1 00:00:00,000 --> 00:00:29,980 Thank you. 2 00:00:30,000 --> 00:00:56,940 Check, check. 3 00:01:00,000 --> 00:01:06,320 Checky, checky. 4 00:01:30,000 --> 00:01:59,980 Thank you. 5 00:02:00,000 --> 00:02:29,980 Thank you. 6 00:02:30,000 --> 00:02:59,980 Thank you. 7 00:03:00,000 --> 00:03:29,980 Thank you. 8 00:03:30,000 --> 00:03:37,000 Thank you. 9 00:03:37,000 --> 00:03:38,000 All right. 10 00:03:38,000 --> 00:03:40,500 Thanks, everybody, for being here. 11 00:03:40,500 --> 00:03:42,500 Thank you so much for letting us do this. 12 00:03:42,500 --> 00:03:44,500 It means a lot. 13 00:03:44,500 --> 00:03:47,500 You guys know my partner, Rob Hamilton. 14 00:03:47,500 --> 00:03:48,500 Rob Hamilton. 15 00:03:48,500 --> 00:03:49,500 Hello, hello. 16 00:03:49,500 --> 00:03:54,000 Yeah, I also am on the stage every month for the Nashville bit devs. 17 00:03:54,000 --> 00:03:56,500 Unlike the Austin bit devs, we haven't stopped. 18 00:03:56,500 --> 00:03:58,500 And we're going to keep on going. 19 00:03:58,500 --> 00:04:02,980 So most of you guys met me over the last couple days. 20 00:04:03,120 --> 00:04:04,000 I'm Fundamentals. 21 00:04:04,240 --> 00:04:05,740 Brian, it's great. 22 00:04:06,160 --> 00:04:11,600 If you've talked to me, you know right now this is where I want to be talking to you guys. 23 00:04:12,380 --> 00:04:15,000 So, all right, quick show of hands. 24 00:04:16,260 --> 00:04:20,360 How many people think they're really, really bad at math? 25 00:04:23,040 --> 00:04:25,040 Okay, and how many people think they're good at it? 26 00:04:25,040 --> 00:04:35,420 all right okay i'm not judging i don't actually care what your assessment is of yourself and the 27 00:04:35,420 --> 00:04:40,180 the protocol doesn't care either so if you think you're bad at math you can still operate the 28 00:04:40,180 --> 00:04:45,020 protocol you can still do everything we're gonna try to tell you to do maybe just to jump in kind 29 00:04:45,020 --> 00:04:50,420 of we're five episodes in now with the podcast and the whole premise was what if you were always 30 00:04:50,420 --> 00:04:54,200 after a bit devs people go out and grab drinks and stuff and what if it was just two guys at a 31 00:04:54,200 --> 00:05:01,420 bar after bit devs just talking about some of the math behind bitcoin we're not i mean i got a uh 32 00:05:01,420 --> 00:05:08,000 my college degree one of my majors was math but the whole angle of this show is just meeting everyone 33 00:05:08,000 --> 00:05:12,620 where they're at and scale like scaling it down we're going to this a little bit so you could 34 00:05:12,620 --> 00:05:19,180 just start understanding the pieces more yeah exactly and like um you know kind of like what 35 00:05:19,180 --> 00:05:26,780 if we had a sports-like conversation where we just start getting used to, you know, you 36 00:05:26,780 --> 00:05:31,320 don't have to sit down and be frustrated with hard problems. We just got to listen and get 37 00:05:31,320 --> 00:05:36,920 used to the jargon. And when the time comes to, I do believe the time is going to come 38 00:05:36,920 --> 00:05:42,500 in Bitcoin that we need to have a serious mathematical conversation. And when the time 39 00:05:42,500 --> 00:05:47,660 comes, hopefully, my hope is a lot of us are loaded up with at least the language and are 40 00:05:47,660 --> 00:05:54,660 used to talking to each other about it. And that's really what it is we're doing here. 41 00:05:54,660 --> 00:06:01,660 So I have another question. This one might have some audience participation. So do you 42 00:06:01,660 --> 00:06:08,160 know the saying, don't trust, verify? You guys know that, right? How many people believe 43 00:06:08,160 --> 00:06:10,360 that they've verified their Bitcoin? 44 00:06:14,680 --> 00:06:16,320 To your own liking, I'd say. 45 00:06:16,680 --> 00:06:18,460 To your own comfort. 46 00:06:18,480 --> 00:06:19,660 Where you feel good about it. 47 00:06:19,720 --> 00:06:21,320 You feel like I've verified this and we're good. 48 00:06:23,520 --> 00:06:26,160 I'm curious to know if anybody would be willing to... 49 00:06:27,200 --> 00:06:30,360 And I'm not going to address the response, 50 00:06:30,480 --> 00:06:32,360 but I just want to know if anyone's willing to say 51 00:06:32,360 --> 00:06:36,560 or share what they did to get to that point. 52 00:06:36,560 --> 00:06:39,720 anyone willing to just say 53 00:06:39,720 --> 00:06:41,540 this was my 54 00:06:41,540 --> 00:06:43,700 I'll get you a mic 55 00:06:43,700 --> 00:06:45,240 because we're recording this 56 00:06:45,240 --> 00:06:51,580 I verified the UTXO 57 00:06:51,580 --> 00:06:53,180 using my own mempool 58 00:06:53,180 --> 00:06:54,840 running on my own node 59 00:06:54,840 --> 00:06:55,400 alright 60 00:06:55,400 --> 00:06:59,980 yeah thanks for that 61 00:06:59,980 --> 00:07:00,700 I mean that's probably 62 00:07:00,700 --> 00:07:01,520 you know 63 00:07:01,520 --> 00:07:03,840 I'm going to 64 00:07:03,840 --> 00:07:06,780 I'm going to just explain really quick 65 00:07:06,780 --> 00:07:08,480 what my process was 66 00:07:08,480 --> 00:07:10,280 for verifying 67 00:07:10,280 --> 00:07:13,260 and I didn't raise my hand 68 00:07:13,260 --> 00:07:14,940 just for whatever it's worth 69 00:07:14,940 --> 00:07:16,180 and so I want to just share with you 70 00:07:16,180 --> 00:07:17,960 my sense of verification 71 00:07:17,960 --> 00:07:21,420 and that path has me sitting here 72 00:07:21,420 --> 00:07:22,480 talking to you guys right now 73 00:07:22,480 --> 00:07:24,180 so I mean 74 00:07:24,180 --> 00:07:25,980 I think I was like a lot of people 75 00:07:25,980 --> 00:07:27,440 when I got Bitcoin 76 00:07:27,440 --> 00:07:29,700 I read every book I could 77 00:07:29,700 --> 00:07:31,760 and then especially the technical books 78 00:07:31,760 --> 00:07:32,860 like Mastering Bitcoin 79 00:07:32,860 --> 00:07:35,100 programming Bitcoin 80 00:07:35,100 --> 00:07:37,580 but like really the ability to understand 81 00:07:37,580 --> 00:07:39,420 the transactions to know what I was even 82 00:07:39,420 --> 00:07:41,580 looking at on my node in the mempool 83 00:07:41,580 --> 00:07:43,520 going to the 84 00:07:43,520 --> 00:07:44,760 GitHub repo 85 00:07:44,760 --> 00:07:47,400 the GitHub repo really was a big one where 86 00:07:47,400 --> 00:07:49,140 okay this is amazing you see 87 00:07:49,140 --> 00:07:50,440 the formulas 88 00:07:50,440 --> 00:07:52,920 there's the difficulty adjustment 89 00:07:52,920 --> 00:07:55,360 there's the halving 90 00:07:55,360 --> 00:07:56,780 there's 91 00:07:56,780 --> 00:07:59,400 you know it started to click and feel 92 00:07:59,400 --> 00:08:00,720 really good and 93 00:08:00,720 --> 00:08:06,160 Bitcoin was starting to make a lot of sense to me at that point in time. 94 00:08:07,660 --> 00:08:12,900 Then I guess that wasn't enough for me, for whatever it's worth. 95 00:08:12,900 --> 00:08:21,660 And so I started having to look at the cryptography because I was looking at transactions and the transactions make sense. 96 00:08:21,660 --> 00:08:32,040 but how does the Bitcoin stack flip a one when it pairs a signature and a pub key? 97 00:08:32,160 --> 00:08:37,580 So I go to the SEC256P1 website and that GitHub, 98 00:08:38,500 --> 00:08:46,320 and I had a personal existential crisis because I absolutely had no idea what I was looking at. 99 00:08:46,480 --> 00:08:47,900 It's 50,000 lines of code. 100 00:08:47,900 --> 00:08:52,600 what I saw first was just a sea of hard-coded numbers. 101 00:08:53,480 --> 00:08:55,640 It almost looked like wingdings. 102 00:08:56,740 --> 00:08:58,640 I had no idea what I was looking at. 103 00:08:59,340 --> 00:09:02,200 And I already jumped out of the Bitcoin plane. 104 00:09:03,160 --> 00:09:05,320 So this is now like, oh, no. 105 00:09:05,520 --> 00:09:07,020 I'm really now pulling the parachute. 106 00:09:07,320 --> 00:09:08,020 Nothing's happening. 