Thank you.
Check, check.
Checky, checky.
Thank you.
All right.
Thanks, everybody, for being here.
Thank you so much for letting us do this.
It means a lot.
You guys know my partner, Rob Hamilton.
Rob Hamilton.
Hello, hello.
Yeah, I also am on the stage every month for the Nashville bit devs.
Unlike the Austin bit devs, we haven't stopped.
And we're going to keep on going.
So most of you guys met me over the last couple days.
I'm Fundamentals.
Brian, it's great.
If you've talked to me, you know right now this is where I want to be talking to you guys.
So, all right, quick show of hands.
How many people think they're really, really bad at math?
Okay, and how many people think they're good at it?
all right okay i'm not judging i don't actually care what your assessment is of yourself and the
the protocol doesn't care either so if you think you're bad at math you can still operate the
protocol you can still do everything we're gonna try to tell you to do maybe just to jump in kind
of we're five episodes in now with the podcast and the whole premise was what if you were always
after a bit devs people go out and grab drinks and stuff and what if it was just two guys at a
bar after bit devs just talking about some of the math behind bitcoin we're not i mean i got a uh
my college degree one of my majors was math but the whole angle of this show is just meeting everyone
where they're at and scale like scaling it down we're going to this a little bit so you could
just start understanding the pieces more yeah exactly and like um you know kind of like what
if we had a sports-like conversation where we just start getting used to, you know, you
don't have to sit down and be frustrated with hard problems. We just got to listen and get
used to the jargon. And when the time comes to, I do believe the time is going to come
in Bitcoin that we need to have a serious mathematical conversation. And when the time
comes, hopefully, my hope is a lot of us are loaded up with at least the language and are
used to talking to each other about it. And that's really what it is we're doing here.
So I have another question. This one might have some audience participation. So do you
know the saying, don't trust, verify? You guys know that, right? How many people believe
that they've verified their Bitcoin?
To your own liking, I'd say.
To your own comfort.
Where you feel good about it.
You feel like I've verified this and we're good.
I'm curious to know if anybody would be willing to...
And I'm not going to address the response,
but I just want to know if anyone's willing to say
or share what they did to get to that point.
anyone willing to just say
this was my
I'll get you a mic
because we're recording this
I verified the UTXO
using my own mempool
running on my own node
alright
yeah thanks for that
I mean that's probably
you know
I'm going to
I'm going to just explain really quick
what my process was
for verifying
and I didn't raise my hand
just for whatever it's worth
and so I want to just share with you
my sense of verification
and that path has me sitting here
talking to you guys right now
so I mean
I think I was like a lot of people
when I got Bitcoin
I read every book I could
and then especially the technical books
like Mastering Bitcoin
programming Bitcoin
but like really the ability to understand
the transactions to know what I was even
looking at on my node in the mempool
going to the
GitHub repo
the GitHub repo really was a big one where
okay this is amazing you see
the formulas
there's the difficulty adjustment
there's the halving
there's
you know it started to click and feel
really good and
Bitcoin was starting to make a lot of sense to me at that point in time.
Then I guess that wasn't enough for me, for whatever it's worth.
And so I started having to look at the cryptography because I was looking at transactions and the transactions make sense.
but how does the Bitcoin stack flip a one when it pairs a signature and a pub key?
So I go to the SEC256P1 website and that GitHub,
and I had a personal existential crisis because I absolutely had no idea what I was looking at.
It's 50,000 lines of code.
what I saw first was just a sea of hard-coded numbers.
It almost looked like wingdings.
I had no idea what I was looking at.
And I already jumped out of the Bitcoin plane.
So this is now like, oh, no.
I'm really now pulling the parachute.
Nothing's happening.
So this was like a serious, serious crisis for me personally.
