Fundamentals. @Fundamentals21m
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AverageGary
npub160t5zfxalddaccdc7xx30sentwa5lrr3rq4rtm38x99ynf8t0vwsvzyjc9
Dr. Peyam Youtube
https://www.youtube.com/c/drpeyam
BIP340
https://github.com/bitcoin/bips/tree/master/bip-0340
In this episode, we dive into the world of mathematics and cryptography, exploring the nuances of teaching and learning math as an art form. We discuss the importance of passionate educators and the impact they have on students, drawing parallels between teaching and creative expression. The conversation touches on the struggles of learning complex subjects, like math, and the joy that can be found in understanding and mastering them. We also highlight the role of coding in appreciating math as an art and the satisfaction that comes from solving complex problems through code.
We further explore the intricacies of cryptographic protocols, focusing on Schnorr signatures and their advantages over ECDSA, particularly in the context of multisignature schemes. The discussion delves into the technical aspects of Schnorr's linearity and closure properties, and how protocols like Frost and Musig enhance its functionality. We also touch on the broader implications of cryptography in ensuring privacy and sovereignty, emphasizing the need for a deeper understanding of math to fully grasp these concepts. The episode concludes with reflections on the importance of local collaboration and the potential for Bitcoin to drive hyper-localization in cryptographic practices.
[00:00:26]
Unknown:
It is all good. Hey, Gary. How you doing? Hello, fundamentals. How are you? Oh, pretty good. Pretty good, my friend. Another week of math. You know? We just keep doing it. Not really sure. You know? So, like, I do it every day, and I'm not really sure why sometimes. But we just do it because we know we're supposed to.
[00:00:46] Unknown:
I looked at Schnorr signatures again today. That's good. That's good. And I was,
[00:00:53] Unknown:
you know, continue to be inspired reading the mathematicians lament, and that continues to, just really shine a lot of just shine a lot of light for me. It's just good to know that that guy the guy that wrote it Do you feel like you're lamenting? Like Yeah. I do. And I feel very privileged to have some of the, teachers that I'm that, like, that my kids have had because, you know, we the way that the teachers breaks down how shitty most teachers have to be. It's exceptional. It's more it's like a gift. You know? It's like a it's a creative art in itself just to figure out how to be somebody somebody who could effectively teach an art and who'd care enough like, who cares enough about their students to even want to do that?
[00:01:46] Unknown:
Yeah. I think that's that's interesting because, I actually lived with a couple teachers when I when I was stationed in Hawaii, and they were very clearly teachers, for because of passion. Right? Like, they enjoyed Yeah. They they wanted they felt compelled deep down in them to to do this thing. And it was, you know, not ideal conditions that they were teaching in. But I think most people do go into teaching for those reasons. Most people do, but I've met some people that, like, you meet whoever it is, and it's just a job. Like, they just end up winning. That's what that's what it becomes Ugh. Clearly pretty quickly.
[00:02:25] Unknown:
You know, I I was gonna I was gonna mention a little bit just my, you know, my oldest daughter's a math major, and Mhmm. She's starting to deal with, like, literally the joy of the like, not being able to find the joy because something she's finally hit something that's so hard, and it's run into the pressure of, like, she's afraid of failing class, and she's grinding really hard to get through it. And I know she will. It's just that the joy is gone. And, so that's, like, where my listening, I don't know. Like, that's the thing I can listen for. Like, I can it's the first time I've seen it, like, since she's, like, nine years old. Like, it's the first time I've seen the joy gone.
[00:03:10] Unknown:
Because what she was doing is so difficult.
[00:03:13] Unknown:
It's just be I guess wherever she is in the grind and the need to succeed. Right? And the prioritization of that has displaced the has displaced the ability to access joy. And so the my the only, my only follow-up to that is that there is this, there's this YouTube professor that I do recommend people checking out because this guy is this unbelievably autistic Indian guy named doctor Payam. I don't like him in the show. Okay. P e y a m. And it's like, this dude exudes joy in teaching math. And it's just like, watch you just watch one video, and you just feel like, holy crap. Like, what a time to be alive with this dude. It Interesting.
Like, he's one yeah. It's just, he has no idea pro like, he he occurs like he has no idea. He's online, and he just makes it he he just is love of the game. He's like Freddie Mercury. Like, if Freddie Mercury were a math teacher.
[00:04:22] Unknown:
Yeah. Alright.
[00:04:24] Unknown:
So I that's the thing I had to tell my daughter. I'm like, you need doctor Pam. You go go back, get online, and go watch one of his videos, would you, and understand what this is all about.
[00:04:35] Unknown:
I'll commit to watching one of his videos for you.
[00:04:38] Unknown:
Yeah. Just Yeah. I'll link it to I'll link it in the shoutouts.
[00:04:42] Unknown:
That I mean, I think that's what, that's what I hope for a return to, though. Right? It's like the educator like, people educating about a topic, subject, what have you need to have that passion, because otherwise, it's you get captured.
[00:04:57] Unknown:
It's also the I mean, and it goes back to connecting to the fact that it's an art, and it's a creative art. It's an you know, math is a deep creative art. It's a long, you know, like that this is I'm almost quoting the book right now, but, like, it's a long Go do I. Well, I was thinking of reading a passage from it. I'm not sure if you really wanna do that, but, I mean, I won't be reading it. I have a paragraph here. Listen to it. Mathematics is an art, and art should be taught by working artists. Or if not, at least by people who appreciate the art form and can recognize it when they see it. It is not necessary that you learn music from a professional composer, but would you want yourself or your child to be taught by someone who doesn't even play an instrument and has never listened to a piece of music in their lives?
Would you accept as an art teacher someone who's never picked up a pencil or step foot in a museum? Why is it that we accept math teachers who have never produced an original piece of mathematics, know nothing of the history and philosophy of the subject, nothing about recent developments, nothing in fact beyond what they are expected to present to their unfortunate students. What kind of a teacher is that? How can someone teach something that they themselves don't do?
[00:06:23] Unknown:
I think that's I mean, that's just like in general. It that's interesting. That makes me think about, I've always been sort of, like, anti college. Not like anti college, but it was never for me, and it always seemed like a waste of time and money. And I I can't remember where it was, but I heard, it's like those that can't do teach or something along those lines applied to, like, college professors. Oh, it's when I was going in this when I was looking at, like, software stuff because there's this there's, like, this, like, this stark difference between sort of the education that you get in a computer science degree where it's, like, the same guy see teaching the same, like, things. And, don't get me wrong. Some of it is, like, very, very fundamental and foundational for computer science stuff.
But a lot of, like, the practices, techniques, and languages even that were used in, like, your comp sci courses were not applicable in the modern world. And it's like, there's two things to it. One is, like, it's a factor of just how fast technology moves, but then also it's a factor of, like, it's people that are not doing software development anymore. They just have this curriculum that they've they've, you know, been teaching for a decade, and they just, like, continue to do it. But they're not doing the thing. They're not creating. They you know, maybe at one point they were, but, they they are no longer.
[00:07:46] Unknown:
It goes back to reducing an art to, like, the thing that goes on the medium. Like, so for math, you're reducing it to computation. For pottery, we're reducing it to the ashtray. Right? It it's, which is what people who have no appreciation for the art in positions of educating people will do. Right? They they don't even know any better.