107 00:09:08,220 --> 00:09:12,000 So this was like a serious, serious crisis for me personally. 108 00:09:12,000 --> 00:09:14,860 Because now I'm like, I don't know how to get comfortable. 109 00:09:14,860 --> 00:09:23,000 you know not understanding the cryptography for me would mean testing my bitcoin over and over 110 00:09:23,000 --> 00:09:29,160 again to make sure i can continue to spend it okay which is impractical and you probably shouldn't do 111 00:09:29,160 --> 00:09:37,840 it um so i i bought a cryptography book and then you know started in this massive rabbit hole 112 00:09:37,840 --> 00:09:43,960 at some point in time in that rabbit hole i realized i could probably do a decent job of 113 00:09:43,960 --> 00:09:48,460 trying to explain this to people, and started a math podcast, 114 00:09:49,620 --> 00:09:52,740 which I'm not going to ask for hands, but who thinks starting a math podcast? 115 00:09:52,960 --> 00:09:54,160 Math podcast is psychotic. 116 00:09:57,560 --> 00:10:01,160 So, you know, that's where I am. 117 00:10:01,160 --> 00:10:11,100 I think I might be unique or rare, but I cannot sleep unless I can verify my Bitcoin. 118 00:10:11,100 --> 00:10:15,000 and so that's where we are 119 00:10:15,000 --> 00:10:15,560 is right here 120 00:10:15,560 --> 00:10:18,720 and you may not be in that position 121 00:10:18,720 --> 00:10:21,580 but maybe consider that 122 00:10:21,580 --> 00:10:22,960 you might get there 123 00:10:22,960 --> 00:10:25,520 once you get to wherever you are 124 00:10:25,520 --> 00:10:27,020 you may find yourself 125 00:10:27,020 --> 00:10:29,020 wanting to learn the cryptography 126 00:10:29,020 --> 00:10:31,220 and sort of having a panic attack 127 00:10:31,220 --> 00:10:31,700 like I did 128 00:10:31,700 --> 00:10:35,260 so you might now wonder 129 00:10:35,260 --> 00:10:36,320 what we're looking at back here 130 00:10:36,320 --> 00:10:39,340 this is not just a placemat 131 00:10:39,340 --> 00:10:44,220 I'm thinking we 132 00:10:44,220 --> 00:10:46,560 what I'm going to attempt to do here 133 00:10:46,560 --> 00:10:48,480 what Rob and I are going to attempt to do here today 134 00:10:48,480 --> 00:10:50,900 is actually leave you with 135 00:10:50,900 --> 00:10:52,760 a sense of 136 00:10:52,760 --> 00:10:55,080 how knowing the math 137 00:10:55,080 --> 00:10:55,900 actually 138 00:10:55,900 --> 00:10:59,260 gives you power in understanding 139 00:10:59,260 --> 00:11:00,760 that your Bitcoin is valid 140 00:11:00,760 --> 00:11:02,140 yeah 141 00:11:02,140 --> 00:11:04,180 and jumping in here 142 00:11:04,180 --> 00:11:07,160 for the size of the space 143 00:11:07,160 --> 00:11:08,860 who knows here 144 00:11:08,860 --> 00:11:11,080 roughly how many possible 145 00:11:11,080 --> 00:11:12,920 Bitcoin public 146 00:11:12,920 --> 00:11:14,220 private keys can exist. 147 00:11:14,800 --> 00:11:17,180 Like how many? It's not hundreds. 148 00:11:17,400 --> 00:11:18,540 It's not thousands or millions. 149 00:11:19,420 --> 00:11:21,080 Does anyone have a rough idea? 150 00:11:22,800 --> 00:11:23,060 Yeah. 151 00:11:24,280 --> 00:11:25,260 So it's 152 00:11:25,260 --> 00:11:27,020 said here, there are 153 00:11:27,020 --> 00:11:29,080 more possible Bitcoin 154 00:11:29,080 --> 00:11:31,300 keys than there are atoms 155 00:11:31,300 --> 00:11:32,480 in the universe. 156 00:11:33,100 --> 00:11:34,640 The number is roughly 157 00:11:34,640 --> 00:11:36,940 2 to the 256 power. 158 00:11:37,080 --> 00:11:38,820 So 2 times 2 times 2. 159 00:11:38,860 --> 00:11:46,220 256 times. And that number is so cosmically large, you could almost view having a Bitcoin 160 00:11:46,220 --> 00:11:55,080 private key as a cosmic level on the atomic level needle in a haystack. That's how massive the space 161 00:11:55,080 --> 00:12:00,460 is. And what we're doing here today is instead of being that really massive number, we're just 162 00:12:00,460 --> 00:12:05,760 going to pull it down to the number seven. We're going to use the number seven to explain some of 163 00:12:05,760 --> 00:12:07,580 the basic concepts that are happening here. 164 00:12:08,480 --> 00:12:08,640 Yeah. 165 00:12:09,500 --> 00:12:23,747 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 166 00:12:23,847 --> 00:12:26,407 In fact, you can't even string all the computers in the world together. 167 00:12:26,587 --> 00:12:30,367 It's also not secure because then that pen and paper, the piece of paper then is your private key. 168 00:12:30,447 --> 00:12:31,787 And if someone got that, they could take your money. 169 00:12:31,887 --> 00:12:32,867 So you don't want to do that anyway. 170 00:12:33,547 --> 00:12:33,707 Yeah. 171 00:12:34,647 --> 00:12:38,307 So what we have here is, looks like a bunch of numbers. 172 00:12:38,307 --> 00:12:43,927 So there's two concepts I want to get across today, and I think we're going to be able to do it. 173 00:12:44,747 --> 00:12:46,327 This is a times table. 174 00:12:46,667 --> 00:12:48,167 You guys all learned times table, right? 175 00:12:49,747 --> 00:12:56,307 The times table, you learned, if we took like three times three, you might say nine, okay? 176 00:12:56,607 --> 00:13:04,527 That's like a regular times table in the number system called the real numbers, or a number system called the integers. 177 00:13:05,907 --> 00:13:07,107 Three times three is nine. 178 00:13:08,307 --> 00:13:16,567 In cryptography and in Bitcoin, we use a number system that is more of the remainders. 179 00:13:17,127 --> 00:13:18,507 It's a number system of remainders. 180 00:13:18,507 --> 00:13:21,007 So who remembers doing long division in school? 181 00:13:21,487 --> 00:13:25,707 You remember you would get to the end and you'd have remainder three, remainder seven, whatever it is. 182 00:13:26,227 --> 00:13:27,787 That's what we're talking about here today. 183 00:13:27,787 --> 00:13:38,767 Okay. So when Rob said the number you divide by in Bitcoin is 2 to the 256 minus 2 to the 184 00:13:38,767 --> 00:13:42,407 232 minus 2 to the 16 minus 2 to the 8 minus 16. 185 00:13:42,407 --> 00:13:47,967 Some ungodly number. But in order to understand what it really looks like, we're going to 186 00:13:47,967 --> 00:13:54,487 just use a small number like 7. So let's pretend 7 was the number we divide by in Bitcoin. 187 00:13:54,487 --> 00:13:56,807 Then we would have six private keys possible. 188 00:13:57,267 --> 00:13:57,387 Okay? 189 00:13:57,667 --> 00:13:59,067 One, two, three, four, five, six. 190 00:14:00,067 --> 00:14:04,827 And everything we do here is what's called modulo seven. 191 00:14:05,467 --> 00:14:09,247 Meaning after we divide by seven, we're looking at the remainder. 192 00:14:09,527 --> 00:14:12,187 So, for example, just take the three line. 193 00:14:12,587 --> 00:14:13,707 Three times one is three. 194 00:14:14,107 --> 00:14:14,387 Okay. 195 00:14:15,187 --> 00:14:17,807 Even with a remainder of seven, no change. 196 00:14:18,307 --> 00:14:19,947 Three times two is six. 197 00:14:20,327 --> 00:14:20,527 All right? 198 00:14:21,027 --> 00:14:22,747 Still, we're still probably good. 199 00:14:23,207 --> 00:14:24,467 Here comes the speed bone. 200 00:14:24,487 --> 00:14:26,367 3 times 3 is 2. 201 00:14:26,627 --> 00:14:28,587 What the hell did you just say? 202 00:14:29,367 --> 00:14:34,267 3 times 3 is 9, but then after you divide by 7, the remainder is 2. 203 00:14:35,207 --> 00:14:40,107 We're dividing by 7 in every single cell, and we're taking the remainder. 204 00:14:41,667 --> 00:14:48,547 3 times 3 in a mod 7 system is 2. 