash it.

1295
01:23:35,774 --> 01:23:36,734
And that gives you a number.

1296
01:23:37,634 --> 01:23:38,594
It's a hash and a hash.

1297
01:23:38,674 --> 01:23:39,594
And the reason why this is important

1298
01:23:39,594 --> 01:23:41,634
is because since no one else knows your private key,

1299
01:23:41,794 --> 01:23:45,435
they aren't able to be able to reasonably reverse engineer what your private key is.

1300
01:23:45,435 --> 01:23:51,315
And also, if you use the same Bitcoin public address, if you reuse your address,

1301
01:23:51,395 --> 01:23:52,754
you have to reuse your private key.

1302
01:23:53,034 --> 01:23:54,654
You do not want to reuse your nonce.

1303
01:23:54,994 --> 01:23:57,654
And that's why you're deterministically linking your private key

1304
01:23:57,654 --> 01:24:02,395
with the specific metadata you're signing to make sure that no one is ever able to do that.

1305
01:24:02,794 --> 01:24:05,294
And when you throw into the hash function, you're going to get a unique value

1306
01:24:05,294 --> 01:24:08,834
that no one else is going to be able to start with, which is when you do a SHA-256 hash,

1307
01:24:08,834 --> 01:24:11,094
and say number between zero and two to the 256,

1308
01:24:11,414 --> 01:24:13,254
which again, all ties together

1309
01:24:13,254 --> 01:24:14,454
why we use that number for the curve.

1310
01:24:15,355 --> 01:24:17,815
I think we might've missed a little bit of context

1311
01:24:17,815 --> 01:24:21,654
slightly in so far as I think we spent a lot of time

1312
01:24:21,654 --> 01:24:24,014
on why the private key works

1313
01:24:24,014 --> 01:24:25,154
and generates the whole curve.

1314
01:24:26,174 --> 01:24:27,534
The context we might've missed is

1315
01:24:27,534 --> 01:24:29,574
once we go into the public space,

1316
01:24:29,734 --> 01:24:32,014
which Bitcoin requires you to do,

1317
01:24:32,234 --> 01:24:33,574
and it's the why Bitcoin works,

1318
01:24:33,574 --> 01:24:35,315
that you start moving out of your,

1319
01:24:35,315 --> 01:24:40,294
you move into a, into the public square, right?

1320
01:24:40,614 --> 01:24:41,355
The Bitcoin box.

1321
01:24:41,454 --> 01:24:44,114
And now you're moving, you know, in order to operate, right?

1322
01:24:44,114 --> 01:24:50,435
Because you can send, you can send money to yourself all you want without really, you

1323
01:24:50,435 --> 01:24:54,315
know, you can send, you know, in order to change is when you're in public though.

1324
01:24:54,395 --> 01:24:58,014
In order to move Bitcoin, you have to now go to this public square called the Bitcoin

1325
01:24:58,014 --> 01:25:02,734
blockchain, this public place that like the PO box that everyone can see through.

1326
01:25:02,734 --> 01:25:05,435
You have to actually go there and interact.

1327
01:25:06,294 --> 01:25:10,134
And like in the Y equals MX plus B example, right?

1328
01:25:11,114 --> 01:25:17,134
What you want to do is you want to give that second point and draw the line without revealing what your first point is.

1329
01:25:17,355 --> 01:25:18,054
That's like the key.

1330
01:25:18,174 --> 01:25:26,794
Now what you're really worried about is giving any information that reveals what your private key is, what your private number is.

1331
01:25:27,214 --> 01:25:31,935
You don't want to reveal any of that with anything you expose.

1332
01:25:31,935 --> 01:25:33,554
And that's what Rob is talking about.

1333
01:25:33,674 --> 01:25:35,994
That's what the nonce does.

1334
01:25:36,334 --> 01:25:38,374
In other words, you have to provide something.

1335
01:25:38,954 --> 01:25:42,895
You can actually provide your own private key to make the whole thing work.

1336
01:25:43,274 --> 01:25:44,474
You don't want to do that.

1337
01:25:44,954 --> 01:25:45,554
Technically, you could.

1338
01:25:45,754 --> 01:25:47,154
Your nonce could be your private key.

1339
01:25:48,114 --> 01:25:50,654
Technically, you could.

1340
01:25:50,994 --> 01:25:52,174
You don't want to do that.

1341
01:25:52,614 --> 01:25:57,054
But when you're talking about entering the public square, you have to enter the game theory of hostile actors.

1342
01:25:57,054 --> 01:26:04,554
And you need to understand that within a contained system, talking to yourself, you can have certain trust assumptions, but you have to be trustless when you enter the public square.

1343
01:26:04,895 --> 01:26:05,014
That's right.

1344
01:26:05,074 --> 01:26:14,974
And that's why all of these requisite little pieces are designed in such a way with the assumption of if you can keep your private key private, you can prove ownership without compromising the secret.

1345
01:26:15,534 --> 01:26:16,754
And that's how this all works, right?

1346
01:26:17,154 --> 01:26:21,714
That's why I just want to address why are we talking – what the hell – all of a sudden you introduced this thing called a nonce.

1347
01:26:21,815 --> 01:26:23,974
And like why is that – why are we doing that?

1348
01:26:23,974 --> 01:26:32,774
The reason why is you need to provide subsequent data to the Bitcoin blockchain, proving you know what that private key is without revealing it.

1349
01:26:33,114 --> 01:26:44,731
So in theory if someone just sent me Bitcoin and I never spend it I just gave them a public key and I never spent it then nothing really matters then because I never at any point in the future come back to prove ownership of that information

1350
01:26:45,492 --> 01:26:52,032
But basically, spending Bitcoin is proving that you know a private key, that you know a number.

1351
01:26:52,571 --> 01:26:53,472
That's all it is.

1352
01:26:53,872 --> 01:26:56,811
All of the Bitcoin, everything is, I know a number.

1353
01:26:57,452 --> 01:26:57,591
That's right.

1354
01:26:57,591 --> 01:26:58,472
That's all.

1355
01:26:58,771 --> 01:27:05,552
So the reason why you need a nonce is when you go to the network, you went to it the first time when you gave it the public key.

1356
01:27:05,631 --> 01:27:07,512
You did your transformation from your private key to a public key.

1357
01:27:07,731 --> 01:27:11,591
That was your first time you revealed information to the network saying you can send me money here.

1358
01:27:11,952 --> 01:27:22,771
Now, when it's time for you to prove that you own it, you need to do an additional operation that shows that you own, that you know the number that belong, that private key.

1359
01:27:23,252 --> 01:27:24,972
But you don't want to reveal the private key.