[00:08:09] Unknown:
Yeah. And I think the art the, like, the art is taking what's in your mind, though, and and putting it onto the medium. And, like, the the medium is in in and of itself is not the art, but it's the representation of the idea that is the art. And and in order for your mind to go to some place to create something new, artistic, and beautiful, you you kinda have to have it in your mind.
[00:08:33] Unknown:
Yeah. Computer science can be is an is a beautiful like, a it is, like, actually really a beautiful pursuit, and I've seen some of just the most elegant expression of ideas. Like, almost it's like almost can't believe that human beings can articulate themselves in code sometimes. Like, when I see, and it it you know? Yes. I'm impressed when certain things can be reduced to the smaller lines of code through ideas. Like, that does impress me. But it's more of, like, how's you know, like, the ways what somebody had to think in order to make a leap that enabled them to do that. And then some of the most one of the most satisfying things that I've ever experienced in my life is having an idea about how to abstract code and pull off something I know no one's ever thought of and then see it work, which if you don't code, you actually can't do it. And so, like, you can appreciate math as the art that it is, but if you I also truly believe you must code.
It's just like you can be a pottery, but if you don't do it, you still have to make the ashtray. Right? You don't express you don't get to express yourself Yeah. Unless you actually do it and see it in the world. And so it's both of those things. And, you know, we talk about it in Bitcoin, like, having the physical being attached to the metaphysical. And I think that's probably the best generalization. You you know, with math, you have to do it whether it's with a pen and pencil or behind a computer. But, like, the art of computer science to me, like, if you study discrete math, it is it can be absolutely beautiful.
[00:10:18] Unknown:
And is is is that because the function of a computer is to expand the the computing capabilities of humans? Right? So it's like humans can think of ideas in math, but, like, I mean, public private key cryptography is one of those things. Right? Like, we don't you can do it by hand,
[00:10:38] Unknown:
but we don't. You can. But, I mean, you know, like, like, you can and you should sometimes. We actually do. I'm pretty sure there are, like, paper wallets, and we do do these things sometimes. Yeah. And but it's more for, like, you know, at the very least, use a computer for prototyping your ideas. You know? Ask yourself if you understand an idea. At least, like, when I go through a math book, a lot of times, I'm also building a library of code to test whether or not I'm actually able to I'd really understand this stuff. That sounds useful. So, like, all the things we went through with the Euclidean algorithm and the Euler's function, I've, like, I've built my own libraries of code to do those things. They're very clunky. When I go online and ask for versions of the Euclidean algorithm, I see one line of code, and I can't believe somebody thought to do it that way. Mine's, like, 50 lines. You know? Well yeah. Yeah.
But but I am but you can see more of how I think if you look at my I I actually, I I do have a git I think out out of this, in out of this, I should be also using the GitHub to show, you know, show my code for these things. I think that would that might be helpful for people. But Yep. That is how you show how you think. And and when I managed I managed math PhDs. I'm not a math PhD, but I managed I managed them regularly throughout my career. And reading their code is how I see how they think. It's how I actually can assess whether or not they're even thinking.
[00:12:23] Unknown:
Right. That's interesting. Yeah. I never can say because everybody it's like it's its own style. There's a there's a million ways to skin a cat.
[00:12:33] Unknown:
Right. But you can tell if some you could really it's it's the way to communicate with somebody, and it's the way you actually can see how someone's thinking just by seeing their thought process. It's not that there's one right way. It's actually great that I'm not that I'm not an accomplished, like, mathematician or a coder because I don't I don't have dogmas about how it's supposed to look. So I can just look at somebody and say, are you actually commune are you actually communicating a struggle? And, like, do I see it, you know, do I see it in your code, like, that you're trying to solve a struggle? Like, you're actually trying to solve a problem.
And you've attacked it a certain way. Right? And now it's like now in this day and age, if you're managing somebody like that, you're gonna wanna be able to assess whether or not they're thinking, especially now because they are gonna have AI generate their code, and that's prob that might be fine. But you're gonna wanna tell you still wanna know you still wanna know if they're thinking.
[00:13:29] Unknown:
That that you actually brought up what was on my mind about this whole, like, vibe coding thing that everybody's talking about where it's like you just you just talk, like, they turn on, and I've done this. It's it's it's it's surprisingly works well. Like, I don't it's not perfect by any means, but you can turn on, like, dictation on your computer. And then, like, I hit a key twice, and it turns on like, it starts listening, and it starts right typing it all out. And so I just sit here, and you can just talk to it and, like, go back and forth.
But it's not it's not necessarily like, it's you're you're giving it, like, higher level ideas and maybe some details on, like, the implementation of how you would like it to be done, but you're not actually conveying it in the code.
[00:14:22] Unknown:
There's a place for that shit. There is. Yeah. There's a place for it. And you know what else? There is also a place for really struggling to make your code work, like, struggling with like, the people that I find who have understood what they were doing the best and have with the best at what they do, A lot of it is because they sat there with, like, literally one line that said, like, fucking a equals three, print a, and a prints something other than three, and they sit there pulling their freaking hair out Yeah. Yeah. Trying to figure out what the hell. And it's like that, you know, that struggle. As Yeah. So, like Yeah. Yeah. Which Well, even that struggle though is That is actually work. Right? That's the actual and work is how you get good at life. Yeah. Right? But, you know, the ability to get through that struggle and to understand not like, oh, this is something I just shouldn't do because it doesn't make sense. It's more that this is like, okay. I know my you know, it's pretty useful in those moments to know your math is good so that you're not questioning that, and then you're just like, oh, I'm just having a I don't know what's going on making this code work. I don't get it.
[00:15:33] Unknown:
Yeah. Right?
[00:15:35] Unknown:
Yeah. You know what I'm talking about because you're an implementer. That is just you know, that is, like, the in my mind, the core struggle. Right? Absolutely. Yeah. If you're wondering if you feel like that you don't know like, if you feel that you have some type of inferiority complex around math, you're gonna have a hard time getting through those moments. He's like, that's why so, you know, having the math down enables you to take those moments and just focus on
[00:16:04] Unknown:
pushing through, and that's what building Yeah. Because otherwise, you have to side quest to go like, oh, well, like, this Euclidean algorithm, like, is this is this right? Does this work? How does it how does it know? And then it also goes to, though, you know, we're all we're building on the shoulders of giants. So it's it's like a balance, man. It's it's always I always go back and forth. Right? Because there's there's the there's the, I don't know what you call it, the implementer. Right? So it's like doing doing the thing. And I don't know if this is a lower high time preference idea, but it's like, you know, how what is the what is the trade off? Right? There's no solutions. There's only trade offs. So it's like, what is the trade offs with having it all nailed down versus knowing how it works, validating that it works, and then having some reference point to touch on Yeah. For a working implementation.
[00:17:05] Unknown:
And I I I think you want you wanna have it all. It's like if you think that the see, the the risk is you take the you think the implementation is the object of the game. And it's like another quote. I I think it's the opening quote of the mathematicians lament. Literally, the opening quote says, if I wanna build a boat, instead of finding a bunch of people who understand how to hammer and nails, just train a bunch of people that yearn to be at sea. Yeah. Okay. Yep.
[00:17:35] Unknown:
I butchered that, but you get the No. Yeah. And I've heard I've heard that quote before. Not quiz. Yeah. It's yeah.