Because now I'm like, I don't know how to get comfortable.
you know not understanding the cryptography for me would mean testing my bitcoin over and over
again to make sure i can continue to spend it okay which is impractical and you probably shouldn't do
it um so i i bought a cryptography book and then you know started in this massive rabbit hole
at some point in time in that rabbit hole i realized i could probably do a decent job of
trying to explain this to people, and started a math podcast,
which I'm not going to ask for hands, but who thinks starting a math podcast?
Math podcast is psychotic.
So, you know, that's where I am.
I think I might be unique or rare, but I cannot sleep unless I can verify my Bitcoin.
and so that's where we are
is right here
and you may not be in that position
but maybe consider that
you might get there
once you get to wherever you are
you may find yourself
wanting to learn the cryptography
and sort of having a panic attack
like I did
so you might now wonder
what we're looking at back here
this is not just a placemat
I'm thinking we
what I'm going to attempt to do here
what Rob and I are going to attempt to do here today
is actually leave you with
a sense of
how knowing the math
actually
gives you power in understanding
that your Bitcoin is valid
yeah
and jumping in here
for the size of the space
who knows here
roughly how many possible
Bitcoin public
private keys can exist.
Like how many? It's not hundreds.
It's not thousands or millions.
Does anyone have a rough idea?
Yeah.
So it's
said here, there are
more possible Bitcoin
keys than there are atoms
in the universe.
The number is roughly
2 to the 256 power.
So 2 times 2 times 2.
256 times. And that number is so cosmically large, you could almost view having a Bitcoin
private key as a cosmic level on the atomic level needle in a haystack. That's how massive the space
is. And what we're doing here today is instead of being that really massive number, we're just
going to pull it down to the number seven. We're going to use the number seven to explain some of
the basic concepts that are happening here.
Yeah.
You want to be able to do some things on a pen and paper Because in the end state you can do it on a pen and paper You can take your own private key and do any math on it on a pen and paper
In fact, you can't even string all the computers in the world together.
It's also not secure because then that pen and paper, the piece of paper then is your private key.
And if someone got that, they could take your money.
So you don't want to do that anyway.
Yeah.
So what we have here is, looks like a bunch of numbers.
So there's two concepts I want to get across today, and I think we're going to be able to do it.
This is a times table.
You guys all learned times table, right?
The times table, you learned, if we took like three times three, you might say nine, okay?
That's like a regular times table in the number system called the real numbers, or a number system called the integers.
Three times three is nine.
In cryptography and in Bitcoin, we use a number system that is more of the remainders.
It's a number system of remainders.
So who remembers doing long division in school?
You remember you would get to the end and you'd have remainder three, remainder seven, whatever it is.
That's what we're talking about here today.
Okay. So when Rob said the number you divide by in Bitcoin is 2 to the 256 minus 2 to the
232 minus 2 to the 16 minus 2 to the 8 minus 16.
Some ungodly number. But in order to understand what it really looks like, we're going to
just use a small number like 7. So let's pretend 7 was the number we divide by in Bitcoin.
Then we would have six private keys possible.
Okay?
One, two, three, four, five, six.
And everything we do here is what's called modulo seven.
Meaning after we divide by seven, we're looking at the remainder.
So, for example, just take the three line.
Three times one is three.
Okay.
Even with a remainder of seven, no change.
Three times two is six.
All right?
Still, we're still probably good.
Here comes the speed bone.
3 times 3 is 2.
What the hell did you just say?
3 times 3 is 9, but then after you divide by 7, the remainder is 2.
We're dividing by 7 in every single cell, and we're taking the remainder.
3 times 3 in a mod 7 system is 2.
3 times 4
now becomes 5
and then 3 times 5 is an interesting one
so 3 times 5 is 15
but dividing by 7, 7 goes into 15 twice
becomes 14 and then you have a remainder of 1
so when you have two numbers
that multiply to 1 in this system
it's similar to in
earth, in real number
earth, when we say
I have the number 5
and I multiply it by 1 fifth
and I get 1
so like in the system
we grew up in, 5 times 1 fifth
equals 1 and those are called inverses
of each other
it's an important concept that
we're going to get to later
so you always want to know that there's a number
there's always a number you can
multiply by to get you to one or essentially to nullify, you know, to nullify the, or like undo
it, the system. Yeah, or undo it. Now in this system, there's only six numbers. One, two, three,
four, five, and six. There's no one fifth, right? There's no one third to multiply by three to get
to one, but there is the number five. So even in our system, we weren't taught this, but the way we
divide is by multiplying, right?