1360
01:27:24,972 --> 01:27:30,111
So you need to do a new mathematical proof, basically, of I understand this information.

1361
01:27:30,231 --> 01:27:36,552
And you don't want to – it's like you just don't want to unintentionally reveal the private – did you ever watch The Wire?

1362
01:27:37,271 --> 01:27:37,532
Yes.

1363
01:27:37,932 --> 01:27:38,211
Okay.

1364
01:27:38,352 --> 01:27:53,912
So I'm thinking – I want to say that season four opens with this scene where Prez Beluski is leading the class and he's asking – this class is so disengaged and he's doing some basic math problem.

1365
01:27:53,912 --> 01:28:04,532
It's almost like he's being – I don't know what the word is, but like really kind of pathetically trying to relate to these kids.

1366
01:28:04,752 --> 01:28:12,432
So he's like, oh, let me put it in terms you understand and like this drug dealer does this – he collects this much money.

1367
01:28:12,651 --> 01:28:16,872
And he's like trying to really reach these kids really hard and no one's listening.

1368
01:28:17,872 --> 01:28:23,792
And he has these four answers on the board and he's asking the question like what's the answer?

1369
01:28:23,912 --> 01:28:29,992
And one of the kids with that almost like Gauss surprising the teacher, like doesn't do any work and just answers the question.

1370
01:28:30,292 --> 01:28:31,711
And he's like, how did you know?

1371
01:28:31,711 --> 01:28:36,392
And he had all these chalk marks because he kept pointing to the right answer as he was asking the question.

1372
01:28:36,711 --> 01:28:38,412
And the kid's just like the dinks.

1373
01:28:38,591 --> 01:28:39,972
That answer has all the dinks.

1374
01:28:41,231 --> 01:28:51,052
And it's like he like he's unintentionally revealing the answer by trying to get the job that he's trying to get done.

1375
01:28:51,052 --> 01:28:53,872
And he's unintentionally revealing the actual answer.

1376
01:28:53,912 --> 01:29:16,052
And that's what we're trying to – that's why we use annonce to avoid – you're showing a point on that elliptic curve and you want to make sure your eyes are not on your private key and anyone can figure out what your private key is when you decide to show a point on that curve in public.

1377
01:29:16,651 --> 01:29:17,091
Right.

1378
01:29:17,091 --> 01:29:19,552
Because the signature, you have to present publicly.

1379
01:29:19,552 --> 01:29:23,591
So the integrity, and since it's public, anyone can look at it.

1380
01:29:23,671 --> 01:29:28,691
So you need to have a secure way in revealing that public message that doesn't compromise your private key.

1381
01:29:29,372 --> 01:29:29,792
And so-

1382
01:29:29,792 --> 01:29:30,552
You don't want to show the dinks.

1383
01:29:31,332 --> 01:29:31,532
Right.

1384
01:29:31,691 --> 01:29:32,372
Yeah, exactly.

1385
01:29:32,771 --> 01:29:34,972
And so you have this signature.

1386
01:29:35,832 --> 01:29:48,611
And what you're able to do mathematically is you could look at the signature and you can do a little bit of algebra, which we can get into, but you could do a little bit of algebra and say, with this signature, it's related to this public key.

1387
01:29:49,552 --> 01:29:57,332
and you're able to prove the signature is linked to the public key in which the money was sent to

1388
01:29:57,332 --> 01:30:07,171
and i mean it's somewhat elegant insofar as like how it all works um like a sniper

1389
01:30:07,171 --> 01:30:10,972
it's very hard for a sniper to get a shot off without revealing its position

1390
01:30:13,071 --> 01:30:16,271
yes right so like they're very judicious because they know they're going to reveal

1391
01:30:16,271 --> 01:30:21,992
their position and you know that's the thing about bitcoin is like you want to be able to spend

1392
01:30:21,992 --> 01:30:28,771
to move at utxo without revealing the secret that that gave it to you that's the whole point of

1393
01:30:28,771 --> 01:30:33,691
public key cryptography here right but but this is in the operation so like this isn't the thing

1394
01:30:33,691 --> 01:30:38,512
you're going to find in a math book what you're this is the thing that actually is going to um

1395
01:30:38,512 --> 01:30:44,131
i think jimmy song did a really good job on this one thing of showing the math as to why if you do

1396
01:30:44,131 --> 01:30:53,111
actually give away this nonce you're screwed like it's it's actually trivially easy and it is a and

1397
01:30:53,111 --> 01:30:59,792
it is a y equals mx plus b it is that simple to just now find your find your private key if you

1398
01:30:59,792 --> 01:31:04,852
do so if you do this so it's an important it's an important pile of shit not to step into

1399
01:31:04,852 --> 01:31:10,651
absolutely yeah and so like working through the chain i'm going to go through it at a high level

1400
01:31:10,651 --> 01:31:15,832
here, you have this Bitcoin transaction because you want to spend your Bitcoin. That's basically

1401
01:31:15,832 --> 01:31:23,211
a message that you broadcast to the network. You hash that. You now have this hash of a message.

1402
01:31:23,631 --> 01:31:28,532
And what you do is you take that hash of a message and combine it with your private key,

1403
01:31:28,952 --> 01:31:33,231
because no one else knows what your private key is, and you hash it. So now you have like a,

1404
01:31:33,651 --> 01:31:38,972
you now have a number that exists on the curve that no one else knows what it is.

1405
01:31:38,972 --> 01:31:48,651
Because to be able to get to that point without randomly guessing all possible numbers, you would need that private – that your private key.

1406
01:31:49,372 --> 01:31:53,832
Now, that then gives you your deterministic nonce.

1407
01:31:54,252 --> 01:32:08,512
And you would say that the nonce point that you're starting with is the generator that you're putting numbers in through the equation plus your nonce, your number only using once, which is this combined number of your private key in the message.

1408
01:32:08,512 --> 01:32:15,372
Yeah. And so now you now have a challenge that's called in cryptography.

1409
01:32:15,372 --> 01:32:19,231
The challenge is proving that, Hey, can you prove to me you own this?

1410
01:32:19,492 --> 01:32:21,972
Like, you know, the private key corresponding to this public key.

1411
01:32:22,191 --> 01:32:26,071
And that ultimately is a hash of all of this together.

1412
01:32:26,552 --> 01:32:33,472
The nonce point, the message and your original, you know,

1413
01:32:33,472 --> 01:32:39,372
it's the combination of both the hash of your nonce point this random number you're only using

1414
01:32:39,372 --> 01:32:45,512
once the hash is like making soup right what does it takes any data and it collapses it to the field

1415
01:32:45,512 --> 01:32:49,372
of the prime numbers that the curve operates on there's a reason because remember we this goes

1416
01:32:49,372 --> 01:32:53,332
back all the way to the beginning we're talking about like modular arithmetic it's this two to

1417
01:32:53,332 --> 01:33:01,352
the 256 minus two to the 232 minus 977 is a prime number which encompasses all that that when you

1418
01:33:01,352 --> 01:33:04,832
apply it onto a field, you will always get something within there.