[00:17:43] Unknown:
Yeah. You get but but but but you must know the fundamentals of what you're doing. Right? You can't just hire you can't just bring a bunch of dreamers who think they can ignore the, you know, the underpinnings. Right? Right. Right. Right. So that's and I think it's a good that it's the struggle. That's the struggle. Right? The and we talked about this last week with the generalists. The generalist lament. Right? Specialists versus gen I mean, you just you know, the thing is you I what's it's going to take longer doing it the right way, and that's where the time your your time preference comes in. If you don't have the time preference, I don't I I don't like moralizing it. But I'd I one of the reasons I like time preference because it's it's a trade off. It doesn't moralize it. It just says, you know what? If you want it, you know, if you want an ashtray, if you want you you know, you can make one. Right? It's kinda like if I, you know, if I take an obese person and they wanna lose weight, I'm like, I can cut off one of your legs.
Right. And we can get that, you know, we can get the job done. Weight down. Yeah. Yeah. Yes. We can get the job done more as opposed to, you know, am I building something great? That just takes a lower time preference and be and it's slower. It's just slower because you really need to be you have at least toll gates, which is like, am I doing the right thing all the way that need to be governed? Yeah. Okay. Right? And so the the so I think coding, right, and particularly cryptography, maybe not so much the kind of cryptography that protects your passwords, but the type of cryptography that protects value.
[00:19:27] Unknown:
How are they different?
[00:19:28] Unknown:
Because I think when they protect value, it is, that we have skin in the game. It matters more. It just, you know, it just matters. I think it just matters a lot more.
[00:19:43] Unknown:
Yeah. I guess in my mind, I was getting very pedantic of, like, well, I mean, your passwords are some somehow protecting some amount of value.
[00:19:50] Unknown:
I I get it. But, like, it's just, you know, when it's being used to protect value, It meant it in my opinion value is it protecting? Right? That that's the other question. In in well, in some ways, it matters more because it's now costly to it's costly to, like, replicate and attack. When you're just protecting a password, right, you can probably you can print a lot of money and attack this thing a lot easier than if it's protecting value. And it's, you know, so it it has to be slower. It has to be slower, and that's this is I mean, maybe the whole my my entire, like, life's work right now around math is trying to convince people that this thing matters because of what we're actually you know, because of what we're protecting matters so much that, you know, we might have gone through life not thinking it really mattered
[00:20:47] Unknown:
to So what is the what is the
[00:20:50] Unknown:
yearn for the sea here? Like, what is the what what is the yearn for, when it comes to motivating the math? Right? Like, what is the It's true. It's the true, sovereignty promise. The sovereignty. Yeah. That's the prompt the the you know, which the sovereignty associated with being able to protect value behind cryptography, behind and cryptography is just a shallow word for, like, a human being's ability to keep his own secret. And that appeals to people because it's something people are capable of doing, presumably. Right?
It seems to be something Yeah. It's not. Like, it's something you get almost endowed by God, like an ability to just keep your own secret. But you've never but the ability to truly protect your value and protect, you know, to protect, sorry, to protect value behind it, you know, and the the the sovereignty promise that that offers and that we've seen a a history of humanity suffer under the inability to do that.
[00:21:51] Unknown:
When when you say I mean, in in the idea of keeping our own secrets too, that that that in and of itself is privacy. Right? Like, it's the the ability to selectively reveal oneself.
[00:22:02] Unknown:
That is It's literally that of the the word ability. You know? It's Yeah. The ability to do that because we don't you know, that's not like, it's not endowed. You have to ongoingly, claim it and exercise it. It's not something you just have that static forever. You have to it's something that you have to Right. Actively,
[00:22:27] Unknown:
What's the whole concept of rights are are taken and defended? They're not they're not given. But free speech is actively
[00:22:34] Unknown:
actively you no one gives it to you. Right. You defend it ongoingly forever, and this is you know, maybe this is an extension of free speech. Yeah. But you like, in order to keep a secret, it takes active like, a lifetime of eternal vigilance and active work. Right? And I guess I'm here to say that I think that leveling up in math is gonna be an essential part of that. I don't think you're gonna make it. I think some people maybe are special enough that will, but most people need to upgrade their math ability to be to be that sovereign and to really see this dream. I, you know, I got infected by the dream. You know, my whatever I got into Bitcoin, I got infected by all the dreaming.
[00:23:16] Unknown:
Yeah. Well, there it it gives you there's an escape hatch. Right? Like, there's this this parallel system that is and this is something that keeps myself motivated on a number of fronts is, like, there is there is greatness to be had in this new world on a Bitcoin standard. And with how early we are in it, the the things, the initiatives, the the projects that we create have the potential of of going in perpetuity.
[00:23:50] Unknown:
Right? They do. But I I see people sell that dream out so easily. Yeah. It hurts. And sometimes there's this risk of demoralization where it's like, oh my god. No one's really gonna wanna do this. And I know better. I know it's possible. And I know that, you know, sort of maintaining that dream and commitment is of vital importance. But I do see pea it is discouraging to see people so easily give up on that dream. Right? Because I think most people see it. And then some people like, well, it's not practical. I can't really. It's not, you know, it's too hard. Blah blah blah. And I I and so then I think, like, well, maybe it's only too hard because you don't have the skills. You just there's certain core skills you don't have. And so Yeah.
There's a lot of people that say you need to be more fit to keep a secret, and I think they'd be right. Maybe some people would say you need to read a lot to keep a secret, and I think they'd be right. You need to But, yeah, no but nobody's gonna do all the things. Right? And that's the that's the no solutions, only trade offs. Right? Like, there's not I don't see anybody telling people you need to level up in math, and I'm I believe that's Yeah. So that's why that's why I that's what I that's who I see myself as in the world.
[00:25:05] Unknown:
Well and and I and I wonder too, like, what does, you know, if it's if it's just us and Dan and April that that continue this motivation on math, is that sufficient? Like, what is the what is the critical mass of of of people that need, you know, mathematical sovereignty? Acknowledging that we will not like, acknowledging that no matter how much you might motivate, there there are just gonna there's a huge group of people out there that will just delegate everything. It doesn't have to be everybody.
[00:25:41] Unknown:
Yeah. It only has to be people who yearn to be free, and that's probably gonna be a small minority of people anyway, but it's enough.
[00:25:48] Unknown:
Well, Well, this to me, this is the same question of, like, the whole, like, not your keys, not your coin thing. Right? Like, there's there's there's some people I know that just, like, no way in hell that they will ever have the desire, to to hold their own keys. And if they did, they would they would flub it completely. I mean yeah. But I I
[00:26:06] Unknown:
I did okay. Look. I'm sympathetic to that argument. But I see if you take any one of those people and you hand them a circumstance Mhmm. There is I say there exists a circumstance where that will be untrue. There exists a situation if they, you know, somebody if, you know, all of a sudden the bank steals all their fucking money, they're gonna they they are going to flip. So it's a think all of those people just have not income encountered the use case. Right? They Well, and, also, I think the They live in the illusion. They, you know, they continue to live in the illusion that their money is safe, and,
[00:26:47] Unknown:
they don't get it. And that's When I think I think also in in my mind when I made the statement, and and I wanna correct it, and probably in your mind, like, you were thinking of, like, an adult. And I think that's probably the misconception here is because, you know, once you're in adulthood and you're developed and everything, there's not a lot of people with the neuroplasticity to sort of, like, adjust their worldviews and stuff. And that's more and more people have. Don't get me wrong. Buy that either. I think that well, I think the fund like, I think that, like, the next generation
[00:27:15] Unknown:
As a 50 year old, I don't that I don't who you know? How many in your peer group, though? Now or or three years ago?