You divide by
five by multiplying by one-fifth.
Well, in this
scenario, you divide by three
by multiplying by five.
And you get what's called your inverse.
Three times five is one
mod seven.
Anything you want to add to that?
No, I think we're good.
We're making good time.
You know, when I'm just sitting around with nothing to do,
I literally create these times...
I just doodle around with these times tables.
It's a useful exercise at these smaller number levels just to get acquainted.
So, you know, you're not going to go run a marathon just because you learn how to move your legs.
But, you know, this is the beginning of, like, the substrate of if you want to get comfortable with this
and really start to learn how this works.
It's a very low effort.
It could be fun exercise that you can do.
So that's the times table.
and the inverse is the one we want to focus on, right?
So back to the question of verifying.
I once asked Rob this on the podcast.
I said, when you went to the Bitcoin store to go buy your Bitcoin,
you probably should have asked to see the manager, okay,
and asked them, how actually do I know that this Bitcoin you're selling me
has a valid private key.
Okay, right?
How do I know?
And I'm pretty sure,
we went through this thought exercise
and actually,
kind of shocking
how few of us probably
even thought this through.
Most of us just hand the money over
and then either we pray
that it hits our wallet
in a valid address
or we just expect it to
and we don't worry,
we don't maybe stress about it.
But like,
very few of us
are actually asking the question,
how do I know
Bitcoin is going to reconcile to a point on the elliptic curve.
Do we need to back up and talk about the elliptic curve?
Very briefly, just for the sake of conversation.
If you remember graphing charts in school, the Bitcoin curve, if this is the y-axis and
this is the x-axis, it basically, and we won't have time to get into it today, you can go
back and listen to our previous episodes if you're interested, basically looks like this.
It's on the back of the postcard that I left on your chair.
Yeah. And so the one little note about this curve is really interesting is in 2011, Hal Finney makes a post on the Bitcoin Talk forum and says, why did we use this curve?
and Greg Maxwell and Christian Decker
and many prolific Bitcoin developers
are talking, having a conversation.
And the actual answer is simple and amazing.
It was the one curve at the time
when Satoshi discovered or invented Bitcoin
was the only one that didn't have any weird quirks to it.
So it was the one curve he looked at
and said, this is reasonably secure.
And as one last little addendum,
what tends to happen with these cryptography
the elliptic curves is NIST or someone puts out a standard
and then they do some weird tweaking.
And that weird tweaking allows you to basically backdoor the entire system.
So Satoshi was hypercritical in evaluating the curve.
So he went and did the verification before putting it as the Bitcoin network.
And you can view this curve rather than it being a continuous line,
it's a bunch of points.
And each of those points is a public private key link.
In this case would be six points.
For this curve it would be six points.
And there's a really good page in Mastering Bitcoin, I think it's chapter four, where he shows mod seven and he shows the six points that make the elliptic curve.
And then he shows mod like 17.
Then it starts to fill out a little more.
And then I think he does mod 37 and it starts 36 points.
It really starts to draw out the curve.
Now we're talking about two to the 256 minus – yeah, minus two to the 36.
And so whenever you actually – going to the Bitcoin store ultimately is saying I'm going to give you a point on this curve.
that point is my public key.
And what you're going to do on your side
is you're going to give me some Bitcoin that you hold
and you're going to sign a message with your private key
and give me the Bitcoin.
That's a Bitcoin transaction at the end of the day.
And in case nobody knows this,
your public key, mathematically,
is Bitcoin's generator point times your private key.