205 00:14:48,547 --> 00:14:52,567 3 times 4 206 00:14:52,567 --> 00:14:55,347 now becomes 5 207 00:14:55,347 --> 00:15:01,627 and then 3 times 5 is an interesting one 208 00:15:01,627 --> 00:15:03,667 so 3 times 5 is 15 209 00:15:03,667 --> 00:15:07,067 but dividing by 7, 7 goes into 15 twice 210 00:15:07,067 --> 00:15:09,967 becomes 14 and then you have a remainder of 1 211 00:15:09,967 --> 00:15:12,867 so when you have two numbers 212 00:15:12,867 --> 00:15:16,567 that multiply to 1 in this system 213 00:15:16,567 --> 00:15:19,107 it's similar to in 214 00:15:19,107 --> 00:15:21,447 earth, in real number 215 00:15:21,447 --> 00:15:23,387 earth, when we say 216 00:15:23,387 --> 00:15:25,047 I have the number 5 217 00:15:25,047 --> 00:15:27,067 and I multiply it by 1 fifth 218 00:15:27,067 --> 00:15:28,067 and I get 1 219 00:15:28,067 --> 00:15:31,527 so like in the system 220 00:15:31,527 --> 00:15:33,167 we grew up in, 5 times 1 fifth 221 00:15:33,167 --> 00:15:35,607 equals 1 and those are called inverses 222 00:15:35,607 --> 00:15:36,267 of each other 223 00:15:36,267 --> 00:15:39,027 it's an important concept that 224 00:15:39,027 --> 00:15:40,527 we're going to get to later 225 00:15:40,527 --> 00:15:43,567 so you always want to know that there's a number 226 00:15:43,567 --> 00:15:45,327 there's always a number you can 227 00:15:45,327 --> 00:15:51,967 multiply by to get you to one or essentially to nullify, you know, to nullify the, or like undo 228 00:15:51,967 --> 00:15:57,407 it, the system. Yeah, or undo it. Now in this system, there's only six numbers. One, two, three, 229 00:15:57,507 --> 00:16:03,507 four, five, and six. There's no one fifth, right? There's no one third to multiply by three to get 230 00:16:03,507 --> 00:16:10,507 to one, but there is the number five. So even in our system, we weren't taught this, but the way we 231 00:16:10,507 --> 00:16:12,587 divide is by multiplying, right? 232 00:16:13,027 --> 00:16:14,487 You divide by 233 00:16:14,487 --> 00:16:16,407 five by multiplying by one-fifth. 234 00:16:16,587 --> 00:16:18,567 Well, in this 235 00:16:18,567 --> 00:16:20,147 scenario, you divide by three 236 00:16:20,147 --> 00:16:22,027 by multiplying by five. 237 00:16:22,887 --> 00:16:24,607 And you get what's called your inverse. 238 00:16:24,787 --> 00:16:26,547 Three times five is one 239 00:16:26,547 --> 00:16:27,847 mod seven. 240 00:16:29,187 --> 00:16:30,447 Anything you want to add to that? 241 00:16:30,707 --> 00:16:31,287 No, I think we're good. 242 00:16:31,687 --> 00:16:33,327 We're making good time. 243 00:16:33,987 --> 00:16:36,267 You know, when I'm just sitting around with nothing to do, 244 00:16:36,327 --> 00:16:38,187 I literally create these times... 245 00:16:38,187 --> 00:16:40,507 I just doodle around with these times tables. 246 00:16:40,627 --> 00:16:45,647 It's a useful exercise at these smaller number levels just to get acquainted. 247 00:16:46,507 --> 00:16:50,087 So, you know, you're not going to go run a marathon just because you learn how to move your legs. 248 00:16:50,207 --> 00:16:55,147 But, you know, this is the beginning of, like, the substrate of if you want to get comfortable with this 249 00:16:55,147 --> 00:16:57,587 and really start to learn how this works. 250 00:16:58,207 --> 00:16:59,387 It's a very low effort. 251 00:17:01,047 --> 00:17:03,987 It could be fun exercise that you can do. 252 00:17:05,027 --> 00:17:06,487 So that's the times table. 253 00:17:06,487 --> 00:17:09,807 and the inverse is the one we want to focus on, right? 254 00:17:11,787 --> 00:17:13,807 So back to the question of verifying. 255 00:17:14,467 --> 00:17:16,687 I once asked Rob this on the podcast. 256 00:17:16,807 --> 00:17:21,727 I said, when you went to the Bitcoin store to go buy your Bitcoin, 257 00:17:22,267 --> 00:17:25,667 you probably should have asked to see the manager, okay, 258 00:17:26,607 --> 00:17:34,327 and asked them, how actually do I know that this Bitcoin you're selling me 259 00:17:34,327 --> 00:17:37,047 has a valid private key. 260 00:17:38,767 --> 00:17:39,327 Okay, right? 261 00:17:39,387 --> 00:17:40,007 How do I know? 262 00:17:40,247 --> 00:17:41,227 And I'm pretty sure, 263 00:17:41,427 --> 00:17:43,027 we went through this thought exercise 264 00:17:43,027 --> 00:17:44,327 and actually, 265 00:17:44,567 --> 00:17:45,267 kind of shocking 266 00:17:45,267 --> 00:17:46,867 how few of us probably 267 00:17:46,867 --> 00:17:49,007 even thought this through. 268 00:17:49,147 --> 00:17:50,927 Most of us just hand the money over 269 00:17:50,927 --> 00:17:54,167 and then either we pray 270 00:17:54,167 --> 00:17:55,367 that it hits our wallet 271 00:17:55,367 --> 00:17:56,247 in a valid address 272 00:17:56,247 --> 00:17:57,767 or we just expect it to 273 00:17:57,767 --> 00:17:58,687 and we don't worry, 274 00:17:58,847 --> 00:18:00,027 we don't maybe stress about it. 275 00:18:00,127 --> 00:18:00,507 But like, 276 00:18:01,327 --> 00:18:02,147 very few of us 277 00:18:02,147 --> 00:18:03,467 are actually asking the question, 278 00:18:03,547 --> 00:18:03,967 how do I know 279 00:18:03,967 --> 00:18:10,507 Bitcoin is going to reconcile to a point on the elliptic curve. 280 00:18:11,107 --> 00:18:13,967 Do we need to back up and talk about the elliptic curve? 281 00:18:14,227 --> 00:18:16,687 Very briefly, just for the sake of conversation. 282 00:18:16,847 --> 00:18:23,427 If you remember graphing charts in school, the Bitcoin curve, if this is the y-axis and 283 00:18:23,427 --> 00:18:28,547 this is the x-axis, it basically, and we won't have time to get into it today, you can go 284 00:18:28,547 --> 00:18:33,367 back and listen to our previous episodes if you're interested, basically looks like this. 285 00:18:33,967 --> 00:18:36,967 It's on the back of the postcard that I left on your chair. 286 00:18:36,967 --> 00:18:53,267 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? 287 00:18:53,267 --> 00:18:56,687 and Greg Maxwell and Christian Decker 288 00:18:56,687 --> 00:18:59,227 and many prolific Bitcoin developers 289 00:18:59,227 --> 00:19:01,027 are talking, having a conversation. 290 00:19:01,367 --> 00:19:04,067 And the actual answer is simple and amazing. 291 00:19:04,527 --> 00:19:06,247 It was the one curve at the time 292 00:19:06,247 --> 00:19:09,407 when Satoshi discovered or invented Bitcoin 293 00:19:09,407 --> 00:19:15,447 was the only one that didn't have any weird quirks to it. 294 00:19:15,607 --> 00:19:17,287 So it was the one curve he looked at 295 00:19:17,287 --> 00:19:18,567 and said, this is reasonably secure. 296 00:19:19,207 --> 00:19:20,827 And as one last little addendum, 297 00:19:21,067 --> 00:19:22,707 what tends to happen with these cryptography 298 00:19:22,707 --> 00:19:26,727 the elliptic curves is NIST or someone puts out a standard 299 00:19:26,727 --> 00:19:28,707 and then they do some weird tweaking. 300 00:19:28,927 --> 00:19:31,967 And that weird tweaking allows you to basically backdoor the entire system. 301 00:19:32,587 --> 00:19:35,227 So Satoshi was hypercritical in evaluating the curve. 302 00:19:35,307 --> 00:19:38,447 So he went and did the verification before putting it as the Bitcoin network. 303 00:19:39,127 --> 00:19:42,707 And you can view this curve rather than it being a continuous line, 304 00:19:42,807 --> 00:19:43,847 it's a bunch of points. 305 00:19:44,367 --> 00:19:47,727 And each of those points is a public private key link. 306 00:19:48,487 --> 00:19:49,767 In this case would be six points. 307 00:19:50,167 --> 00:19:51,747 For this curve it would be six points. 308 00:19:51,747 --> 00:20:00,227 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. 309 00:20:00,307 --> 00:20:02,087 And then he shows mod like 17. 310 00:20:02,367 --> 00:20:04,307 Then it starts to fill out a little more. 311 00:20:04,407 --> 00:20:07,467 And then I think he does mod 37 and it starts 36 points. 312 00:20:07,787 --> 00:20:09,247 It really starts to draw out the curve. 313 00:20:09,367 --> 00:20:14,347 Now we're talking about two to the 256 minus – yeah, minus two to the 36. 314 00:20:14,347 --> 00:20:20,107 And so whenever you actually – going to the Bitcoin store ultimately is saying I'm going to give you a point on this curve. 