[00:27:25] Unknown:
Sure. Yeah. I mean, it Okay. Okay. Alright. I'll concede yeah. I'll see that. Yeah. Yeah. But what I was getting at is more of, like, the, having it a fundamental curriculum.
[00:27:37] Unknown:
Oh, and by the way, not to just not to interrupt you from Yeah. But neuroplasticity, if, first of all, if anyone if we really buy into what that means. Okay. Let's assume that this neuroplasticity argument is true. Spending a couple hours in the morning doing math, I think, is a is likely a great way to, ensure ensure that you have the neuroplasticity to do anything you want.
[00:28:06] Unknown:
That's good. Interesting. I wonder, like, I the the idea just jumped in my mind, so I'm gonna say it out loud. I think about, like, those daily calendars that you'd like to peel off calendars. Yeah. And it's like there should be, you know, the the fundamentals of cryptography daily calendar of, like, a math problem to to solve. And I imagine something like that might already exist, but it's it's an idea.
[00:28:31] Unknown:
Yeah. That's cool. I would just like a daily calendar that just says, don't quit. Just keep going.
[00:28:38] Unknown:
Don't quit. That's it. Like, you can request the one message. Over and over again. It's just the same message. That's probably Fundamentals will call will will find your brain
[00:28:47] Unknown:
and fuck you up if you quit.
[00:28:51] Unknown:
That sounds really aggressive.
[00:28:56] Unknown:
Don't do that. Don't get demoralized.
[00:28:59] Unknown:
I didn't. I looked at snore signatures this morning. So I didn't do math. I didn't do any math by hand, but I I did I did ask about snore signatures and that sort of, like, their linearity property.
[00:29:14] Unknown:
And then You know, I'd feel better about Schnorr signatures if it didn't have such a goofy name. What do you wanna call them? I don't know. I I I don't know. I'm gonna I accept it. I I I do accept it. Okay. It's like, it's kinda like I was saying yesterday, like, the name Lutnick does not inspire confidence and, like, the name, like, Lutnick is like the kind of guy that gets splashed by a cab who gets you know, every day, the second he walks by this puddle, a cab just splashes him with water.
[00:29:43] Unknown:
Okay.
[00:29:45] Unknown:
But I'll accept Schnorr for what it is.
[00:29:48] Unknown:
The signature is as defined in BIP three forty, which just rolls off the tongue.
[00:29:54] Unknown:
Yeah. BIP three forty. And, you know, one of these days I one of these days, I'm gonna commit to going through this BIP. It's right here. Something that I like, before I got into a math rabbit hole Yeah. I was, I used to just pair print out the BIPs and go through them character by character. I did it with all the lighting, the bolts up to 11. And, Really? Yeah. So, like, right literally all the fields mapping together. Like, it was Yeah. You know, commitment to understand these things. So three forty was never something that was on my in my radar nowadays.
[00:30:28] Unknown:
You should definitely do it because there's, like, a wall of numbers at one point, and there's a bunch of math equations.
[00:30:36] Unknown:
I love the thing you said the, the set p GitHub that you sent me that was written in Python. Did you go through that one? I scanned through it. I think that would be a cool thing for us to, do together potentially with crew with a group.
[00:30:52] Unknown:
Well, in the code review. Like a like a code like a code review. Yeah. Yeah. Yeah. Well, in the the the implementation, right, was, like, experimentation, education, and prototyping. And that that education piece just stuck out to me. I was like, oh, this like, I need to send this fundamentals because Very cool.
[00:31:08] Unknown:
Yes. This is this is it. If I had seen this first and not the other one, I might not be here.
[00:31:14] Unknown:
Well, that's kind of a that's a big assertion.
[00:31:17] Unknown:
I'm just saying I might not have panicked and decided I needed to learn all this math two and a half years ago or when
[00:31:24] Unknown:
Well, I'm glad that you did, first of all. I would have been like, oh, this is the answer. Okay. No problem. I get this. Okay. One end of end of finalize, it's it's it's titled sec p two fifty six k one lab, and that's the organization name and the repository name. And it just has, like, low level sec p k one field and group arithmetic,
[00:31:45] Unknown:
which is, like, things we've been talking about. I'm just kidding. Be not to beat a dead horse.
[00:31:49] Unknown:
Beat it away.
[00:31:51] Unknown:
It's through validation that you realize you don't you find the thing you don't have the aptitude for or you don't the current aptitude for it. Oh, yeah. Failure is the best way to success. And that you know? And so I'm pretty sure I would have found myself here regardless one way or the other.
[00:32:07] Unknown:
Yeah. Like, failure repeated failures, how do you get to ultimate success? So alright. But there's snore shining and verification according to BIP three forty, so you could get the BIP out and go directly into this. And then it lift elliptic curve, DV helmet key exchange Yes. Which is important for other math that I'm into, like blinded signatures.
[00:32:33] Unknown:
And here's a question. Here's a question, I guess, you I'll ask you to sit with. Okay. If we had started with Schnorr, would it ever even matter? Would would there ever be a reason to have to learn ECDSA? If we just started with Schnorr, is it even, you know, is it even relevant? It Schnorr feels like a much a more general it's just a question to sit with. Is that, like, would we even if Schnorr was there first, would we even would anybody even know what ECDSA is? Does it add Probably probably did not. Does it add any like, that's so it's just a question I would say Yeah. Does it add anything to, like, the corpus of knowledge?
Because Schnorr feels like the answer we always wanted to get to.
[00:33:21] Unknown:
Yeah. But there was stupid intellectual property things.
[00:33:24] Unknown:
It's just anyway anyway, it's just stuff I like to sit with.
[00:33:28] Unknown:
Yeah. I mean, I don't I don't think it would be a yeah. Just off the cuff, it seems like nothing that would be widely like, what other unless you were into, like, security research. Right? Like, the info infosec
[00:33:41] Unknown:
information. I mean, this is a different type of elliptic curve signature. It's a different formula. Right? Yeah. But I'm saying I mean, it's just because it doesn't it doesn't call itself elliptic curve digital signature algorithm. It it is a elliptic curve digital signature algorithm. You know? Yeah. It it is that. So I guess that maybe that's the thing I will will put a pin in. So let's so what do you have in mind here?
[00:34:11] Unknown:
Just we we talked, you had made the observation that because of the way that you can do, batch verification and, like, these the the multisignature
[00:34:24] Unknown:
things. That it's closed under the it's like closed like, it's like the group axiom. It's closed under the operation of the signature. That's what we that's what we had observed the last time, and then we were like, okay. Is that is it does that mean is, you know, is it a group? Right? Is it Yeah. Is that what it did? Does it is it, like, literally leveraging the properties of a group to
[00:34:49] Unknown:
be more, you know, to be as powerful as it is? And and the answer that at least reading through this made sense was, like, it depends
[00:34:58] Unknown:
sort of thing. That's, like, pretty cool. So it's not a no. Yeah. It's it's not it's it's the because it did feel that way. And then I, you know, I I hear about, this nomenclature in Monero called ring signature, which maybe I've I've heard of that as well. Yeah. Something worth looking into as well. Well, what's a ring? Right? Yep. Like, I never thought about it. I never associated the word ring with the algebraic structure until
[00:35:23] Unknown:
recently. Right? Until, like Oh, yeah. Yeah. Okay.