So it's the Bitcoin generator point repeatedly added a certain amount of times
And the amount of times is actually whatever the number is on your private key
So the point of cryptography is that it's actually very hard to guess how many times
How many times a generator number was added together to get the public key
It's very hard to go back and figure out your private key
It's actually more than very hard
It's worldly impossible
The one visual metaphor I like to use for going from a private key to a public key, imagine you have a fresh billiards table.
It's freshly queued.
All of the balls are hit up there.
And you can go anywhere you want on the table, put the ball down whenever you want, hit the ball at whatever angle you want and at whatever speed and spin you want.
And then the balls break and they all scatter all over the place.
if you walked over after the ball was hit and you see all of the pool balls sitting everywhere
randomly you would not be able to know oh you must have hit it from this curve at this angle
with this spin you can't reverse engineer that reasonably and that's ultimately when you're
this generator point you're doing these hops that's the shuffling you're doing around but
visually i always like think about it like a pool table if i were to walk over randomly hit it
and then show someone later wherever the balls are sitting like hey that's my that's my public
key send my money to this arrangement and then i'm the only one who knows the exact angle spin
power all of that stuff that went into hitting the thing and that's so right so there's no way
even for yourself to really know that your private key is on that elliptic curve except for the fact
that you're told it okay right so there's no way for you to act to you know this you have a public
key, you kind of want to understand, you want to know your private key sits on that curve.
That's pretty important, right? So then the question is, how do you know and what are we
talking about? And so it just ends up because, so if you do the math, private key times big G,
which is this big generator number that everybody knows what it is, private key times big G is big P,
your public key, right?
So given the public key,
how do you back in algebraically to your private key
is that you have to multiply by the inverse.
Basically, you have to isolate the private key by itself.
So you have to know that it's invertible.
That's why we started with inverses here.
Yes, and so what you see here
in the six-dimensional version of the story
is that every single number,
which is every single point on an elliptic curve mod seven,
which is six points,
every single one of them you can actually see has an inverse.
One times one is one, so one has an inverse, right?
Two times four, remember mod seven, is one.
Two times four is eight divided by seven, remainder one.
And down the line, all the way down to, if you can see the 6 down here, 6 times 6 is 36, but mod 7 is 1, because 7 times 5 is 35.
So the key insight is every single point, because of the algebraic structure of an elliptic curve, this is this, just a lot bigger numbers.
but it is a fact that every single point actually has an inverse on this curve.
So as long as you can validate that the public key is a point on the elliptic curve,
then you know it has an inverse And you know which means you know you can back into your private key and that when you go signing with your private key it would be avowed
spent
as far as
we have eight minutes left
I was worried we were going to get to the end of that
yeah you thought we weren't going to get there
so maybe
just as a closing thought here
a version of this is also basically done
when you go to provide a signature
when you have a signature we don't have a slide for today but just to think about this i always
view a bitcoin transaction like a paper check you have a date field you have an amount field
you have a two field you also have a from field my bank account but in this case it's your previous
utxo i can't send you bitcoin unless i already have bitcoin right and then that signature what
it is what what is it actually signing it takes all of that that data on the check and it hashes
it and then you get like this little flag of sig hash you and that's the and that's what gets signed
and when you do the signature you can say ah yes you signed this data and additionally this
signature came from the private key belonging to this public key and that's the really important
distinction for when the network is running a signature verification to verify like it's doing
it's collapsing in large big time space all these operations and it's really a testament to the
quality of the software bitcoin protocol developers like the libsec p library when satoshi
released the original client it was like four or five hundred lines of code and he was importing
from random libraries and what the libsec p project is is bitcoin core's attempt of how do we remove
the dependencies it was using open ssl and how do we make it better more consistent faster more
optimized to better scale the network and then you have the protocol level and then basically that
libsec p library every single hardware wallet imports and just uses that it's like the most
trusted part of the bitcoin code base in the sense of everyone is saying we're keeping an eye on this
and this is actually how all signatures are done and that's like all that core cryptography lives
in one part of the bitcoin code base and then on top of that you have applications right because
most people one aren't using the bitcoin core node to run their wallets you have applications whether
it's a mobile wallet, a desktop app, or even like protocol things like, not protocols,
like toolkits, like Bitcoin dev kit that Steve works on, basically employ a bunch of guard
rails to run these checks for you and know that if you type in an address wrong, they'll
say, hey, this is not a valid address.