315 00:20:20,107 --> 00:20:22,047 that point is my public key. 316 00:20:22,427 --> 00:20:23,807 And what you're going to do on your side 317 00:20:23,807 --> 00:20:26,547 is you're going to give me some Bitcoin that you hold 318 00:20:26,547 --> 00:20:29,607 and you're going to sign a message with your private key 319 00:20:29,607 --> 00:20:30,727 and give me the Bitcoin. 320 00:20:30,827 --> 00:20:32,467 That's a Bitcoin transaction at the end of the day. 321 00:20:33,547 --> 00:20:37,207 And in case nobody knows this, 322 00:20:37,307 --> 00:20:39,067 your public key, mathematically, 323 00:20:39,567 --> 00:20:46,107 is Bitcoin's generator point times your private key. 324 00:20:46,107 --> 00:20:53,127 So it's the Bitcoin generator point repeatedly added a certain amount of times 325 00:20:53,127 --> 00:20:57,447 And the amount of times is actually whatever the number is on your private key 326 00:20:57,447 --> 00:21:02,587 So the point of cryptography is that it's actually very hard to guess how many times 327 00:21:02,587 --> 00:21:08,347 How many times a generator number was added together to get the public key 328 00:21:08,347 --> 00:21:11,507 It's very hard to go back and figure out your private key 329 00:21:11,507 --> 00:21:13,287 It's actually more than very hard 330 00:21:13,287 --> 00:21:15,487 It's worldly impossible 331 00:21:15,487 --> 00:21:21,507 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. 332 00:21:21,807 --> 00:21:22,707 It's freshly queued. 333 00:21:22,787 --> 00:21:23,867 All of the balls are hit up there. 334 00:21:24,227 --> 00:21:33,367 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. 335 00:21:33,727 --> 00:21:35,967 And then the balls break and they all scatter all over the place. 336 00:21:35,967 --> 00:21:42,067 if you walked over after the ball was hit and you see all of the pool balls sitting everywhere 337 00:21:42,067 --> 00:21:46,887 randomly you would not be able to know oh you must have hit it from this curve at this angle 338 00:21:46,887 --> 00:21:51,127 with this spin you can't reverse engineer that reasonably and that's ultimately when you're 339 00:21:51,127 --> 00:21:54,847 this generator point you're doing these hops that's the shuffling you're doing around but 340 00:21:54,847 --> 00:21:58,567 visually i always like think about it like a pool table if i were to walk over randomly hit it 341 00:21:58,567 --> 00:22:02,887 and then show someone later wherever the balls are sitting like hey that's my that's my public 342 00:22:02,887 --> 00:22:08,347 key send my money to this arrangement and then i'm the only one who knows the exact angle spin 343 00:22:08,347 --> 00:22:13,767 power all of that stuff that went into hitting the thing and that's so right so there's no way 344 00:22:13,767 --> 00:22:22,407 even for yourself to really know that your private key is on that elliptic curve except for the fact 345 00:22:22,407 --> 00:22:29,627 that you're told it okay right so there's no way for you to act to you know this you have a public 346 00:22:29,627 --> 00:22:36,287 key, you kind of want to understand, you want to know your private key sits on that curve. 347 00:22:36,567 --> 00:22:41,567 That's pretty important, right? So then the question is, how do you know and what are we 348 00:22:41,567 --> 00:22:51,467 talking about? And so it just ends up because, so if you do the math, private key times big G, 349 00:22:51,467 --> 00:22:57,347 which is this big generator number that everybody knows what it is, private key times big G is big P, 350 00:22:57,347 --> 00:22:58,607 your public key, right? 351 00:22:58,947 --> 00:23:00,467 So given the public key, 352 00:23:01,487 --> 00:23:05,547 how do you back in algebraically to your private key 353 00:23:05,547 --> 00:23:08,747 is that you have to multiply by the inverse. 354 00:23:09,187 --> 00:23:12,487 Basically, you have to isolate the private key by itself. 355 00:23:12,887 --> 00:23:15,767 So you have to know that it's invertible. 356 00:23:17,347 --> 00:23:19,947 That's why we started with inverses here. 357 00:23:20,527 --> 00:23:22,447 Yes, and so what you see here 358 00:23:22,447 --> 00:23:27,407 in the six-dimensional version of the story 359 00:23:27,407 --> 00:23:29,307 is that every single number, 360 00:23:30,487 --> 00:23:34,327 which is every single point on an elliptic curve mod seven, 361 00:23:34,487 --> 00:23:35,387 which is six points, 362 00:23:35,627 --> 00:23:38,587 every single one of them you can actually see has an inverse. 363 00:23:39,847 --> 00:23:43,267 One times one is one, so one has an inverse, right? 364 00:23:43,267 --> 00:23:46,827 Two times four, remember mod seven, is one. 365 00:23:46,907 --> 00:23:49,747 Two times four is eight divided by seven, remainder one. 366 00:23:49,747 --> 00:24:02,287 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. 367 00:24:02,807 --> 00:24:15,627 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. 368 00:24:15,627 --> 00:24:21,107 but it is a fact that every single point actually has an inverse on this curve. 369 00:24:21,187 --> 00:24:25,287 So as long as you can validate that the public key is a point on the elliptic curve, 370 00:24:26,047 --> 00:24:36,254 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 371 00:24:36,254 --> 00:24:36,614 spent 372 00:24:36,614 --> 00:24:40,354 as far as 373 00:24:40,354 --> 00:24:41,954 we have eight minutes left 374 00:24:41,954 --> 00:24:44,594 I was worried we were going to get to the end of that 375 00:24:44,594 --> 00:24:46,574 yeah you thought we weren't going to get there 376 00:24:46,574 --> 00:24:47,794 so maybe 377 00:24:47,794 --> 00:24:50,174 just as a closing thought here 378 00:24:50,174 --> 00:24:54,014 a version of this is also basically done 379 00:24:54,014 --> 00:24:55,134 when you go to provide a signature 380 00:24:55,134 --> 00:25:00,974 when you have a signature we don't have a slide for today but just to think about this i always 381 00:25:00,974 --> 00:25:06,014 view a bitcoin transaction like a paper check you have a date field you have an amount field 382 00:25:06,014 --> 00:25:10,494 you have a two field you also have a from field my bank account but in this case it's your previous 383 00:25:10,494 --> 00:25:16,214 utxo i can't send you bitcoin unless i already have bitcoin right and then that signature what 384 00:25:16,214 --> 00:25:21,714 it is what what is it actually signing it takes all of that that data on the check and it hashes 385 00:25:21,714 --> 00:25:26,494 it and then you get like this little flag of sig hash you and that's the and that's what gets signed 386 00:25:26,494 --> 00:25:33,514 and when you do the signature you can say ah yes you signed this data and additionally this 387 00:25:33,514 --> 00:25:39,914 signature came from the private key belonging to this public key and that's the really important 388 00:25:39,914 --> 00:25:45,054 distinction for when the network is running a signature verification to verify like it's doing 389 00:25:45,054 --> 00:25:51,054 it's collapsing in large big time space all these operations and it's really a testament to the 390 00:25:51,054 --> 00:25:56,994 quality of the software bitcoin protocol developers like the libsec p library when satoshi 391 00:25:56,994 --> 00:26:02,054 released the original client it was like four or five hundred lines of code and he was importing 392 00:26:02,054 --> 00:26:07,714 from random libraries and what the libsec p project is is bitcoin core's attempt of how do we remove 393 00:26:07,714 --> 00:26:13,654 the dependencies it was using open ssl and how do we make it better more consistent faster more 394 00:26:13,654 --> 00:26:18,194 optimized to better scale the network and then you have the protocol level and then basically that 395 00:26:18,194 --> 00:26:23,134 libsec p library every single hardware wallet imports and just uses that it's like the most 396 00:26:23,134 --> 00:26:27,534 trusted part of the bitcoin code base in the sense of everyone is saying we're keeping an eye on this 397 00:26:27,534 --> 00:26:31,554 and this is actually how all signatures are done and that's like all that core cryptography lives 398 00:26:31,554 --> 00:26:37,194 in one part of the bitcoin code base and then on top of that you have applications right because 399 00:26:37,194 --> 00:26:41,894 most people one aren't using the bitcoin core node to run their wallets you have applications whether 400 00:26:41,894 --> 00:26:47,754 it's a mobile wallet, a desktop app, or even like protocol things like, not protocols, 401 00:26:47,934 --> 00:26:54,854 like toolkits, like Bitcoin dev kit that Steve works on, basically employ a bunch of guard 402 00:26:54,854 --> 00:26:59,994 rails to run these checks for you and know that if you type in an address wrong, they'll 403 00:26:59,994 --> 00:27:01,234 say, hey, this is not a valid address. 