[00:35:27] Unknown:
Right? And but that's it seems as though maybe it's very similar. I mean, ring is this is is just a, slightly, modified version of a group, right, where you have addition and multiplication. You have all the group properties for addition, not necessarily for multiplication.
[00:35:44] Unknown:
Yeah. But, like, what is the what is the key contextual piece that makes something a ring?
[00:35:50] Unknown:
Close well, so closed under, you know, all the group axioms under addition. Mhmm. And then it's also closed under multiplication and associative under multiplication, and thereby you have the distributed property. That is what make that is, like, the technical definition of a rank.
[00:36:08] Unknown:
Right. So I wonder maybe we should look at those signatures to, like, understand what that is. Because in this one, the, like, the ultimate conclusion was it's not necessarily it's not closed under not not generally, like, closed under group, but with, like, certain conditions. And that that's where these, like, multisignature protocols. So it's you're basically putting additional constraints on it to get something that is
[00:36:40] Unknown:
close like, has closure. Yeah. So that's what the tech so the technique act
[00:36:45] Unknown:
The the technique of Schnorr Schnorr itself
[00:36:48] Unknown:
doesn't have this property, but it it the techniques of Musig and Frost are able to somehow manipulate them in a way to make them groups so that they can have these so that they can be used in this way. Is that correct?
[00:37:05] Unknown:
I believe so. Yes. Yeah. Yeah. It's it's only under controlled settings. So, like, you have to, like, put additional, like, guardrails, which that's the that was one of the things of, like, the group itself is is, like, you have to define it as what the real was it real numbers or whatever? Or there's, like, a certain it's it's all about setting the definition of what the box is that you're operating within Yeah. Yeah. For saying if this is a group or not.
[00:37:32] Unknown:
Right. And, like, as in, like, specifying the operation. Yeah. Okay. I think what I'm I think what you are referring to is when we talked about the integers, the set of integers under, like, multiplications, not a group, but it is under addition. Because under addition, you have an the identity elements there with zero and you have an inverse, which is the integer minus, you know, plus the negative of the, you know, the negative of that number is the inverse. Whereas the multiplication, you don't have that because you would need a fraction to multiply back to the identity.
Right. Right. Right. Yeah. That was yeah. That's that's that specification. But I think it's interesting that Schnorr in and of itself may not be actually what's useful. Schnorr, you Well, let's talk about it. By Musig or Frost.
[00:38:22] Unknown:
Well and it's not it's not even that. Like, the Musig and the the Multisig protocols is, like, it offers closure, but it's not, like, a general group closure for, like, all of the signatures.
[00:38:36] Unknown:
Okay. I think I'm gonna have to really read this spec. The spec is are are you in bit is this what I'm looking at? Three BIP three forty, or is it well, there's a yeah. There's a few I think this is an article that This is BIP three forty. But I will send you Yeah. Okay. Yeah. I will send I will send all these things. When I'm looking at, there are headings like group closure. Yeah. And that's not in the BIP. No. No. No. No. Yeah. Not at all.
[00:39:03] Unknown:
But, yeah, it's it's worth it. And there's this this Aline Tamescu, which I don't know. It was something that came up in in the search, but it was titled shore signatures, everything you wanted to know but were afraid to ask. And it goes into, like, batch verification and some other things. It also goes into some, like, mistakes that you can make, like pitfalls, which I think are some of these are pretty common, like reusing nonces, which again allow you to, like, mathematically back up Yep. Back out of a signature into a private key.
[00:39:34] Unknown:
Universal a universal law, it seems, do not reuse nonces.
[00:39:40] Unknown:
Yes. Oh, and look at that. Look at the you you in the conclusion of this, it says why you should prefer Schnorr over ECDSA. So it could even, potentially ask, you know, it it sort of summarizing the findings, as to why.
[00:39:57] Unknown:
So You wanna just provide a a highlight of what they're saying? Just
[00:40:03] Unknown:
Yeah. It's, I guess, I didn't read this part. I just literally just saw the link as we were discussing it. So, one is the threshold is thresholdizable, it says, which that's an interesting thing. Weird word. You well, it you can't do threshold signatures. Right? So frost is a threshold variation using Schnorr, but you can't do that with eCDSA because you don't have the linearity to combine the different
[00:40:28] Unknown:
pieces. So threshold meaning
[00:40:32] Unknown:
Threshold meaning Multi sig.
[00:40:34] Unknown:
A number of have it being able to set a number of Yes. That are needed.
[00:40:39] Unknown:
Three out of five multi sig sort of thing or two out of three or x or t out of m is just how I've often seen it displayed.
[00:40:48] Unknown:
And I think isn't the re so Schnorr is presents a multisig as make makes it look identical to o single sig because of this closure. Right? Because the signature is the signature itself is closed under the operation of addition, whereas in ECDSA, the signature itself is not. And so you have to you have to show all three SIGs in the and then list them in the pub key. Whereas what you see under snore, it seems it looks like it looks identical to a single SIG because that's what it because it has closure. Right?
[00:41:32] Unknown:
Yeah. Yeah. Yeah. Because you end up with another point on the same cur like, you end up Yeah. Still within the same Like, a signature plus a signature is another something is a signature. Correct. Yes. Yes. True in ECDSA.
[00:41:45] Unknown:
Yeah. And that goes into the whole, like, batch verification thing. A point plus a point is a the points have closure, but the signature does not. That was an under e under ECDSA. Right? The points are a group are an abelian group. Right? So they a point plus a point is a point.
[00:42:03] Unknown:
Yes. But when you put it through the signature algorithm is not does not have that property.
[00:42:08] Unknown:
In Schnorr, it does. That's what and that that's really well, that's why it looks like a single sig. Well, that's the linearity piece of it is That's called that they're called that's otherwise known as linearity. Right? Yeah. That makes sense. I would say otherwise known as closure under the operation of, you know, the signature is closed has closure under the operation of addition. The same way the point does.
[00:42:36] Unknown:
Right. Right. Right. Yeah. Right. Because you can you can combine the things and still stay within the thing. But once again, in ECDSA,
[00:42:43] Unknown:
the signature does not have that property. Yeah. Right? So you have this clunky you have to list them all out. It's not that it's clunky. It's that it docks as the purpose. You don't get to Schnorr has the very powerful ability to abstract the fact that you're using a multisig. It's really powerful. I mean, you know, a multisig is, much less secure if somebody finds a key and knows it's part of the multisig.
[00:43:15] Unknown:
Right? Well and it's interesting though because there there's, like, again, no no solutions, only trade offs though. Because to a certain degree, though, if I'm making a signature with a quorum of people, maybe I do wanna know, like, okay. Who didn't sign? Sure. Or who didn't participate? Or if there were some sort of can do that. Malfeasance.