1419
01:33:04,952 --> 01:33:06,631
But you can't guess the recipe of the soup.

1420
01:33:07,151 --> 01:33:07,372
No.

1421
01:33:07,512 --> 01:33:08,332
You can only know.

1422
01:33:09,111 --> 01:33:10,992
And that is really where you're getting it now.

1423
01:33:11,191 --> 01:33:14,731
So hashing is like, okay, we're going to make soup with the knots.

1424
01:33:15,532 --> 01:33:15,771
Yep.

1425
01:33:15,952 --> 01:33:18,452
You're collapsing it into the field of the curve.

1426
01:33:19,111 --> 01:33:25,052
Because SHA-256, what you're hashing this with is two to the 256 possible opportunities,

1427
01:33:25,171 --> 01:33:26,571
which is the opportunity size of the curve.

1428
01:33:26,631 --> 01:33:30,912
So you're collapsing any data whatsoever to be able to be mapped onto this field.

1429
01:33:31,352 --> 01:33:34,352
The sideways bell curve with a bunch of little points for all of the pieces.

1430
01:33:34,611 --> 01:33:34,731
Yeah.

1431
01:33:35,151 --> 01:33:37,392
Now you have your hash message,

1432
01:33:37,472 --> 01:33:38,332
which is the transaction.

1433
01:33:38,332 --> 01:33:41,671
You get your deterministic nonce by smashing it together with your public key.

1434
01:33:42,032 --> 01:33:42,811
And then when you hash it,

1435
01:33:42,872 --> 01:33:44,512
you just roll it to a random,

1436
01:33:44,671 --> 01:33:45,932
like a number on the curve that only,

1437
01:33:46,052 --> 01:33:46,332
you know,

1438
01:33:46,591 --> 01:33:47,912
so you now have two numbers that only,

1439
01:33:48,032 --> 01:33:48,271
you know,

1440
01:33:48,532 --> 01:33:49,191
the nonce,

1441
01:33:49,512 --> 01:33:54,271
which is derived in part from your private key and your private key.

1442
01:33:54,631 --> 01:33:56,372
You then have this challenge statement.

1443
01:33:56,792 --> 01:33:59,332
And what you're able to do is combine a signature where you combine the

1444
01:33:59,332 --> 01:34:04,752
the challenge statement plus your nonce times your private key that many generation points

1445
01:34:04,752 --> 01:34:05,012
through.

1446
01:34:05,392 --> 01:34:07,191
And you now have a signature.

1447
01:34:07,651 --> 01:34:14,252
And that signature has two points, R and S, basically, because at any point on the curve,

1448
01:34:14,332 --> 01:34:15,711
there's going to be like the two points.

1449
01:34:16,832 --> 01:34:22,292
And this signature, what you can do with it for verification, this is what's so beautiful,

1450
01:34:22,671 --> 01:34:28,211
is you can take this signature and you're able to basically take the R and the S values

1451
01:34:28,211 --> 01:34:28,771
in the signature.

1452
01:34:30,792 --> 01:34:32,492
For a second, let's just say like...

1453
01:34:32,492 --> 01:34:33,392
So we're off the curve.

1454
01:34:33,591 --> 01:34:35,752
I want to do this a little slower here, I think.

1455
01:34:35,972 --> 01:34:37,091
We're off the curve now.

1456
01:34:37,432 --> 01:34:41,191
Once you hash, once you do the hash...

1457
01:34:41,191 --> 01:34:41,892
You're on the curve.

1458
01:34:42,311 --> 01:34:42,792
You're on, yeah.

1459
01:34:42,932 --> 01:34:45,211
Because even a hash of...

1460
01:34:47,071 --> 01:34:49,552
So you're saying the hash function still guesses,

1461
01:34:49,872 --> 01:34:51,952
still puts, the result of the hash function

1462
01:34:51,952 --> 01:34:52,972
is still a point on the curve.

1463
01:34:53,472 --> 01:34:53,811
Yes.

1464
01:34:54,032 --> 01:34:56,111
So the curve is closed under hashing.

1465
01:34:56,111 --> 01:35:00,052
any data that you hash with SHA-256 will live on the curve.

1466
01:35:00,372 --> 01:35:01,432
And that's why you hash things.

1467
01:35:01,492 --> 01:35:02,111
So then-

1468
01:35:02,111 --> 01:35:03,571
To be able to make the mathematical transformation.

1469
01:35:03,952 --> 01:35:05,912
And so you still, so when you hash something,

1470
01:35:05,912 --> 01:35:12,992
you still have an XY coordinate that lives on the curve.

1471
01:35:14,671 --> 01:35:15,151
Yes.

1472
01:35:15,271 --> 01:35:15,452
Right?

1473
01:35:16,071 --> 01:35:18,031
So what is all, you just then said,

1474
01:35:18,252 --> 01:35:19,292
but then you have all,

1475
01:35:19,671 --> 01:35:22,131
this is why I was maybe just introducing

1476
01:35:22,131 --> 01:35:24,912
the idea of Apollo coordinates showing the same thing.

1477
01:35:24,912 --> 01:35:29,952
thing is this what is like is that is that what's happening now whereas we actually know

1478
01:35:29,952 --> 01:35:35,071
we have different dimension of what makes the curve we're not looking at an xy anymore

1479
01:35:35,071 --> 01:35:40,892
now we're looking at two different components that essentially build the same thing yep

1480
01:35:40,892 --> 01:35:46,271
yes personally this is where i found it super confusing it's like what's r and s now

1481
01:35:46,271 --> 01:35:50,691
no so this is interesting right so r being the actual like signed output proving the message

1482
01:35:50,691 --> 01:35:56,131
S is actually a point on the curve that's kind of hiding your private key.

1483
01:35:56,792 --> 01:36:00,372
And the reason why it's hiding it is because you use a deterministic non so people can't

1484
01:36:00,372 --> 01:36:00,872
reverse engineer.

1485
01:36:01,252 --> 01:36:05,332
If you wrote, if you rolled your own cryptography by hand and you're like, I'm just going to

1486
01:36:05,332 --> 01:36:08,052
always multiply by 12, right?

1487
01:36:08,052 --> 01:36:11,852
And then someone could start looking at your S values and start just walking through random

1488
01:36:11,852 --> 01:36:14,171
field operations and be like, oh, I found the private key.