Those are all bumpers and guard rails that kind of sit on top of this.
And to make it full circle a little bit, the verification journey, you kept going down
and down.
this is getting close to rock bottom.
What we're talking about is pretty close
as you can get to the foundation of the security
and how Bitcoin works.
Yeah.
So closing thoughts, I think what I'll do with the time left,
I'm going to show the website for a second.
Before I do that, I would say, look, a lot of focus,
a lot of the media focus
or what we think about in the knowledge systems
is centered around Bitcoin Core for good reason.
I would just say don't sleep on the fact that LibSec256K1
is a super important GitHub, and don't sleep on it.
And there's a big world out there of things to worry about
and things to understand.
So I'm going to just talk about magic internet math for a minute,
and then I think we'll do questions.
Magic Internet Math is a site I created
after basically Rob showed me the power.
The power of Claude Code compelled me.
It was over the holiday break, like Christmas time, whatever,
and I was like, you've got to check this out,
which is funny enough, I originally got onto Claude Code
because Michael Goldstein was here at Bitcoin Park in October
and I was catching up with him.
I'm like, oh yeah, I'm using this.
He's like, have you checked out Claude Code?
I was like, no.
He's like, go check it out.
And then two days later, I was like, I can't believe I didn't know this sooner.
And then I had that same version of a conversation with Brian.
Well, Rob really thought he was flexing.
He was showing like he basically said, hey, send me a PDF of your book.
I wrote a book last year called Bitcoin for Institutions, by the way.
But he goes, send me a copy of that book.
And he's like, look at what I could do with it.
And he made the most beautiful like it made like a course on my book with the most beautiful UX.
and I was shocked at how much it understood.
Like 12 minutes.
Yeah.
But my thought wasn't like, oh, what more can I do with my book?
My thought was like, I could do this with any math book?
Are you kidding me?
And I'm a lover of math books.
And I wanted to see all of my beloved math books that I've been through in this format.
And I realized I could create – I can actually create something now.
And so I have a website that has over 100 courses on it,
and they're all mostly math books that I've personally curated.
I haven't been through every single one of them,
but the ones I haven't been through, I know what they do,
and I know why they're there.
You can go from the most basic algebra, like basic, basic, basic beginner algebra.
So if you raised your hand and said you didn't think you were good at math,
you could check out basic algebra.
I have beginner's calculus, which, by the way, is easier than basic algebra.
I'm pretty certain.
So we go as basic as that to all the way up to advanced graduate level cryptography.
You know, abstract algebra, Galois theory.
I mean, I'd say you name it, it's on there.
And then I didn't stop at math books because, you know, why do that?
all of the Austrian economics
sentimental texts are converted
into this format.
When Rob told that
story on the podcast about Hal Finney's
post, I had the idea
to take all of Satoshi's 546
Bitcoin talk posts and
make a class out of it. So now there's
a class out of that and a YouTube
series just on that.
And you figured out how to
make a YouTube series. There's a YouTube series
on how to go essentially
start with the conversation we had here in basic arithmetic
in terms of modular arithmetic and it takes you all the way to
elliptic curve, cryptography, even like Musig and Frost.
So I'm really now
just all in building this magic internet math website.
I'm all in in educating this community
this community and beyond
and I'll be making many more
many more classes I guess the last thing
to mention is the context
of the reason
why I said in the beginning that
your assessment maybe
I'm not judging your assessment
of yourself and math I think most people have a negative
experience of math
because you know
it was like required
it was taught in a mandatory way
and you know
I view math as an art very much as a liberal art,
and I very much want to teach it that way.
And I think we have come together on the podcast of like mind in this.