[00:43:35] Unknown:
You're you're nothing's stopping like, nothing's stopping somebody from doing from displaying those things. Maybe you don't have to display it to the to the whole chain, though, potentially. Right? Right. Right. Yeah. You don't have to let the world know.
[00:43:50] Unknown:
That's true. That's true. Yeah. It would be it would be sort of out of band from, it it'd be in the signing protocol, not in the actual Bitcoin protocol where Docking docksing lightning.
[00:44:02] Unknown:
Sorry. Doxing lightning channels because, you know, two zero two multisig is clearly is, you know, almost always gonna be a lightning channel. So you don't snore abstracts that so that you don't dox a lightning channel. But, also, I mean yeah. I mean, the the key if if if a person if an attacker doesn't know it's in a multisig, then, you know, it's it's a world of difference than if they do.
[00:44:33] Unknown:
You know? Yeah. It's it's the fog of war. Right? Like, in in the event of an attacker, the fog of war is, is this a single sig? Is this multi sig? You know, if I'm even if I'm going to hit you with a $5 well, it's a $15 wrench now. But a $15 wrench attack, even if I show up at your house, if I see that you have some multisig set up on chain, now I know how many keys I'm looking for. That's right. And if I show up, and I have no, I mean, I have no idea how many keys I'm looking for, there's some plausible deniability there,
[00:45:05] Unknown:
where maybe If you don't know that if you think your mission is over, right, and that you just hit a dead end Yeah. Yeah. And even if you don't like, let's say you're smart and you're like, I'm this isn't working. I know this is a multisig. You better, you know he doesn't know what the quorum is. He doesn't know if it's two or three, a three or five. He doesn't know how he doesn't know what he doesn't know. That's the that's the key. You don't know what you When the other the other interesting thing that I just thought of is there's, like, a way
[00:45:39] Unknown:
so in, like, a frost quorum, you can add additional keys to to the quorum, like, using math. You're you're just, like, finding additional points, but that doesn't invalidate all the previous, key shares that you used. Right? So or the keys. Right? So if you had, like, a three out of five and then all of a sudden, you know, you get you get robbed or whatever. I I wonder about just like, you know, two of your key or your your three keys are are taken of your five or whatever, but maybe you still have the data, to add additional keys. And so you can't change the threshold, but you can change, like, the the keys that are valid within the threshold.
And so you can make it like a three six or three seven or three of eight. And now it's a race between you and the attacker to go, like, sign and broadcast something. Something that just came to mind. So, like, let's not, let's not quote me on that. You still need all the x bugs and all that to be able to use do you still need all That's what I'm not concrete on. Yeah. I think you're you're gonna need there's, like, a certain level of knowledge that you still need because you're you're essentially you're you're adding I I I don't wanna say it the wrong way, but in my mind, I wanna say you're adding another coefficient to, like, the polynomial that is the the the frost quorum.
[00:47:07] Unknown:
Right. And I don't know if those are the right words. Asking. Yeah. And I have a question that I guess it's good to have your own questions when you go through these things so that you know what you're searching. You know, you have the location to search for. My other question would be, how does it know it's easy to in the ECDSA, you it's easy to know the answer to the question, what is the quorum? How do you and, you know, in Schnorr, how does how does it know what the quorum actually is?
[00:47:34] Unknown:
Well, to be clear, it's Schnorr is not Schnorr is just a signature algorithm. Right. In the transact what I'm saying is Frost is the threshold quorum. The like, these are two distinct things. So that's
[00:47:46] Unknown:
What's that? That's right. So that's maybe that's also why, like, Schnorr in and of itself is just a signature, but Frost is the is the is the implementation of it. Like, where in a transaction, hex would I see the quorum itself? Or maybe you don't like, how how would one maybe you just that that's the whole key. You don't see it from the you don't see it publicly. But how would one know?
[00:48:14] Unknown:
For
[00:48:15] Unknown:
the you're talking about in the quorum? If you're using, yeah, you're using schnorr, you're using, you know, you've put a multi you put a two or three together with frost. Mhmm.
[00:48:26] Unknown:
That that's all done by the people doing the signing. It's not it's not visible on chain at all.
[00:48:33] Unknown:
I we I don't I don't know. Like, I've been These are my bosses. A long time. Yeah. Yeah. If we're gonna do, like, a code review or a BIP review Yeah. Yeah. With, people that in our audience that wanna do that, those would be some of my motivating questions to try to figure out.
[00:48:49] Unknown:
Well, in the You know? Definitely. I definitely and I don't know. I we need I I I think the next thing I'll do is I'll go and dive into Frost to see because there's a certain way of basically taking the different keys existing keys that can be used for creating snore signatures, like different s c, sec p keys, and then combining them to create this, like, shared key
[00:49:27] Unknown:
sort of thing. I feel like I need another an another base 58 class that does it on that
[00:49:34] Unknown:
uses Like, just
[00:49:36] Unknown:
oh, interesting. You know? Because that's every most of what I learned was through doing the base 58 transactions class. Yeah. Yeah. Yeah. Yeah. At least that's where I got my base. No pun intended.
[00:49:49] Unknown:
Oh, here it is. This is okay. So this is a good one from from the I see a picture of Andrew Polster. Yeah. Blackstream's glossary, Frost flexible round optimization or signature threshold signatures is a protocol that minimizes number of rounds of communication between participants in a signature scheme. So Frost is a way of, like, in the rounds or, like, how how much back and forth we have to do between us if we're doing signatures together. And so frost is is, like, way of doing that in a very, very, it well, it says maximum three rounds for signing. So So you just okay. So the actual exercise of doing the signing is now also different. So it's a different Yes. User experience. That's what I'm saying. You could you on your own with a single key can just do a Schnorr signature. Right? You don't need anybody else's participation.
Right. But if you wanna do these multisignature or threshold signature things, then you have to coordinate the mathematics and the nonces and all these other things. You have to coordinate them all together with all participants. Well, if if you're doing this in a trust minimized way, right, because I don't necessarily like, we're we're dealing with, you know, 10,000 Bitcoin in this wallet. Well, you don't want me to screw you over and somehow sweep the coins myself. So Frost is is a is a communication protocol for sort of doing a snore signature together with other people.
Right? And it does it in this, you know, minimal rounds of train like, because the more and this is a general thing in cryptography of interactive versus noninteractive.
[00:51:30] Unknown:
Yeah.
[00:51:31] Unknown:
So, like, for instance, the Bitcoin cryptography in Bitcoin is, like, noninteractive. Right? You can just you can just validate it all on your own. You do all the signature validation, everything like that. You don't need to talk to necessarily anybody else. You just need to get the data. Right? But, you know, Frost in this instance is an interact or Moosig is an interactive protocol where two parties have to communicate to exchange data, and there's sort of these rounds that happen, and each rounds have its own, like, state along the way. Uh-huh. And if you're not following a specific protocol, you know, there's a way to sort of, like, maliciously
[00:52:14] Unknown:
use certain numbers or or nonces or anything like that. In the middle attack piece. I mean and then, you know, I'm curious, curious about also, like, how MiniScript would work in this context as well. And I think that's I think this is separate. MiniScript is For multi six. I'm if it's but they're not maybe they're not using Schnorr.