1489
01:36:14,571 --> 01:36:19,031
And that's why you need a random number for this one time use to sign the data.

1490
01:36:19,031 --> 01:36:21,932
and that random number is tied to the message you're signing

1491
01:36:21,932 --> 01:36:25,512
because the R is the signature.

1492
01:36:26,052 --> 01:36:28,171
S is the point on the curve

1493
01:36:28,171 --> 01:36:29,912
that's kind of hiding your private number,

1494
01:36:30,472 --> 01:36:32,332
your private key within the transformation.

1495
01:36:33,111 --> 01:36:35,972
So these objects are also...

1496
01:36:35,972 --> 01:36:39,792
So in other words, you can plot XY, right?

1497
01:36:40,372 --> 01:36:43,731
You can also use the fact that a hash is on the curve

1498
01:36:43,731 --> 01:36:47,332
and a hash can be decomposed into something called R and S.

1499
01:36:48,512 --> 01:36:48,651
Yeah.

1500
01:36:49,031 --> 01:36:54,872
that have a little more meaning now in how Bitcoin works.

1501
01:36:56,531 --> 01:36:58,191
The R and S are what have meaning.

1502
01:36:58,392 --> 01:37:00,012
The X and Y, not necessarily.

1503
01:37:00,651 --> 01:37:02,651
It's now the R and the S that have meaning.

1504
01:37:03,311 --> 01:37:05,311
It's kind of like how when we drew the circle,

1505
01:37:05,432 --> 01:37:10,512
the angle and the radius had meaning that maybe the points didn't have.

1506
01:37:11,131 --> 01:37:11,292
Yeah.

1507
01:37:12,731 --> 01:37:15,432
And so basically you can verify,

1508
01:37:15,432 --> 01:37:18,932
to tie this all together.

1509
01:37:19,031 --> 01:37:22,792
If you have the signature values of R and S,

1510
01:37:23,492 --> 01:37:25,392
you have your public key.

1511
01:37:25,872 --> 01:37:27,811
What you're able to do is you're able to take R

1512
01:37:27,811 --> 01:37:32,531
plus your public key

1513
01:37:32,531 --> 01:37:35,372
times your hashed message.

1514
01:37:36,372 --> 01:37:39,292
So there's a very simple multiplication

1515
01:37:39,292 --> 01:37:42,191
and it's multiplication over the field of the

1516
01:37:42,191 --> 01:37:47,392
and plus R equals the signed message.

1517
01:37:47,671 --> 01:37:49,531
And what that allows you to do algebraically

1518
01:37:49,531 --> 01:37:51,752
is you can actually break things out

1519
01:37:51,752 --> 01:37:53,231
and show that in three line,

1520
01:37:53,392 --> 01:37:55,252
like this is where I wish we just had a whiteboard

1521
01:37:55,252 --> 01:37:55,952
so I could just literally,

1522
01:37:56,271 --> 01:37:57,031
I'm realizing that like,

1523
01:37:57,071 --> 01:37:57,972
this is like one of those moments

1524
01:37:57,972 --> 01:37:59,711
that a whiteboard would be really, really important.

1525
01:38:00,631 --> 01:38:02,932
That you're basically able to do substitution

1526
01:38:02,932 --> 01:38:04,952
and you can verify that this signature

1527
01:38:04,952 --> 01:38:07,012
is tied to this public key.

1528
01:38:07,392 --> 01:38:10,131
I'm thinking of making a video, not myself,

1529
01:38:10,271 --> 01:38:11,912
but now that I have my AI tools,

1530
01:38:11,912 --> 01:38:14,131
I'm thinking of making a video that does just this.

1531
01:38:14,211 --> 01:38:15,052
That's what I just wrote down.

1532
01:38:15,731 --> 01:38:15,892
Yeah.

1533
01:38:16,012 --> 01:38:17,271
Like literally just this.

1534
01:38:17,512 --> 01:38:26,571
Like, because this is like the culminating point I think we would probably want to get to today is going from like what is Bitcoin crypto?

1535
01:38:26,771 --> 01:38:27,832
Like what is this thing?

1536
01:38:27,892 --> 01:38:41,191
And getting all the way to now we've gotten all the way through the high level mathematical concepts between, you know, coherence and set theory and like finite fields and Mersane primes and the generator point.

1537
01:38:41,191 --> 01:38:46,912
we've all got and why this curve, we've all got to the point of the magic is that I'm able to do

1538
01:38:46,912 --> 01:38:55,012
with some pretty trivial algebra, a proof to you that I have the private key material related to

1539
01:38:55,012 --> 01:38:59,992
the public key that I gave you. And the rest of the network can all independently verify that

1540
01:38:59,992 --> 01:39:03,771
within fractions of a second. We're talking on the scale of microseconds.

1541
01:39:03,992 --> 01:39:06,071
The proof doesn't reveal the key.

1542
01:39:06,492 --> 01:39:07,832
And the proof does not reveal the key.

1543
01:39:07,912 --> 01:39:10,352
Ever. Yeah, that's the net, right?

1544
01:39:10,352 --> 01:39:14,912
It's so remarkable, but that's a really important piece.

1545
01:39:15,952 --> 01:39:17,052
Yes, exactly.

1546
01:39:18,151 --> 01:39:22,932
Who needs a quantum computer when you can just wait for somebody to reuse their knots?

1547
01:39:23,752 --> 01:39:26,912
Well, so it's not really even hypothetical or abstract.

1548
01:39:27,412 --> 01:39:30,631
This was a very common thing that wrecked people in early days of Bitcoin.

1549
01:39:30,631 --> 01:39:30,892
Totally.

1550
01:39:30,892 --> 01:39:37,872
Someone would roll their own cryptography library and oopsie doopsie, I was doing something.

1551
01:39:37,872 --> 01:39:43,031
and there's like multiple there's like there's many layers here that can break if you're talking

1552
01:39:43,031 --> 01:39:46,671
about in the real world of like not abstract whiteboarding on how this works but like how

1553
01:39:46,671 --> 01:39:52,352
you actually write this in software there's called um timing timing side channel attacks where you do

1554
01:39:52,352 --> 01:39:56,992
timing analysis and you can actually infer based on the cpu cycles to do each of these individual

1555
01:39:56,992 --> 01:40:01,092
pieces that someone in theory could actually reverse engineer your private key because if

1556
01:40:01,092 --> 01:40:05,552
you're not doing all operations in constant time this is in the document by the way i'm pretty sure

1557
01:40:05,552 --> 01:40:13,731
this because this is um um jonas's partner on libsec there's tim ruffing yes tim ruffing sorry

1558
01:40:13,731 --> 01:40:20,912
there is a um there's actually and i was wondering what this meant now that you're talking about it

1559
01:40:20,912 --> 01:40:26,611
this is actually also in the document um yeah about how libsec was actually created for something

1560
01:40:26,611 --> 01:40:31,631
called tls and i don't know what that stands for but it was not ssl ls which is like https

1561
01:40:31,631 --> 01:40:33,271
like your open SSL library,

1562
01:40:33,412 --> 01:40:34,531
like how you do encryption on the web.