I would just check out the first episode.
It's called Teaching Math as a Liberal Art.
And the math courses I have are very story-based.
They feel like Greek heroic epics.
You feel like a hero's journey.
I was going to say the one thing I think you and I have in common is we don't like how
math is taught in schools
it's something we both mutually share
I mentioned I got a bachelor's degree in math
I almost failed 7th grade math
so just to understand
the context and the structure
in which and how you learn things
is as important as the actual
content you're learning yourself
and in general
math as a liberal art is something that's definitely lost
it's kind of like do your times tables do this do that
and it's like
math in its own self of pursuit
is its own enriching experience
and it gives you a deep appreciation
for the complexities of life
so with that
we'll open up to questions
what's up Joe
Yeah, the obvious ignorant question here is the math relationship to quantum computing.
And what is that relationship?
And is it valid?
And I know it's trendy and FUD and all that.
It's funny.
Our last episode was about this exactly.
You want to take it first?
I'll go listen to it then.
So, I mean, like.
No, this is.
No, you don't have to listen to it.
question i'm just it's funny because it's timing yeah you should but like you don't have like the
so everything we talked about with this curve and the generator point and like the pool table
the whole idea is that you have something called the discrete log problem that's the big mathematical
concept and what that means in english is that incrementally if i give you a public key
you have no idea where to go is the number is the private key higher or lower i have no idea
and you can't reasonably it's constant randomness like there's no signal anywhere the concept
behind quantum computing is that you're actually able to with a public key over iterations the way
i approximate is like is the number higher or lower higher or lower and to the point where you
could actually walk the whole way backwards right um from a strictly abstract idea like mathematically
it is a threatened concern like just from just from a pure theoretical like no one's actually
been able to ever prove that the bitcoin cryptography that we use is provably secure
it is just so it's that cosmic needle in a haystack size of problem where like your best
chance of being able to get it is guessing every single number, which at that point,
you're better off mining Bitcoin than guessing numbers. For the latest advancements,
I actually tweeted that maybe a day or two ago. I'm keeping a cautious eye out for the latest
Claude models that are coming out later this month, the Claude Opus 5 and Sonnet 5 models.
And I'm saying that because people with Opus, like the current generation models,
I'm not sure if you saw that guy who was able to cure cancer for his dog.
So if Model 4 is curing cancer, what's Model 5 going to do?
And I think over the next month or so and change, we'll see that if a bunch of breakthroughs all over the place start happening,
then it's a concern, and that's just on a plan to execute.
There are so many problems around the problems that have getting quantum computers.
are they able these run for fractions of a second before they break down and they lose coherence
which is like their ability to sustain compute um additionally you have we've never we're talking
about like numbers we basically are doing is like for these public keys you're factoring you're
trying to basically reverse engineer a really large number a quantum computer has never been
able to factor a number larger than 15 like three times five one times 15 like a quantum computer has
not been able to do that yet so my thesis as it sits right now is even if these new models that
come out are massively expansionary and like start moving things it's still going to be a multi-year
build out to get the requisite resources and the additional energy and the additional like all of the different pieces there so many pieces that are still strictly theoretical that we would have years to be able to address it
And at that point, Blockstream and others have put out research papers
around a new, it'd be a significant change.
It'd be the biggest change Bitcoin has ever had to update Bitcoin
because we're basically taking this entire curve
and everything we just talked about that's been the basis
since Bitcoin started and throwing it out the window.
There is a way, though, to advance.
There are things that quantum computers are not good at
that we would be upgrading our signature mechanisms to.
So all of that to say, I'll let you jump in too,
but as the kids say, I'm monitoring the situation.
That's what I'm doing right now.
Yeah, that's a great answer.
Just because something is FUD doesn't mean there's not a real threat behind it.
It can be both.
A lot of what it makes for good FUD is the fact that
You have a threat that's someday one day.
It's not near today.
But yeah, you can create an industry to basically say, no, it's urgent.
This is urgent to do now.