[00:52:37] Unknown:
I think MiniScript is more of, like, templating for a transaction. Right? So you have, like, a MiniScript for a type of transaction, and maybe that transaction is a a multisig, like, a two out of three multisig using, your standard ECDSA
[00:52:51] Unknown:
signatures or something, and that would be like a template. Yeah. So they're not and they're not they're not using this math.
[00:52:57] Unknown:
No. Not necessarily. No. It it's it MiniScript is more for the scripting aspect of Bitcoin transactions and less so for the how the signature is accomplished. So the implications of the mathematical
[00:53:08] Unknown:
breakthrough we're using here is just that a little bit of the procedure need now needs to be, managed.
[00:53:17] Unknown:
Yeah. Yeah. Right? Yep. Well, as so before the price of extraction
[00:53:21] Unknown:
is having more, maybe, it's more of the signers involvement, it seems.
[00:53:27] Unknown:
Yeah. Definitely. Because I get you know, before you could do a presigned or partially signed Bitcoin transaction where it's like a multisig and you're, like, passing this thing around. But I know like, I can give this to you, this PSBT. I can give a multisig PSBT to you with my signature already done. That's right. And you can just do your signature then and then broadcast it. Right? And everything's fine and dandy. Feels the way God intended it in some ways. But if we're doing if we're doing a frost signature or music's music signature Mhmm. At the time of the signature generation, we need to be coordinating and communicating. And that's what it that's what it refers to in these rounds of communication.
Mhmm. It's like how many times do we need to do, like, an exchange of data to finalize a signature?
[00:54:10] Unknown:
Interesting. It feels like the environment just needs to be managed the whole way.
[00:54:15] Unknown:
Yeah. And you also have to you know, if you're thinking closed literally
[00:54:19] Unknown:
like, closed doesn't just mean the math. Closed also means the entire environment that it's all being done in.
[00:54:28] Unknown:
Yes and no. Like, there that's that's one of the things. Right? Because I mean, the dev environment. I just mean the gen as a general word. Yeah. Yeah. Well, if you're doing things in a close like, if you and I go into a secure bank vault room, you know Mhmm. SCIF facility, whatever, and do key stuff, that is a lot easier. But the assumption, at least my understanding of the assumptions made with, like, Frost and Musig is, the communication may or may not, like, may or may not be public. Right? Like, you you have this, like Yeah. You have other parties involved. Right? Like, you you are involved, and you're not a part you're not me. So there's there's this, like So it's a it's more of a local versus global thing now. It's more of a local, like, the
[00:55:16] Unknown:
this multi six scheme, things need to happen locally before it goes on the global chain. Yeah. Yeah. Before it's a sort of broadcast and living in the global world.
[00:55:27] Unknown:
I totally agree.
[00:55:29] Unknown:
Also kinda cool. It feels like it feels like that is just another way of human beings want wanting to be, you know Well, and I think tool privacy tool, potentially.
[00:55:40] Unknown:
Well, and one of my within groups. Absolutely.
[00:55:42] Unknown:
Groups of people. Sorry. Not that.
[00:55:45] Unknown:
Yeah. Is it an billion group of people or it's a Bitcoin or group of people. This is, I mean, this is just this is almost like reaffirming my ongoing thesis of, like, the the hyper localization that Bitcoin is going to drive forward because you're you're gonna wanna do these key ceremonies.
[00:56:04] Unknown:
Yeah. Pre broadcast. It's like once you broadcast, you're out in the wild. But before you can do more before you broadcast, that's local.
[00:56:11] Unknown:
Yeah. Support local Bitcoin or sign sign sign local. Screw buy local. Sign local. You know? Thanks, everybody. Couple of do songs.
It is all good. Hey, Gary. How you doing? Hello, fundamentals. How are you? Oh, pretty good. Pretty good, my friend. Another week of math. You know? We just keep doing it. Not really sure. You know? So, like, I do it every day, and I'm not really sure why sometimes. But we just do it because we know we're supposed to.
[00:00:46] Unknown:
I looked at Schnorr signatures again today. That's good. That's good. And I was,
[00:00:53] Unknown:
you know, continue to be inspired reading the mathematicians lament, and that continues to, just really shine a lot of just shine a lot of light for me. It's just good to know that that guy the guy that wrote it Do you feel like you're lamenting? Like Yeah. I do. And I feel very privileged to have some of the, teachers that I'm that, like, that my kids have had because, you know, we the way that the teachers breaks down how shitty most teachers have to be. It's exceptional. It's more it's like a gift. You know? It's like a it's a creative art in itself just to figure out how to be somebody somebody who could effectively teach an art and who'd care enough like, who cares enough about their students to even want to do that?
[00:01:46] Unknown:
Yeah. I think that's that's interesting because, I actually lived with a couple teachers when I when I was stationed in Hawaii, and they were very clearly teachers, for because of passion. Right? Like, they enjoyed Yeah. They they wanted they felt compelled deep down in them to to do this thing. And it was, you know, not ideal conditions that they were teaching in. But I think most people do go into teaching for those reasons. Most people do, but I've met some people that, like, you meet whoever it is, and it's just a job. Like, they just end up winning. That's what that's what it becomes Ugh. Clearly pretty quickly.
[00:02:25] Unknown:
You know, I I was gonna I was gonna mention a little bit just my, you know, my oldest daughter's a math major, and Mhmm. She's starting to deal with, like, literally the joy of the like, not being able to find the joy because something she's finally hit something that's so hard, and it's run into the pressure of, like, she's afraid of failing class, and she's grinding really hard to get through it. And I know she will. It's just that the joy is gone. And, so that's, like, where my listening, I don't know. Like, that's the thing I can listen for. Like, I can it's the first time I've seen it, like, since she's, like, nine years old. Like, it's the first time I've seen the joy gone.
[00:03:10] Unknown:
Because what she was doing is so difficult.
[00:03:13] Unknown:
It's just be I guess wherever she is in the grind and the need to succeed. Right? And the prioritization of that has displaced the has displaced the ability to access joy. And so the my the only, my only follow-up to that is that there is this, there's this YouTube professor that I do recommend people checking out because this guy is this unbelievably autistic Indian guy named doctor Payam. I don't like him in the show. Okay. P e y a m. And it's like, this dude exudes joy in teaching math. And it's just like, watch you just watch one video, and you just feel like, holy crap. Like, what a time to be alive with this dude. It Interesting.
Like, he's one yeah. It's just, he has no idea pro like, he he occurs like he has no idea. He's online, and he just makes it he he just is love of the game. He's like Freddie Mercury. Like, if Freddie Mercury were a math teacher.
[00:04:22] Unknown:
Yeah. Alright.
[00:04:24] Unknown:
So I that's the thing I had to tell my daughter. I'm like, you need doctor Pam. You go go back, get online, and go watch one of his videos, would you, and understand what this is all about.
[00:04:35] Unknown:
I'll commit to watching one of his videos for you.
[00:04:38] Unknown:
Yeah. Just Yeah. I'll link it to I'll link it in the shoutouts.
[00:04:42] Unknown:
That I mean, I think that's what, that's what I hope for a return to, though. Right? It's like the educator like, people educating about a topic, subject, what have you need to have that passion, because otherwise, it's you get captured.