1563
01:40:35,231 --> 01:40:35,352
Yeah.

1564
01:40:35,452 --> 01:40:36,412
And so that was not,

1565
01:40:36,571 --> 01:40:38,311
they needed to actually make it more,

1566
01:40:38,311 --> 01:40:40,012
more time.

1567
01:40:40,191 --> 01:40:40,592
Yes.

1568
01:40:40,611 --> 01:40:42,131
More time based for,

1569
01:40:42,452 --> 01:40:43,332
you know,

1570
01:40:43,432 --> 01:40:43,771
for this.

1571
01:40:43,872 --> 01:40:44,892
Everything needs to be constant.

1572
01:40:45,231 --> 01:40:48,052
Everything needs to be a constant time operation to prevent side channel

1573
01:40:48,052 --> 01:40:48,372
attacks.

1574
01:40:48,432 --> 01:40:52,231
So they literally took this initial code base and this as a way to kind of

1575
01:40:52,231 --> 01:40:53,231
like full circles,

1576
01:40:53,352 --> 01:40:54,512
begin closing out the episode.

1577
01:40:54,792 --> 01:40:57,472
This is the difference between sec P two 56 K one,

1578
01:40:57,552 --> 01:41:01,052
the curve and lib sec P two 56 K one.

1579
01:41:01,052 --> 01:41:03,651
And we were joking before about like, oh, what's the lib about?

1580
01:41:03,752 --> 01:41:16,811
The lib is the actual Bitcoin implementation library that takes these abstract mathematical concepts and codifies them into a battled hardened cryptography library that is properly done.

1581
01:41:17,571 --> 01:41:24,631
And when Satoshi originally just kind of pulled it in, it wasn't entirely, it wasn't homegrown.

1582
01:41:24,872 --> 01:41:26,972
It wasn't a perfect puzzle piece at all.

1583
01:41:27,092 --> 01:41:27,552
It wasn't.

1584
01:41:27,892 --> 01:41:28,892
It technically worked.

1585
01:41:28,892 --> 01:41:31,752
There were a lot of compromises that he could see.

1586
01:41:32,211 --> 01:41:32,432
Right.

1587
01:41:32,432 --> 01:41:43,292
It was prescient that the people that followed were able to mold it into Bitcoin before it ever showed any of the vulnerabilities that would have had the thing break.

1588
01:41:44,071 --> 01:41:44,552
Exactly.

1589
01:41:44,872 --> 01:41:46,131
That's how these things work.

1590
01:41:46,651 --> 01:41:54,832
I just want to say this is why – one of the things I really focus on a lot at the Magic Internet Math Academy is math history.

1591
01:41:55,571 --> 01:41:57,811
I've done a lot already to put on –

1592
01:41:57,811 --> 01:42:05,912
And it's because if you understand, like, this is a real aside, but like the history of math, it's not the history of mathematics.

1593
01:42:05,912 --> 01:42:07,872
It's the history of mathematicians.

1594
01:42:09,031 --> 01:42:12,412
And it's important to understand their lives.

1595
01:42:12,631 --> 01:42:15,711
One is like, you know, you have to figure out where you fit in the world.

1596
01:42:16,211 --> 01:42:16,651
Sure.

1597
01:42:16,731 --> 01:42:22,092
As, you know, whether you like it or not, if you're using Bitcoin, you're now a mathematician.

1598
01:42:22,932 --> 01:42:23,191
Yeah.

1599
01:42:23,492 --> 01:42:23,912
Sorry.

1600
01:42:23,912 --> 01:42:34,372
It's just like you are either someone who's going to YOLO the number 12, like Rob said, or you may ignore all of it and you take your risks.

1601
01:42:34,972 --> 01:42:36,372
But you are a mathematician.

1602
01:42:37,111 --> 01:42:37,292
Yep.

1603
01:42:37,571 --> 01:42:43,392
And you are either a first, second, third, fourth, fifth, or a billionth class citizen in this world.

1604
01:42:43,872 --> 01:42:49,191
You don't gain power in this world by doing favors for other politicians.

1605
01:42:49,191 --> 01:42:53,191
You gain power in this – and you don't gain power really by running a note a little bit.

1606
01:42:53,191 --> 01:42:57,972
But you gain power by knowing this, by understanding this.

1607
01:42:59,151 --> 01:43:05,731
And, you know, mathematicians, it's never clean, right?

1608
01:43:05,872 --> 01:43:08,731
Nobody – they never know the answer really.

1609
01:43:09,211 --> 01:43:12,571
Only some really special ones knew certain things.

1610
01:43:12,771 --> 01:43:19,332
But like, you know, you take – Satoshi had a number of like balls of clay that he could have picked for this.

1611
01:43:19,332 --> 01:43:25,292
And he picked the one that he had probabilistically thought had the best likelihood of succeeding.

1612
01:43:25,651 --> 01:43:31,832
And it really was up to guys like Jonas Nick and Tim Ruffing to mold that clay.

1613
01:43:33,151 --> 01:43:34,171
Yeah, no, that's exactly right.

1614
01:43:34,252 --> 01:43:35,752
And you have to think about it from Satoshi's perspective.

1615
01:43:35,872 --> 01:43:42,731
He was already designing a new computer science paradigm of data structure, of the blockchain, and all of these different moving pieces.

1616
01:43:42,731 --> 01:43:47,832
for him he just took what was available from when he desuces a reasonable curve and took the

1617
01:43:47,832 --> 01:43:53,191
available code from the open ssl tls library and threw it in there and that works as a proof of

1618
01:43:53,191 --> 01:44:00,131
concept the math is correct but there are a lot when you go from the abstract here's the whiteboard

1619
01:44:00,131 --> 01:44:05,691
explanation to this is the zeros and ones that run on your machine to do the operations and you're

1620
01:44:05,691 --> 01:44:11,131
dealing with a world where the mathematical computation is money like you're just like the

1621
01:44:11,131 --> 01:44:17,631
the number is money and the transformations to go from number to signature to public key private

1622
01:44:17,631 --> 01:44:22,452
like all these things are our money and any brittleness in any of that could result in

1623
01:44:22,452 --> 01:44:29,031
um things that you were making assumptions for no longer being true and that's where we went from

1624
01:44:29,031 --> 01:44:35,012
where satoshi originally the the libsec p part of the code base was like 500 lines of code and today

1625
01:44:35,012 --> 01:44:40,131
it's 50 000 and there's a reason why is because there was a continual let's go one step deeper

1626
01:44:40,412 --> 01:44:41,332
Let's go one step deeper.