404 00:27:01,234 --> 00:27:06,174 Those are all bumpers and guard rails that kind of sit on top of this. 405 00:27:06,774 --> 00:27:10,414 And to make it full circle a little bit, the verification journey, you kept going down 406 00:27:10,414 --> 00:27:10,754 and down. 407 00:27:10,754 --> 00:27:12,854 this is getting close to rock bottom. 408 00:27:13,194 --> 00:27:15,594 What we're talking about is pretty close 409 00:27:15,594 --> 00:27:18,654 as you can get to the foundation of the security 410 00:27:18,654 --> 00:27:19,614 and how Bitcoin works. 411 00:27:20,974 --> 00:27:21,154 Yeah. 412 00:27:22,154 --> 00:27:25,994 So closing thoughts, I think what I'll do with the time left, 413 00:27:26,634 --> 00:27:28,274 I'm going to show the website for a second. 414 00:27:30,674 --> 00:27:34,294 Before I do that, I would say, look, a lot of focus, 415 00:27:34,914 --> 00:27:38,054 a lot of the media focus 416 00:27:38,054 --> 00:27:40,174 or what we think about in the knowledge systems 417 00:27:40,174 --> 00:27:43,334 is centered around Bitcoin Core for good reason. 418 00:27:43,694 --> 00:27:49,254 I would just say don't sleep on the fact that LibSec256K1 419 00:27:49,254 --> 00:27:53,894 is a super important GitHub, and don't sleep on it. 420 00:27:55,054 --> 00:27:59,414 And there's a big world out there of things to worry about 421 00:27:59,414 --> 00:28:00,994 and things to understand. 422 00:28:03,634 --> 00:28:08,294 So I'm going to just talk about magic internet math for a minute, 423 00:28:08,294 --> 00:28:10,634 and then I think we'll do questions. 424 00:28:13,654 --> 00:28:15,674 Magic Internet Math is a site I created 425 00:28:15,674 --> 00:28:19,274 after basically Rob showed me the power. 426 00:28:19,414 --> 00:28:22,734 The power of Claude Code compelled me. 427 00:28:22,894 --> 00:28:25,674 It was over the holiday break, like Christmas time, whatever, 428 00:28:25,814 --> 00:28:26,814 and I was like, you've got to check this out, 429 00:28:26,834 --> 00:28:29,474 which is funny enough, I originally got onto Claude Code 430 00:28:29,474 --> 00:28:32,954 because Michael Goldstein was here at Bitcoin Park in October 431 00:28:32,954 --> 00:28:33,954 and I was catching up with him. 432 00:28:34,134 --> 00:28:34,994 I'm like, oh yeah, I'm using this. 433 00:28:35,094 --> 00:28:36,034 He's like, have you checked out Claude Code? 434 00:28:36,094 --> 00:28:36,574 I was like, no. 435 00:28:36,574 --> 00:28:38,614 He's like, go check it out. 436 00:28:38,754 --> 00:28:41,414 And then two days later, I was like, I can't believe I didn't know this sooner. 437 00:28:41,594 --> 00:28:44,314 And then I had that same version of a conversation with Brian. 438 00:28:44,754 --> 00:28:46,914 Well, Rob really thought he was flexing. 439 00:28:47,014 --> 00:28:50,654 He was showing like he basically said, hey, send me a PDF of your book. 440 00:28:50,734 --> 00:28:53,534 I wrote a book last year called Bitcoin for Institutions, by the way. 441 00:28:53,934 --> 00:28:55,394 But he goes, send me a copy of that book. 442 00:28:56,254 --> 00:28:57,974 And he's like, look at what I could do with it. 443 00:28:57,994 --> 00:29:04,594 And he made the most beautiful like it made like a course on my book with the most beautiful UX. 444 00:29:04,594 --> 00:29:07,054 and I was shocked at how much it understood. 445 00:29:07,134 --> 00:29:07,714 Like 12 minutes. 446 00:29:08,054 --> 00:29:08,274 Yeah. 447 00:29:09,414 --> 00:29:13,494 But my thought wasn't like, oh, what more can I do with my book? 448 00:29:13,574 --> 00:29:16,114 My thought was like, I could do this with any math book? 449 00:29:16,774 --> 00:29:17,574 Are you kidding me? 450 00:29:18,274 --> 00:29:20,194 And I'm a lover of math books. 451 00:29:20,194 --> 00:29:25,594 And I wanted to see all of my beloved math books that I've been through in this format. 452 00:29:25,994 --> 00:29:30,054 And I realized I could create – I can actually create something now. 453 00:29:30,054 --> 00:29:35,054 And so I have a website that has over 100 courses on it, 454 00:29:35,154 --> 00:29:39,734 and they're all mostly math books that I've personally curated. 455 00:29:40,174 --> 00:29:42,434 I haven't been through every single one of them, 456 00:29:42,654 --> 00:29:46,194 but the ones I haven't been through, I know what they do, 457 00:29:46,254 --> 00:29:47,114 and I know why they're there. 458 00:29:48,034 --> 00:29:53,474 You can go from the most basic algebra, like basic, basic, basic beginner algebra. 459 00:29:53,614 --> 00:29:56,074 So if you raised your hand and said you didn't think you were good at math, 460 00:29:56,914 --> 00:29:58,594 you could check out basic algebra. 461 00:29:58,594 --> 00:30:03,074 I have beginner's calculus, which, by the way, is easier than basic algebra. 462 00:30:03,314 --> 00:30:04,554 I'm pretty certain. 463 00:30:05,714 --> 00:30:12,014 So we go as basic as that to all the way up to advanced graduate level cryptography. 464 00:30:12,814 --> 00:30:15,774 You know, abstract algebra, Galois theory. 465 00:30:15,934 --> 00:30:18,634 I mean, I'd say you name it, it's on there. 466 00:30:18,754 --> 00:30:24,294 And then I didn't stop at math books because, you know, why do that? 467 00:30:24,294 --> 00:30:27,134 all of the Austrian economics 468 00:30:27,134 --> 00:30:29,114 sentimental texts are converted 469 00:30:29,114 --> 00:30:30,514 into this format. 470 00:30:31,674 --> 00:30:33,254 When Rob told that 471 00:30:33,254 --> 00:30:35,494 story on the podcast about Hal Finney's 472 00:30:35,494 --> 00:30:37,234 post, I had the idea 473 00:30:37,234 --> 00:30:39,454 to take all of Satoshi's 546 474 00:30:39,454 --> 00:30:40,754 Bitcoin talk posts and 475 00:30:40,754 --> 00:30:43,254 make a class out of it. So now there's 476 00:30:43,254 --> 00:30:45,314 a class out of that and a YouTube 477 00:30:45,314 --> 00:30:47,494 series just on that. 478 00:30:48,414 --> 00:30:49,434 And you figured out how to 479 00:30:49,434 --> 00:30:51,354 make a YouTube series. There's a YouTube series 480 00:30:51,354 --> 00:30:53,134 on how to go essentially 481 00:30:53,134 --> 00:30:56,954 start with the conversation we had here in basic arithmetic 482 00:30:56,954 --> 00:31:00,814 in terms of modular arithmetic and it takes you all the way to 483 00:31:00,814 --> 00:31:04,394 elliptic curve, cryptography, even like Musig and Frost. 484 00:31:07,874 --> 00:31:11,234 So I'm really now 485 00:31:11,234 --> 00:31:14,734 just all in building this magic internet math website. 486 00:31:14,914 --> 00:31:19,554 I'm all in in educating this community 487 00:31:19,554 --> 00:31:22,394 this community and beyond 488 00:31:22,394 --> 00:31:24,974 and I'll be making many more 489 00:31:24,974 --> 00:31:26,794 many more classes I guess the last thing 490 00:31:26,794 --> 00:31:28,994 to mention is the context 491 00:31:28,994 --> 00:31:30,894 of the reason 492 00:31:30,894 --> 00:31:32,594 why I said in the beginning that 493 00:31:32,594 --> 00:31:34,334 your assessment maybe 494 00:31:34,334 --> 00:31:36,714 I'm not judging your assessment 495 00:31:36,714 --> 00:31:38,834 of yourself and math I think most people have a negative 496 00:31:38,834 --> 00:31:40,954 experience of math 497 00:31:40,954 --> 00:31:42,734 because you know 498 00:31:42,734 --> 00:31:44,614 it was like required 499 00:31:44,614 --> 00:31:46,574 it was taught in a mandatory way 500 00:31:46,574 --> 00:31:48,134 and you know 501 00:31:48,134 --> 00:31:52,014 I view math as an art very much as a liberal art, 502 00:31:52,294 --> 00:31:54,294 and I very much want to teach it that way. 503 00:31:54,414 --> 00:32:00,434 And I think we have come together on the podcast of like mind in this. 504 00:32:01,314 --> 00:32:02,694 I would just check out the first episode. 