You know, the real primary purpose for even being here and doing this work is to demystify,
At the very least, demystify the math so that you're not as impressed with the FUD peddlers as they want you to be.
You could be a little bit on to them, and then you can kind of try to think it through for yourself.
I'm about to make a personal time commitment in understanding the quantum thing,
mainly because I speak into a mic and I want to sound like I know what I'm talking about when I
talk about it. I don't think ordinary people necessarily need to do that. I do think this
will clearly be a threat one day in our lifetime. And it's probably not right now, but the time is
now to get used to the language and get used to maybe upgrade yourself a little bit on the math
side so that when it is a conversation, you guys have agency.
Michael.
Follow up on that quantum hot topic.
So my understanding is, though, that the risk is like the P2PK addresses, Satoshi's and
those.
My Bitcoin, it's in a modern address without reuse.
This is what I meant.
My public key is not exposed, so it's a zero-wist to quantum.
So what you're saying, yes, is correct.
So when we talk about you give someone your public key,
what you actually usually give them is your address.
Satoshi's original coins, this was before that format was really widely distributed.
So he has raw public keys that are available that anyone can start stealing.
Additionally, Jameson Lopp has a really great article of address reuse.
so remember when you go to send bitcoin you say oh here's my key that matches this address
so if you reuse an address that is quantum vulnerable because you have to necessarily
put your public key on the blockchain to prove that you owned that address
if i was a quantum attacker and i was trying to go after the biggest bag
assuming that's my goal i would actually go for binance has 300 000 bitcoin in a three of five
multi-sig that they've been using for years so like realistically if they're going to try and
get someone? Are they going to try and get your UTXO
that has never been seen before, which is
complicated, or are they going to try and go for that?
The one thing I would caveat is that if
anyone has ever seen your output descriptor,
has like your wallet config file,
all of the data,
that information has
your public key in it. So that's just like for
your own awareness. We always say that like
your output descriptor, your wallet information
is
privacy losing because someone could see
your addresses, but they can't take your money.
In the case of a quantum computer,
that then becomes they also could take your money.
Yeah, and so this is actually a good question
because it brings up, I think,
probably the most important thing
an ordinary person can do.
The way you assess risk is in two dimensions,
frequency and severity, okay?
And the mathematical side of quantum
is breaking what's called Shor's algorithm
for your private key
or breaking Grover's algorithm for the hash function?
That's a yes-no, right?
So can they be cracked?
Yes or no, right?
Then there's a magnitude sort of severity question,
which is like, what's the order of operations?
What are the easiest, most vulnerable?
Taking Satoshis are the easiest ones.
You could lift 100 Bitcoin
and a couple hundred Bitcoin a week move from that Satoshi era.
But the reason why they're vulnerable is because you can already go into – you can already go onto the blockchain and see the exposed public keys.
So anywhere you can see a public key, a quantum computer theoretically that can break Shor's algorithm can find the private key.
And it's like four million coins or –
Well, Satoshi has like roughly – we assume Satoshi is like – that group is like roughly like 1.2, 1.3 million I think are in that – maybe – is it actually four million?
made i thought oh yeah that's right satoshi himself has like one to one and a half million
and then there's a couple yeah so there's like a couple there's a couple million yeah p2pk yeah
um just a fun historical application with cryptography in world war ii um everyone was
like alan turing and the turing machine and reverse engineering the germans encryption
does anyone know what they did when they managed to crack enigma and they didn't use it they
intentionally let ships sink.
They allied
troops and ships died
and ships sank because they
realized that if they had
let everyone know that they had cracked it,
they would lose the strategic asymmetry in using
it. So my personal thesis too
is that if a quantum computer becomes valuable,
as valuable as Bitcoin is,
for the US government to be able to reverse engineer
and know all of China's decryption,
likewise too, if China was able to
break encryption, do you think they want to start
moving? Bitcoin may very well be
since it's so public, maybe one of the last things to fall.