1627
01:44:41,651 --> 01:44:43,611
We have dependencies on things we don't like.

1628
01:44:43,691 --> 01:44:45,191
We need to rewrite those from scratch.

1629
01:44:45,412 --> 01:44:49,691
We need to make sure that all of the foundational building blocks for each point that we're building on from scratch

1630
01:44:49,691 --> 01:44:55,111
have sound, not just mathematical abstract ideas, but how it actually gets implemented

1631
01:44:55,111 --> 01:44:57,631
and having operations run in constant time.

1632
01:44:58,211 --> 01:45:00,771
So that if there's a malicious process sitting on your computer,

1633
01:45:01,151 --> 01:45:03,752
that's like looking at the spikes of your CPU,

1634
01:45:03,752 --> 01:45:12,031
they can't see the variance of the computation time and basically find your private key by looking

1635
01:45:12,031 --> 01:45:15,432
at the variances because each number would have a unique signature as it goes through these

1636
01:45:15,432 --> 01:45:20,151
computer operations so that is like the levels upon levels of not just like the mathematical

1637
01:45:20,151 --> 01:45:24,892
high level but then getting to the silicon level and the code level and the assuming a hostile

1638
01:45:24,892 --> 01:45:30,592
environment level how many levels down you need to go to be able to do that and it's not trivial

1639
01:45:30,592 --> 01:45:40,872
And every step you go deeper down the rabbit hole, you have a whole new world of assumptions that you need to be understanding and kind of locking in place and kind of proving mathematically are true.

1640
01:45:41,151 --> 01:45:47,611
And those are all of the transformations and optimizations and security improvements the LibSec P library has had since its original genesis.

1641
01:45:47,872 --> 01:45:56,071
Yeah, there's probably no cryptography, at least that'll be under attack at scale like this because it's money.

1642
01:45:56,071 --> 01:46:03,992
Now, like, yeah, I would go back in time and say, yeah, like, you know, the launch codes, you know, things like –

1643
01:46:03,992 --> 01:46:04,512
Enigma machine.

1644
01:46:05,071 --> 01:46:11,691
Things of those nature I think clearly are going to try to be – things that attack power are going to be under attack.

1645
01:46:11,852 --> 01:46:21,592
But something that is so – you know, like this perfect money also is so – when I say the reward, the reward isn't just like I get to buy more things.

1646
01:46:21,592 --> 01:46:27,472
So you get money that is easily transferred anywhere.

1647
01:46:27,611 --> 01:46:30,932
I mean, the attack surface of this is enormous.

1648
01:46:31,432 --> 01:46:35,992
And it's why it's also anti-fragile.

1649
01:46:36,412 --> 01:46:41,771
It becomes anti-fragile because there's so many attacks happening in real time from its

1650
01:46:41,771 --> 01:46:43,731
infancy that is being adjusted.

1651
01:46:43,932 --> 01:46:48,372
And that's what the 50,000 lines of code is right now.

1652
01:46:48,372 --> 01:46:54,531
and it's you know i think that's i saw those 50 000 lines of code and it was it also wasn't like

1653
01:46:54,531 --> 01:47:02,671
letters it was a lot of it was not legible to a human being really and that's like if your goal

1654
01:47:02,671 --> 01:47:08,452
is to validate you know if you leave a lot of skin in bitcoin you want to validate it you really do

1655
01:47:08,452 --> 01:47:14,552
have to grapple with this at some point i don't see any way around it yeah no entirely and i'm

1656
01:47:14,552 --> 01:47:17,932
actually very proud of what we're able to get through today looking through the study guide

1657
01:47:17,932 --> 01:47:21,832
I know we may have at a point here and there kept it at a higher level.

1658
01:47:22,151 --> 01:47:28,952
And I think certain things like doing little follow up videos, really driving home these specific points of like the nonce with a signature.

1659
01:47:29,111 --> 01:47:34,452
Like there's a couple of real pieces to kind of like like hammer on to really drive the point home.

1660
01:47:34,452 --> 01:47:42,311
but looking through all of this we've been able to at the highest level at least introduce the

1661
01:47:42,311 --> 01:47:48,711
ability for you to at least start to begin to reason and understand where if you had a beer

1662
01:47:48,711 --> 01:47:55,031
if you're at pub key you're having a beer and you want to talk about this stuff you may not be able

1663
01:47:55,031 --> 01:48:00,111
to do the full mathematical proof of every line but at least you understand in aggregate the moving

1664
01:48:00,111 --> 01:48:04,811
pieces and what's important and why things are important to be able to explain how this thing

1665
01:48:04,811 --> 01:48:09,512
works and i think that's the best we can do on the podcast is an opening introductory door

1666
01:48:09,512 --> 01:48:14,151
to bring you in and kind of point your paths go deeper down the rabbit hole where they're

1667
01:48:14,151 --> 01:48:20,892
watching the follow-up videos or do the study guide and like i think this is i think like i

1668
01:48:20,892 --> 01:48:26,972
think every bitcorner should have at least this level of understanding of understanding how the

1669
01:48:26,972 --> 01:48:27,432
I agree.

1670
01:48:28,012 --> 01:48:28,452
And I'm like,

1671
01:48:28,512 --> 01:48:30,571
like you don't have to do the full mathematical everything,

1672
01:48:30,571 --> 01:48:31,031
but like,

1673
01:48:31,392 --> 01:48:35,872
like I'm going to tell you 99 out of a hundred people who hold Bitcoin can't

1674
01:48:35,872 --> 01:48:37,472
explain what we just went through.

1675
01:48:38,151 --> 01:48:38,552
Yeah.

1676
01:48:38,611 --> 01:48:41,151
I think probably 999 out of a thousand.

1677
01:48:41,171 --> 01:48:41,852
You're underestimating,

1678
01:48:41,952 --> 01:48:42,211
but like,

1679
01:48:42,211 --> 01:48:42,432
yeah.

1680
01:48:43,252 --> 01:48:44,131
So the first thing,

1681
01:48:44,131 --> 01:48:46,271
I guess I'm really trying to,

1682
01:48:46,711 --> 01:48:50,531
part of this evolution is me discovering the division of labor between the

1683
01:48:50,531 --> 01:48:51,671
podcast and the other tools.