505 00:32:02,914 --> 00:32:05,154 It's called Teaching Math as a Liberal Art. 506 00:32:06,134 --> 00:32:09,974 And the math courses I have are very story-based. 507 00:32:09,974 --> 00:32:13,754 They feel like Greek heroic epics. 508 00:32:14,594 --> 00:32:17,054 You feel like a hero's journey. 509 00:32:17,054 --> 00:32:20,694 I was going to say the one thing I think you and I have in common is we don't like how 510 00:32:20,694 --> 00:32:22,134 math is taught in schools 511 00:32:22,134 --> 00:32:24,234 it's something we both mutually share 512 00:32:24,234 --> 00:32:26,534 I mentioned I got a bachelor's degree in math 513 00:32:26,534 --> 00:32:28,434 I almost failed 7th grade math 514 00:32:28,434 --> 00:32:30,194 so just to understand 515 00:32:30,194 --> 00:32:32,714 the context and the structure 516 00:32:32,714 --> 00:32:33,974 in which and how you learn things 517 00:32:33,974 --> 00:32:36,694 is as important as the actual 518 00:32:36,694 --> 00:32:37,714 content you're learning yourself 519 00:32:37,714 --> 00:32:39,254 and in general 520 00:32:39,254 --> 00:32:42,594 math as a liberal art is something that's definitely lost 521 00:32:42,594 --> 00:32:44,714 it's kind of like do your times tables do this do that 522 00:32:44,714 --> 00:32:45,414 and it's like 523 00:32:45,414 --> 00:32:48,154 math in its own self of pursuit 524 00:32:48,154 --> 00:32:49,854 is its own enriching experience 525 00:32:49,854 --> 00:32:52,154 and it gives you a deep appreciation 526 00:32:52,154 --> 00:32:53,834 for the complexities of life 527 00:32:53,834 --> 00:32:56,494 so with that 528 00:32:56,494 --> 00:32:57,914 we'll open up to questions 529 00:32:57,914 --> 00:33:13,954 what's up Joe 530 00:33:13,954 --> 00:33:21,434 Yeah, the obvious ignorant question here is the math relationship to quantum computing. 531 00:33:22,194 --> 00:33:24,114 And what is that relationship? 532 00:33:24,474 --> 00:33:26,654 And is it valid? 533 00:33:26,914 --> 00:33:29,974 And I know it's trendy and FUD and all that. 534 00:33:30,274 --> 00:33:30,894 It's funny. 535 00:33:31,574 --> 00:33:37,574 Our last episode was about this exactly. 536 00:33:38,214 --> 00:33:38,834 You want to take it first? 537 00:33:38,954 --> 00:33:39,814 I'll go listen to it then. 538 00:33:39,954 --> 00:33:40,794 So, I mean, like. 539 00:33:40,874 --> 00:33:42,034 No, this is. 540 00:33:42,034 --> 00:33:43,314 No, you don't have to listen to it. 541 00:33:43,314 --> 00:33:47,974 question i'm just it's funny because it's timing yeah you should but like you don't have like the 542 00:33:47,974 --> 00:33:52,674 so everything we talked about with this curve and the generator point and like the pool table 543 00:33:52,674 --> 00:34:02,074 the whole idea is that you have something called the discrete log problem that's the big mathematical 544 00:34:02,074 --> 00:34:09,174 concept and what that means in english is that incrementally if i give you a public key 545 00:34:09,174 --> 00:34:17,194 you have no idea where to go is the number is the private key higher or lower i have no idea 546 00:34:17,194 --> 00:34:22,654 and you can't reasonably it's constant randomness like there's no signal anywhere the concept 547 00:34:22,654 --> 00:34:29,854 behind quantum computing is that you're actually able to with a public key over iterations the way 548 00:34:29,854 --> 00:34:34,794 i approximate is like is the number higher or lower higher or lower and to the point where you 549 00:34:34,794 --> 00:34:44,074 could actually walk the whole way backwards right um from a strictly abstract idea like mathematically 550 00:34:44,074 --> 00:34:49,854 it is a threatened concern like just from just from a pure theoretical like no one's actually 551 00:34:49,854 --> 00:34:54,974 been able to ever prove that the bitcoin cryptography that we use is provably secure 552 00:34:54,974 --> 00:35:01,254 it is just so it's that cosmic needle in a haystack size of problem where like your best 553 00:35:01,254 --> 00:35:05,594 chance of being able to get it is guessing every single number, which at that point, 554 00:35:05,694 --> 00:35:12,574 you're better off mining Bitcoin than guessing numbers. For the latest advancements, 555 00:35:13,474 --> 00:35:17,294 I actually tweeted that maybe a day or two ago. I'm keeping a cautious eye out for the latest 556 00:35:17,294 --> 00:35:23,594 Claude models that are coming out later this month, the Claude Opus 5 and Sonnet 5 models. 557 00:35:24,434 --> 00:35:28,234 And I'm saying that because people with Opus, like the current generation models, 558 00:35:28,234 --> 00:35:31,734 I'm not sure if you saw that guy who was able to cure cancer for his dog. 559 00:35:32,914 --> 00:35:40,094 So if Model 4 is curing cancer, what's Model 5 going to do? 560 00:35:40,714 --> 00:35:47,014 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, 561 00:35:47,614 --> 00:35:51,154 then it's a concern, and that's just on a plan to execute. 562 00:35:51,754 --> 00:35:55,714 There are so many problems around the problems that have getting quantum computers. 563 00:35:55,714 --> 00:36:01,614 are they able these run for fractions of a second before they break down and they lose coherence 564 00:36:01,614 --> 00:36:08,794 which is like their ability to sustain compute um additionally you have we've never we're talking 565 00:36:08,794 --> 00:36:12,874 about like numbers we basically are doing is like for these public keys you're factoring you're 566 00:36:12,874 --> 00:36:17,954 trying to basically reverse engineer a really large number a quantum computer has never been 567 00:36:17,954 --> 00:36:24,974 able to factor a number larger than 15 like three times five one times 15 like a quantum computer has 568 00:36:24,974 --> 00:36:30,994 not been able to do that yet so my thesis as it sits right now is even if these new models that 569 00:36:30,994 --> 00:36:35,674 come out are massively expansionary and like start moving things it's still going to be a multi-year 570 00:36:35,674 --> 00:36:50,461 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 571 00:36:50,521 --> 00:36:53,661 And at that point, Blockstream and others have put out research papers 572 00:36:53,661 --> 00:36:55,841 around a new, it'd be a significant change. 573 00:36:55,921 --> 00:36:58,541 It'd be the biggest change Bitcoin has ever had to update Bitcoin 574 00:36:58,541 --> 00:37:00,521 because we're basically taking this entire curve 575 00:37:00,521 --> 00:37:01,861 and everything we just talked about that's been the basis 576 00:37:01,861 --> 00:37:03,381 since Bitcoin started and throwing it out the window. 577 00:37:05,561 --> 00:37:07,801 There is a way, though, to advance. 578 00:37:07,941 --> 00:37:09,621 There are things that quantum computers are not good at 579 00:37:09,621 --> 00:37:12,081 that we would be upgrading our signature mechanisms to. 580 00:37:12,741 --> 00:37:14,581 So all of that to say, I'll let you jump in too, 581 00:37:14,741 --> 00:37:17,961 but as the kids say, I'm monitoring the situation. 582 00:37:18,261 --> 00:37:19,101 That's what I'm doing right now. 583 00:37:20,541 --> 00:37:22,121 Yeah, that's a great answer. 