Because if you're a state actor, it's infinitely more valuable
to try and break literally anything else
in other people's security systems than to try,
even just to continue eavesdropping.
Because the moment you show your hand that you know it,
people will update and change their encryption.
Let's do one more question.
Yep.
I said one question a little closer to home
in terms of risk factors for most people.
And I don't know if this falls into your math,
any of your math studies,
but the actual randomness
that is used to pick your key
has been the most common attack on Bitcoin.
It's happened a lot.
Yes, no, this is actually really important.
So we were talking about how you have
this whole cosmic universe of anything in the world
that you're, across the entire universe,
picking a single atom.
If you use really bad entropy,
it'd be like, oh, it's somewhere in this room.
And now you've taken the entire universe
and just made it this one little space.
And then you can easily just go through atom by atom
and just like guess everything, right?
So entropy and how you actually start your secret,
if you're familiar with your seed phrases,
each word is actually a bit of entropy.
And they all kind of tie together
to be able to make your master seed phrase,
which then generates all of your child keys.
Entropy is critically important
because that's what allows you to have
the whole universe on your side.
if you don't do that
or people used to do these things called brain wallets
where you could take a poem and make that a Bitcoin key
or you could take a song name and whatever
and then you make it such a narrow search space
that computers can in an hour get trillions of random addresses
that they could just sit there and look at and wait to go.
You're right, that is the most common way people mess up their security.
It's not the actual architecture in the system.
You as a user of Bitcoin, even if you don't understand this stuff,
you're walking through the door using these tools and the one thing that's in your control
the most important thing that's in your i'll say the most important thing that's in your control
is getting good entropy and that's a whole conversation in its own right for sure i'll
just add um it's just kind of incidental um rob and i talk about this all the time that um
we don't have coins anymore but like when i grew up because i'm old i grew up with coins
and we used to flip coins and develop a sense of probability
just from flipping coins.
It's one of the great crimes of removing coins from circulation
is we actually have lost our sense of risk and randomness,
I think, in a certain way
because we don't actually have coins to flip around, right?
Tails.
Well, I didn't tell you what heads and tails was.
Bitcoin.
There you go.
So try to find a coin, play around, flip it, figure out, you know, it's another thing like, you know, you doodle around with arithmetic, but you flip a coin, try to, how many times could you do 10 heads in a row?
Totally.
Getting a sense for how rare that is.
It's good to develop that sense for yourself so that you kind of understand.
I think a lot of people don't even know what it means to make sure you have entropy.
Thank you.
Oh, thank you.
Carl, you got anything for these guys?
he stepped out okay seriously i love how autistic you guys are uh you guys are amazing huge round
of applause for these guys um to brian's point if you love like an area like he loves math rob
loves podcasts. So just do what you love and just like continue to go down those rabbit holes and so
on. So this basically concludes grassroots Bitcoin. I don't really have some like amazing
way to conclude it. I know. Oh, I know we could sleep here if you guys want to. No, I'm just
joking. But Renata had a good idea. Whoever wants to opt in just to do a quick photo outside,
we can all just get on the area outside and someone could take a photo of all of us.
it is my hope you guys establish at least one new connection
one new idea maybe one new podcast rob i don't know
but i just want to say deep down thank you on behalf of andrew
jack the rest of the bitcoin park team for you guys to spend time here
thank you to unchained thank you to feddy thank you to bid key
and then one thing just to jam with me and maybe
in our new feddy community chat actually maybe we sunset the signal group even
though it's easy and do that fetty check because I want to get some survey of next year's date
and new ideas for next year. For example, would it be cool to have like, we're not going away from
the lightning presentations because like I love those. So I'm going to selfishly do that. But if
there's other ideas on like, hey, it would be cool to have this type of speaker cancel Wesley. He
sucks. Like do other things like that. Like we could, oh, sorry, Wesley's here. Okay. Uh, but no,
other things like that um would love love feedback uh as well cool all right thank you
guys we'll meet outside whoever wants to opt in for a photo cheers
Thank you.