1684
01:48:51,872 --> 01:48:52,171
And it's like,

1685
01:48:52,252 --> 01:48:53,191
what's we had,

1686
01:48:53,271 --> 01:48:54,412
this was painful conversation,

1687
01:48:54,611 --> 01:48:54,992
but like,

1688
01:48:55,052 --> 01:48:55,352
you know,

1689
01:48:55,352 --> 01:48:57,052
probably for a little bit,

1690
01:48:57,171 --> 01:48:59,111
but not as bad as it could have been.

1691
01:48:59,171 --> 01:49:01,031
Cause I know like the division of labor is,

1692
01:49:01,131 --> 01:49:03,671
I'm pretty sure now I have these other tools that are going to be pretty

1693
01:49:03,671 --> 01:49:04,031
effective.

1694
01:49:04,392 --> 01:49:08,972
The other thing is we got to talk to Thomas about getting whiteboards at

1695
01:49:08,972 --> 01:49:09,352
Pokey.

1696
01:49:10,031 --> 01:49:10,392
Oh,

1697
01:49:10,432 --> 01:49:10,932
that'd be great.

1698
01:49:11,171 --> 01:49:11,412
Right.

1699
01:49:11,432 --> 01:49:13,992
There's no reason not to have whiteboards on the wall.

1700
01:49:13,992 --> 01:49:14,111
Yeah.

1701
01:49:14,932 --> 01:49:15,252
Well,

1702
01:49:15,412 --> 01:49:16,552
my joke is I,

1703
01:49:16,552 --> 01:49:16,832
I,

1704
01:49:16,832 --> 01:49:18,492
I always show up whenever I'm in New York state,

1705
01:49:18,512 --> 01:49:21,512
I show up at pub key at open and I treat it like a coworking space.

1706
01:49:21,852 --> 01:49:22,252
You know,

1707
01:49:22,252 --> 01:49:23,111
you show up totally.

1708
01:49:23,731 --> 01:49:24,271
You show up at one,

1709
01:49:24,271 --> 01:49:26,592
I show up like one, two o'clock whenever they open in the afternoon.

1710
01:49:26,691 --> 01:49:27,052
Three o'clock.

1711
01:49:27,071 --> 01:49:27,872
In the whole back area.

1712
01:49:28,191 --> 01:49:28,912
Sorry, I've been three.

1713
01:49:29,052 --> 01:49:31,731
But we show up earlier because we believe we're special.

1714
01:49:32,252 --> 01:49:32,852
That's true.

1715
01:49:33,111 --> 01:49:36,252
But like the whole back area, like there's some natural light that comes in.

1716
01:49:36,452 --> 01:49:37,171
It's nice.

1717
01:49:37,552 --> 01:49:42,271
I just hang out, grab a beer, grab some tallow fries or something, and I just work.

1718
01:49:42,992 --> 01:49:44,372
And it's awesome.

1719
01:49:44,892 --> 01:49:45,171
Totally.

1720
01:49:45,571 --> 01:49:46,811
I've gotten plenty of work done there.

1721
01:49:46,852 --> 01:49:47,472
It is a workspace.

1722
01:49:47,472 --> 01:49:54,611
I mean, you know, Evan Kalupas built my ZeusPay site sitting at the end of the bar.

1723
01:49:55,111 --> 01:49:57,252
He built it in an hour for my book.

1724
01:49:57,752 --> 01:49:58,571
You know, it's amazing.

1725
01:49:59,292 --> 01:49:59,392
Yeah.

1726
01:50:00,852 --> 01:50:05,432
Yeah, so I really hope people made, you know, God bless you guys.

1727
01:50:05,512 --> 01:50:06,252
You made it this far.

1728
01:50:06,972 --> 01:50:08,711
I'm pretty proud of this conversation.

1729
01:50:08,872 --> 01:50:14,292
I'm really looking forward to getting it up and talking about it and getting some of the support,

1730
01:50:14,292 --> 01:50:21,472
trying to create some supporting uh tools also this is great this is you know very good we are

1731
01:50:21,472 --> 01:50:27,651
leading that's okay so if you got this far maybe it's okay to reveal we are leading to getting um

1732
01:50:27,651 --> 01:50:33,292
some guests on here to actually you know we we're building for ourselves so we don't sound like

1733
01:50:33,292 --> 01:50:38,311
idiots that's right when we're talking to the real the real folks right what we're saying is

1734
01:50:38,311 --> 01:50:41,832
we're basically near the end of our rope of being able to explain these things so at least you're at

1735
01:50:41,832 --> 01:50:45,472
our level now when we have people on. We've gotten some confirmations, people who want to come on,

1736
01:50:45,492 --> 01:50:50,071
we just have to set up time and schedule. I think a lot of people that work on this stuff are excited

1737
01:50:50,071 --> 01:50:55,752
to just be able to explain what they do, because most of the time, they either have no exposure

1738
01:50:55,752 --> 01:51:00,392
to talk about their work, or it's always in the context of, here's my latest paper doing this

1739
01:51:00,392 --> 01:51:05,792
latest thing. But like a lot of their foundational work is just doing very boring, very important,

1740
01:51:06,012 --> 01:51:11,372
critically, like life support, critical importance to the Bitcoin protocol. But it's not sexy or

1741
01:51:11,372 --> 01:51:13,912
glamorous or it's not a new shiny object. So it kind of gets looked over.

1742
01:51:14,691 --> 01:51:19,832
Yeah. And it's not like, I think one of the things we are really doing here is we'll close

1743
01:51:19,832 --> 01:51:25,531
it maybe on this. It's just the like, especially in the world we live in now. And again, I'm going

1744
01:51:25,531 --> 01:51:28,611
to say this to the end so we don't get into a rabbit hole on it. But like, I feel like the

1745
01:51:28,611 --> 01:51:33,792
average Bitcoin only thinks Bitcoin, like Bitcoin horror or that that's the software and they don't

1746
01:51:33,792 --> 01:51:41,912
see this that like i validated like bitcoin in like a day like that was nothing and then trying

1747
01:51:41,912 --> 01:51:46,311
to validate then getting to this live you know getting to this step was like opened up an entire

1748
01:51:46,311 --> 01:51:51,651
crisis that this whole now apparatus this whole magic internet math apparatus exists to address

1749
01:51:51,651 --> 01:51:59,412
this crisis and you know yeah no i would say out of like to your point like out of 10 000 people

1750
01:51:59,412 --> 01:52:00,292
who hold Bitcoin,

1751
01:52:01,492 --> 01:52:02,872
one out of 10,000

1752
01:52:02,872 --> 01:52:04,792
is probably the people

1753
01:52:04,792 --> 01:52:05,171
that are like,

1754
01:52:05,252 --> 01:52:06,012
oh, and the elliptic curve

1755
01:52:06,012 --> 01:52:06,412
and the generator.