584 00:37:22,121 --> 00:37:26,681 Just because something is FUD doesn't mean there's not a real threat behind it. 585 00:37:28,361 --> 00:37:29,481 It can be both. 586 00:37:31,961 --> 00:37:36,961 A lot of what it makes for good FUD is the fact that 587 00:37:36,961 --> 00:37:40,161 You have a threat that's someday one day. 588 00:37:41,001 --> 00:37:43,101 It's not near today. 589 00:37:43,421 --> 00:37:49,121 But yeah, you can create an industry to basically say, no, it's urgent. 590 00:37:49,261 --> 00:37:50,801 This is urgent to do now. 591 00:37:51,921 --> 00:38:03,721 You know, the real primary purpose for even being here and doing this work is to demystify, 592 00:38:03,721 --> 00:38:16,021 At the very least, demystify the math so that you're not as impressed with the FUD peddlers as they want you to be. 593 00:38:16,841 --> 00:38:22,621 You could be a little bit on to them, and then you can kind of try to think it through for yourself. 594 00:38:23,601 --> 00:38:28,821 I'm about to make a personal time commitment in understanding the quantum thing, 595 00:38:28,821 --> 00:38:34,121 mainly because I speak into a mic and I want to sound like I know what I'm talking about when I 596 00:38:34,121 --> 00:38:41,881 talk about it. I don't think ordinary people necessarily need to do that. I do think this 597 00:38:41,881 --> 00:38:49,841 will clearly be a threat one day in our lifetime. And it's probably not right now, but the time is 598 00:38:49,841 --> 00:38:55,281 now to get used to the language and get used to maybe upgrade yourself a little bit on the math 599 00:38:55,281 --> 00:38:59,441 side so that when it is a conversation, you guys have agency. 600 00:39:05,441 --> 00:39:06,081 Michael. 601 00:39:08,601 --> 00:39:11,221 Follow up on that quantum hot topic. 602 00:39:11,781 --> 00:39:18,441 So my understanding is, though, that the risk is like the P2PK addresses, Satoshi's and 603 00:39:18,441 --> 00:39:18,861 those. 604 00:39:19,401 --> 00:39:24,121 My Bitcoin, it's in a modern address without reuse. 605 00:39:24,121 --> 00:39:25,141 This is what I meant. 606 00:39:25,301 --> 00:39:29,921 My public key is not exposed, so it's a zero-wist to quantum. 607 00:39:30,621 --> 00:39:33,321 So what you're saying, yes, is correct. 608 00:39:33,781 --> 00:39:37,021 So when we talk about you give someone your public key, 609 00:39:37,121 --> 00:39:38,821 what you actually usually give them is your address. 610 00:39:39,081 --> 00:39:42,621 Satoshi's original coins, this was before that format was really widely distributed. 611 00:39:42,801 --> 00:39:45,961 So he has raw public keys that are available that anyone can start stealing. 612 00:39:46,561 --> 00:39:50,441 Additionally, Jameson Lopp has a really great article of address reuse. 613 00:39:50,441 --> 00:39:55,181 so remember when you go to send bitcoin you say oh here's my key that matches this address 614 00:39:55,181 --> 00:39:59,701 so if you reuse an address that is quantum vulnerable because you have to necessarily 615 00:39:59,701 --> 00:40:02,761 put your public key on the blockchain to prove that you owned that address 616 00:40:02,761 --> 00:40:07,041 if i was a quantum attacker and i was trying to go after the biggest bag 617 00:40:07,041 --> 00:40:12,701 assuming that's my goal i would actually go for binance has 300 000 bitcoin in a three of five 618 00:40:12,701 --> 00:40:17,701 multi-sig that they've been using for years so like realistically if they're going to try and 619 00:40:17,701 --> 00:40:20,081 get someone? Are they going to try and get your UTXO 620 00:40:20,081 --> 00:40:21,741 that has never been seen before, which is 621 00:40:21,741 --> 00:40:23,361 complicated, or are they going to try and go for that? 622 00:40:23,661 --> 00:40:25,601 The one thing I would caveat is that if 623 00:40:25,601 --> 00:40:27,841 anyone has ever seen your output descriptor, 624 00:40:28,301 --> 00:40:29,801 has like your wallet config file, 625 00:40:30,001 --> 00:40:31,081 all of the data, 626 00:40:31,721 --> 00:40:33,701 that information has 627 00:40:33,701 --> 00:40:35,701 your public key in it. So that's just like for 628 00:40:35,701 --> 00:40:37,401 your own awareness. We always say that like 629 00:40:37,401 --> 00:40:39,721 your output descriptor, your wallet information 630 00:40:39,721 --> 00:40:40,661 is 631 00:40:40,661 --> 00:40:43,701 privacy losing because someone could see 632 00:40:43,701 --> 00:40:45,701 your addresses, but they can't take your money. 633 00:40:46,161 --> 00:40:47,681 In the case of a quantum computer, 634 00:40:47,701 --> 00:40:49,321 that then becomes they also could take your money. 635 00:40:50,821 --> 00:40:53,021 Yeah, and so this is actually a good question 636 00:40:53,021 --> 00:40:54,781 because it brings up, I think, 637 00:40:54,841 --> 00:40:55,921 probably the most important thing 638 00:40:55,921 --> 00:40:57,981 an ordinary person can do. 639 00:41:00,401 --> 00:41:03,281 The way you assess risk is in two dimensions, 640 00:41:03,601 --> 00:41:06,141 frequency and severity, okay? 641 00:41:06,521 --> 00:41:11,821 And the mathematical side of quantum 642 00:41:11,821 --> 00:41:15,341 is breaking what's called Shor's algorithm 643 00:41:15,341 --> 00:41:17,241 for your private key 644 00:41:17,241 --> 00:41:20,501 or breaking Grover's algorithm for the hash function? 645 00:41:22,621 --> 00:41:24,701 That's a yes-no, right? 646 00:41:24,801 --> 00:41:26,001 So can they be cracked? 647 00:41:26,461 --> 00:41:27,901 Yes or no, right? 648 00:41:28,561 --> 00:41:31,161 Then there's a magnitude sort of severity question, 649 00:41:31,241 --> 00:41:32,981 which is like, what's the order of operations? 650 00:41:33,141 --> 00:41:36,401 What are the easiest, most vulnerable? 651 00:41:36,841 --> 00:41:38,481 Taking Satoshis are the easiest ones. 652 00:41:38,861 --> 00:41:41,021 You could lift 100 Bitcoin 653 00:41:41,021 --> 00:41:45,041 and a couple hundred Bitcoin a week move from that Satoshi era. 654 00:41:45,041 --> 00:41:54,081 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. 655 00:41:54,801 --> 00:42:02,721 So anywhere you can see a public key, a quantum computer theoretically that can break Shor's algorithm can find the private key. 656 00:42:03,301 --> 00:42:05,161 And it's like four million coins or – 657 00:42:05,161 --> 00:42:14,301 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? 658 00:42:15,041 --> 00:42:18,961 made i thought oh yeah that's right satoshi himself has like one to one and a half million 659 00:42:18,961 --> 00:42:23,281 and then there's a couple yeah so there's like a couple there's a couple million yeah p2pk yeah 660 00:42:23,281 --> 00:42:28,981 um just a fun historical application with cryptography in world war ii um everyone was 661 00:42:28,981 --> 00:42:32,801 like alan turing and the turing machine and reverse engineering the germans encryption 662 00:42:32,801 --> 00:42:40,821 does anyone know what they did when they managed to crack enigma and they didn't use it they 663 00:42:40,821 --> 00:42:42,561 intentionally let ships sink. 664 00:42:43,421 --> 00:42:44,861 They allied 665 00:42:44,861 --> 00:42:46,961 troops and ships died 666 00:42:46,961 --> 00:42:48,681 and ships sank because they 667 00:42:48,681 --> 00:42:50,761 realized that if they had 668 00:42:50,761 --> 00:42:52,621 let everyone know that they had cracked it, 669 00:42:52,721 --> 00:42:54,841 they would lose the strategic asymmetry in using 670 00:42:54,841 --> 00:42:56,781 it. So my personal thesis too 671 00:42:56,781 --> 00:42:58,661 is that if a quantum computer becomes valuable, 672 00:42:58,961 --> 00:43:00,261 as valuable as Bitcoin is, 673 00:43:00,661 --> 00:43:02,581 for the US government to be able to reverse engineer 674 00:43:02,581 --> 00:43:04,061 and know all of China's decryption, 675 00:43:04,641 --> 00:43:06,501 likewise too, if China was able to 676 00:43:06,501 --> 00:43:08,641 break encryption, do you think they want to start 677 00:43:08,641 --> 00:43:10,541 moving? Bitcoin may very well be 678 00:43:10,541 --> 00:43:13,661 since it's so public, maybe one of the last things to fall. 679 00:43:14,641 --> 00:43:18,921 Because if you're a state actor, it's infinitely more valuable 680 00:43:18,921 --> 00:43:22,561 to try and break literally anything else 681 00:43:22,561 --> 00:43:26,081 in other people's security systems than to try, 682 00:43:26,201 --> 00:43:27,461 even just to continue eavesdropping. 683 00:43:27,521 --> 00:43:28,961 Because the moment you show your hand that you know it, 684 00:43:28,981 --> 00:43:30,501 people will update and change their encryption. 685 00:43:31,561 --> 00:43:32,761 Let's do one more question. 686 00:43:32,981 --> 00:43:33,121 Yep. 687 00:43:33,601 --> 00:43:36,021 I said one question a little closer to home 688 00:43:36,021 --> 00:43:38,381 in terms of risk factors for most people. 689 00:43:38,661 --> 00:43:40,501 And I don't know if this falls into your math, 690 00:43:40,541 --> 00:43:41,981 any of your math studies, 691 00:43:42,461 --> 00:43:44,661 but the actual randomness 692 00:43:44,661 --> 00:43:47,061 that is used to pick your key 693 00:43:47,061 --> 00:43:50,241 has been the most common attack on Bitcoin. 694 00:43:50,761 --> 00:43:51,701 It's happened a lot. 695 00:43:51,901 --> 00:43:53,301 Yes, no, this is actually really important. 696 00:43:53,441 --> 00:43:54,701 So we were talking about how you have 697 00:43:54,701 --> 00:43:57,261 this whole cosmic universe of anything in the world 698 00:43:57,261 --> 00:43:59,561 that you're, across the entire universe, 699 00:43:59,701 --> 00:44:00,521 picking a single atom. 700 00:44:01,001 --> 00:44:02,261 If you use really bad entropy, 701 00:44:02,961 --> 00:44:06,861 it'd be like, oh, it's somewhere in this room. 702 00:44:07,461 --> 00:44:09,301 And now you've taken the entire universe 703 00:44:09,301 --> 00:44:11,081 and just made it this one little space. 704 00:44:11,501 --> 00:44:13,781 And then you can easily just go through atom by atom 705 00:44:13,781 --> 00:44:15,581 and just like guess everything, right? 706 00:44:16,041 --> 00:44:19,621 So entropy and how you actually start your secret, 707 00:44:19,781 --> 00:44:21,081 if you're familiar with your seed phrases, 708 00:44:21,241 --> 00:44:22,941 each word is actually a bit of entropy. 709 00:44:23,581 --> 00:44:24,801 And they all kind of tie together 710 00:44:24,801 --> 00:44:27,721 to be able to make your master seed phrase, 711 00:44:28,041 --> 00:44:30,021 which then generates all of your child keys. 712 00:44:30,841 --> 00:44:33,101 Entropy is critically important 713 00:44:33,101 --> 00:44:34,501 because that's what allows you to have 714 00:44:34,501 --> 00:44:37,561 the whole universe on your side. 715 00:44:37,561 --> 00:44:39,661 if you don't do that 716 00:44:39,661 --> 00:44:41,421 or people used to do these things called brain wallets 717 00:44:41,421 --> 00:44:43,781 where you could take a poem and make that a Bitcoin key 718 00:44:43,781 --> 00:44:45,981 or you could take a song name and whatever 719 00:44:45,981 --> 00:44:48,701 and then you make it such a narrow search space 720 00:44:48,701 --> 00:44:53,781 that computers can in an hour get trillions of random addresses 721 00:44:53,781 --> 00:44:55,361 that they could just sit there and look at and wait to go. 722 00:44:55,481 --> 00:44:58,661 You're right, that is the most common way people mess up their security. 723 00:44:58,841 --> 00:45:00,541 It's not the actual architecture in the system. 724 00:45:01,361 --> 00:45:05,321 You as a user of Bitcoin, even if you don't understand this stuff, 725 00:45:05,321 --> 00:45:10,941 you're walking through the door using these tools and the one thing that's in your control 726 00:45:10,941 --> 00:45:14,421 the most important thing that's in your i'll say the most important thing that's in your control 727 00:45:14,421 --> 00:45:19,341 is getting good entropy and that's a whole conversation in its own right for sure i'll 728 00:45:19,341 --> 00:45:25,241 just add um it's just kind of incidental um rob and i talk about this all the time that um 729 00:45:25,241 --> 00:45:32,761 we don't have coins anymore but like when i grew up because i'm old i grew up with coins 730 00:45:32,761 --> 00:45:37,721 and we used to flip coins and develop a sense of probability 731 00:45:37,721 --> 00:45:39,341 just from flipping coins. 732 00:45:41,481 --> 00:45:45,741 It's one of the great crimes of removing coins from circulation 733 00:45:45,741 --> 00:45:50,241 is we actually have lost our sense of risk and randomness, 734 00:45:50,241 --> 00:45:51,621 I think, in a certain way 735 00:45:51,621 --> 00:45:53,981 because we don't actually have coins to flip around, right? 736 00:45:55,081 --> 00:45:55,361 Tails. 737 00:45:57,361 --> 00:45:57,961 Tails. 738 00:45:59,401 --> 00:46:00,621 Well, I didn't tell you what heads and tails was. 739 00:46:00,701 --> 00:46:00,901 Bitcoin. 740 00:46:02,761 --> 00:46:03,761 There you go. 741 00:46:05,241 --> 00:46:16,701 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? 742 00:46:16,901 --> 00:46:17,221 Totally. 743 00:46:17,501 --> 00:46:19,101 Getting a sense for how rare that is. 744 00:46:19,721 --> 00:46:23,381 It's good to develop that sense for yourself so that you kind of understand. 745 00:46:23,481 --> 00:46:27,341 I think a lot of people don't even know what it means to make sure you have entropy. 746 00:46:29,101 --> 00:46:29,561 Thank you. 747 00:46:29,621 --> 00:46:30,101 Oh, thank you. 748 00:46:30,441 --> 00:46:32,101 Carl, you got anything for these guys? 749 00:46:32,761 --> 00:46:42,341 he stepped out okay seriously i love how autistic you guys are uh you guys are amazing huge round 750 00:46:42,341 --> 00:46:56,361 of applause for these guys um to brian's point if you love like an area like he loves math rob 751 00:46:56,361 --> 00:47:03,501 loves podcasts. So just do what you love and just like continue to go down those rabbit holes and so 752 00:47:03,501 --> 00:47:08,861 on. So this basically concludes grassroots Bitcoin. I don't really have some like amazing 753 00:47:08,861 --> 00:47:13,941 way to conclude it. I know. Oh, I know we could sleep here if you guys want to. No, I'm just 754 00:47:13,941 --> 00:47:18,961 joking. But Renata had a good idea. Whoever wants to opt in just to do a quick photo outside, 755 00:47:19,201 --> 00:47:23,741 we can all just get on the area outside and someone could take a photo of all of us. 756 00:47:23,741 --> 00:47:27,701 it is my hope you guys establish at least one new connection 757 00:47:27,701 --> 00:47:32,041 one new idea maybe one new podcast rob i don't know 758 00:47:32,041 --> 00:47:36,141 but i just want to say deep down thank you on behalf of andrew 759 00:47:36,141 --> 00:47:39,661 jack the rest of the bitcoin park team for you guys to spend time here 760 00:47:39,661 --> 00:47:42,861 thank you to unchained thank you to feddy thank you to bid key 761 00:47:42,861 --> 00:47:47,361 and then one thing just to jam with me and maybe 762 00:47:47,361 --> 00:47:51,941 in our new feddy community chat actually maybe we sunset the signal group even 763 00:47:51,941 --> 00:47:57,161 though it's easy and do that fetty check because I want to get some survey of next year's date 764 00:47:57,161 --> 00:48:03,081 and new ideas for next year. For example, would it be cool to have like, we're not going away from 765 00:48:03,081 --> 00:48:07,101 the lightning presentations because like I love those. So I'm going to selfishly do that. But if 766 00:48:07,101 --> 00:48:11,801 there's other ideas on like, hey, it would be cool to have this type of speaker cancel Wesley. He 767 00:48:11,801 --> 00:48:17,881 sucks. Like do other things like that. Like we could, oh, sorry, Wesley's here. Okay. Uh, but no, 768 00:48:17,881 --> 00:48:26,341 other things like that um would love love feedback uh as well cool all right thank you 769 00:48:26,341 --> 00:48:29,381 guys we'll meet outside whoever wants to opt in for a photo cheers 770 00:48:47,881 --> 00:48:56,361 Thank you.