1756
01:52:06,531 --> 01:52:06,912
Yeah, yeah, yeah.

1757
01:52:06,952 --> 01:52:07,372
Cool. Got it.

1758
01:52:07,372 --> 01:52:08,472
Yeah, I understand that next.

1759
01:52:08,972 --> 01:52:09,531
Whereas for your point,

1760
01:52:09,592 --> 01:52:10,452
you're like validating Bitcoin

1761
01:52:10,452 --> 01:52:10,992
in a day.

1762
01:52:11,252 --> 01:52:12,631
You had to hold constant

1763
01:52:12,631 --> 01:52:13,552
an assumption of

1764
01:52:13,552 --> 01:52:15,131
this thing must be true.

1765
01:52:15,792 --> 01:52:17,071
And then everything else works.

1766
01:52:17,352 --> 01:52:17,472
Right.

1767
01:52:17,472 --> 01:52:18,292
But then you realize like,

1768
01:52:18,332 --> 01:52:19,332
OK, I need to evaluate

1769
01:52:19,332 --> 01:52:19,932
my assumptions

1770
01:52:19,932 --> 01:52:20,472
and my understands

1771
01:52:20,472 --> 01:52:21,092
how this works.

1772
01:52:21,631 --> 01:52:22,711
And even if like

1773
01:52:22,711 --> 01:52:23,852
you can understand

1774
01:52:23,852 --> 01:52:24,771
why Bitcoin works

1775
01:52:24,771 --> 01:52:26,332
if you kind of hand wave

1776
01:52:26,332 --> 01:52:27,731
elliptic curve cryptography,

1777
01:52:27,992 --> 01:52:28,952
assume this works,

1778
01:52:28,952 --> 01:52:33,012
everything else clicks into place but to actually do the requisite level of understanding of why

1779
01:52:33,012 --> 01:52:38,012
does the elliptic curve cryptography work even if you're a math person like you have to walk through

1780
01:52:38,012 --> 01:52:43,952
all of these pieces like we discussed easily uh a half dozen different like mathematical concepts

1781
01:52:43,952 --> 01:52:47,352
today alone that probably have their own introductions if you're not familiar if you

1782
01:52:47,352 --> 01:52:52,771
don't think in modulo math finite fields um elliptic curve transformations like the generator

1783
01:52:52,771 --> 01:52:57,412
point and being able to do multiplication by adding a number to itself a certain number of times

1784
01:52:57,412 --> 01:53:03,271
And like all of that requires time to kind of break down and decompress so you can understand how it works.

1785
01:53:03,811 --> 01:53:12,671
And I think we did a really good high level conversation going through the next level of removing the abstractions and having tangible pieces to wrestle with.

1786
01:53:12,992 --> 01:53:13,332
That's right.

1787
01:53:13,492 --> 01:53:14,972
We're mixing the glue.

1788
01:53:15,352 --> 01:53:16,352
It takes – it's a slog.

1789
01:53:16,872 --> 01:53:19,352
And I just want to make it possible and make it easier.

1790
01:53:19,852 --> 01:53:20,332
Yes.

1791
01:53:20,332 --> 01:53:28,832
And, you know, hopefully those who are, who have some motivation to really want to learn it won't just get destroyed.

1792
01:53:29,211 --> 01:53:29,651
Right.

1793
01:53:29,771 --> 01:53:31,311
Like we now have a bridge.

1794
01:53:31,392 --> 01:53:33,592
We like, we are building a little bit of a bridge.

1795
01:53:33,592 --> 01:53:37,972
It might, it might be a bridge where you risk, you know, you're jumping.

1796
01:53:38,191 --> 01:53:42,611
It's a bridge of stones perhaps in a, in a, you know, in a tidal wave, but right.

1797
01:53:42,671 --> 01:53:45,131
But that's where we got to start somewhere and that's where we are.

1798
01:53:45,191 --> 01:53:46,512
And I'm pretty happy with this.

1799
01:53:46,731 --> 01:53:47,131
Yeah.

1800
01:53:47,292 --> 01:53:47,952
This is part of the word.

1801
01:53:48,671 --> 01:53:48,992
Parting word.

1802
01:53:48,992 --> 01:53:59,211
Only parting word is that my parting word would be we've done a lot to kind of demystify the one layer down of abstraction of elliptic curve cryptography.

1803
01:53:59,832 --> 01:54:04,611
Each of the points we talked about today are things that you could further drill into and understand more.

1804
01:54:04,872 --> 01:54:11,332
I would recommend the study guide that we're referencing that we kind of loosely based our conversation off of as the starting place.

1805
01:54:11,892 --> 01:54:12,031
Yes.

1806
01:54:12,031 --> 01:54:12,711
You start there.

1807
01:54:13,531 --> 01:54:15,071
That'll prompt it.

1808
01:54:15,071 --> 01:54:21,651
and this is an infinitely recursive rabbit hole you can go down. There's always another layer.

1809
01:54:22,372 --> 01:54:26,171
I think getting to this layer is a huge step in each person's individual understanding

1810
01:54:26,171 --> 01:54:31,711
and just be curious and interested and ask questions and use the study guide. Maybe listen

1811
01:54:31,711 --> 01:54:35,392
to this episode a second time if you really want to, once you get to the end in the aha moment,

1812
01:54:35,691 --> 01:54:40,651
go through one more time to kind of get through the whole process and just keep grinding at it.

1813
01:54:40,651 --> 01:54:59,611
You know, it takes time. This is not stuff that I knew about how it worked in Bitcoin. Genuinely, until like I started Anchor Watch, like where I went, I had to go deep, deep down because I needed to really understand each piece. These are things that I at a high level abstractly understood and maybe a little bit here and there. I understood like a generator point maybe, but I never went into the depth of why the generator point is what it is.

1814
01:54:59,611 --> 01:55:06,092
like just let your follow your curiosity and through it all you're going to get a well-rounded

1815
01:55:06,092 --> 01:55:11,131
appreciation bitcoin but also just kind of understanding and analyzing large complex

1816
01:55:11,131 --> 01:55:14,392
systems and kind of going through there i think it's a good generalized skill to have

1817
01:55:14,392 --> 01:55:20,711
yeah and then um at pub key we don't we can maybe just have placemats that are pages of

1818
01:55:20,711 --> 01:55:24,711
the study guide that'd be kind of cool that's right that'd be fun yeah all right very good

1819
01:55:24,711 --> 01:55:27,111
episode three in the books peace

1820
01:55:27,111 --> 01:55:31,292
that was fucking