[00:04:57] Unknown:
It's also the I mean, and it goes back to connecting to the fact that it's an art, and it's a creative art. It's an you know, math is a deep creative art. It's a long, you know, like that this is I'm almost quoting the book right now, but, like, it's a long Go do I. Well, I was thinking of reading a passage from it. I'm not sure if you really wanna do that, but, I mean, I won't be reading it. I have a paragraph here. Listen to it. Mathematics is an art, and art should be taught by working artists. Or if not, at least by people who appreciate the art form and can recognize it when they see it. It is not necessary that you learn music from a professional composer, but would you want yourself or your child to be taught by someone who doesn't even play an instrument and has never listened to a piece of music in their lives?
Would you accept as an art teacher someone who's never picked up a pencil or step foot in a museum? Why is it that we accept math teachers who have never produced an original piece of mathematics, know nothing of the history and philosophy of the subject, nothing about recent developments, nothing in fact beyond what they are expected to present to their unfortunate students. What kind of a teacher is that? How can someone teach something that they themselves don't do?
[00:06:23] Unknown:
I think that's I mean, that's just like in general. It that's interesting. That makes me think about, I've always been sort of, like, anti college. Not like anti college, but it was never for me, and it always seemed like a waste of time and money. And I I can't remember where it was, but I heard, it's like those that can't do teach or something along those lines applied to, like, college professors. Oh, it's when I was going in this when I was looking at, like, software stuff because there's this there's, like, this, like, this stark difference between sort of the education that you get in a computer science degree where it's, like, the same guy see teaching the same, like, things. And, don't get me wrong. Some of it is, like, very, very fundamental and foundational for computer science stuff.
But a lot of, like, the practices, techniques, and languages even that were used in, like, your comp sci courses were not applicable in the modern world. And it's like, there's two things to it. One is, like, it's a factor of just how fast technology moves, but then also it's a factor of, like, it's people that are not doing software development anymore. They just have this curriculum that they've they've, you know, been teaching for a decade, and they just, like, continue to do it. But they're not doing the thing. They're not creating. They you know, maybe at one point they were, but, they they are no longer.
[00:07:46] Unknown:
It goes back to reducing an art to, like, the thing that goes on the medium. Like, so for math, you're reducing it to computation. For pottery, we're reducing it to the ashtray. Right? It it's, which is what people who have no appreciation for the art in positions of educating people will do. Right? They they don't even know any better.
[00:08:09] Unknown:
Yeah. And I think the art the, like, the art is taking what's in your mind, though, and and putting it onto the medium. And, like, the the medium is in in and of itself is not the art, but it's the representation of the idea that is the art. And and in order for your mind to go to some place to create something new, artistic, and beautiful, you you kinda have to have it in your mind.
[00:08:33] Unknown:
Yeah. Computer science can be is an is a beautiful like, a it is, like, actually really a beautiful pursuit, and I've seen some of just the most elegant expression of ideas. Like, almost it's like almost can't believe that human beings can articulate themselves in code sometimes. Like, when I see, and it it you know? Yes. I'm impressed when certain things can be reduced to the smaller lines of code through ideas. Like, that does impress me. But it's more of, like, how's you know, like, the ways what somebody had to think in order to make a leap that enabled them to do that. And then some of the most one of the most satisfying things that I've ever experienced in my life is having an idea about how to abstract code and pull off something I know no one's ever thought of and then see it work, which if you don't code, you actually can't do it. And so, like, you can appreciate math as the art that it is, but if you I also truly believe you must code.
It's just like you can be a pottery, but if you don't do it, you still have to make the ashtray. Right? You don't express you don't get to express yourself Yeah. Unless you actually do it and see it in the world. And so it's both of those things. And, you know, we talk about it in Bitcoin, like, having the physical being attached to the metaphysical. And I think that's probably the best generalization. You you know, with math, you have to do it whether it's with a pen and pencil or behind a computer. But, like, the art of computer science to me, like, if you study discrete math, it is it can be absolutely beautiful.
[00:10:18] Unknown:
And is is is that because the function of a computer is to expand the the computing capabilities of humans? Right? So it's like humans can think of ideas in math, but, like, I mean, public private key cryptography is one of those things. Right? Like, we don't you can do it by hand,
[00:10:38] Unknown:
but we don't. You can. But, I mean, you know, like, like, you can and you should sometimes. We actually do. I'm pretty sure there are, like, paper wallets, and we do do these things sometimes. Yeah. And but it's more for, like, you know, at the very least, use a computer for prototyping your ideas. You know? Ask yourself if you understand an idea. At least, like, when I go through a math book, a lot of times, I'm also building a library of code to test whether or not I'm actually able to I'd really understand this stuff. That sounds useful. So, like, all the things we went through with the Euclidean algorithm and the Euler's function, I've, like, I've built my own libraries of code to do those things. They're very clunky. When I go online and ask for versions of the Euclidean algorithm, I see one line of code, and I can't believe somebody thought to do it that way. Mine's, like, 50 lines. You know? Well yeah. Yeah.
But but I am but you can see more of how I think if you look at my I I actually, I I do have a git I think out out of this, in out of this, I should be also using the GitHub to show, you know, show my code for these things. I think that would that might be helpful for people. But Yep. That is how you show how you think. And and when I managed I managed math PhDs. I'm not a math PhD, but I managed I managed them regularly throughout my career. And reading their code is how I see how they think. It's how I actually can assess whether or not they're even thinking.
[00:12:23] Unknown:
Right. That's interesting. Yeah. I never can say because everybody it's like it's its own style. There's a there's a million ways to skin a cat.
[00:12:33] Unknown:
Right. But you can tell if some you could really it's it's the way to communicate with somebody, and it's the way you actually can see how someone's thinking just by seeing their thought process. It's not that there's one right way. It's actually great that I'm not that I'm not an accomplished, like, mathematician or a coder because I don't I don't have dogmas about how it's supposed to look. So I can just look at somebody and say, are you actually commune are you actually communicating a struggle? And, like, do I see it, you know, do I see it in your code, like, that you're trying to solve a struggle? Like, you're actually trying to solve a problem.
And you've attacked it a certain way. Right? And now it's like now in this day and age, if you're managing somebody like that, you're gonna wanna be able to assess whether or not they're thinking, especially now because they are gonna have AI generate their code, and that's prob that might be fine. But you're gonna wanna tell you still wanna know you still wanna know if they're thinking.
[00:13:29] Unknown:
That that you actually brought up what was on my mind about this whole, like, vibe coding thing that everybody's talking about where it's like you just you just talk, like, they turn on, and I've done this. It's it's it's it's surprisingly works well. Like, I don't it's not perfect by any means, but you can turn on, like, dictation on your computer. And then, like, I hit a key twice, and it turns on like, it starts listening, and it starts right typing it all out. And so I just sit here, and you can just talk to it and, like, go back and forth.
But it's not it's not necessarily like, it's you're you're giving it, like, higher level ideas and maybe some details on, like, the implementation of how you would like it to be done, but you're not actually conveying it in the code.
[00:14:22] Unknown:
There's a place for that shit. There is. Yeah. There's a place for it. And you know what else? There is also a place for really struggling to make your code work, like, struggling with like, the people that I find who have understood what they were doing the best and have with the best at what they do, A lot of it is because they sat there with, like, literally one line that said, like, fucking a equals three, print a, and a prints something other than three, and they sit there pulling their freaking hair out Yeah. Yeah. Trying to figure out what the hell. And it's like that, you know, that struggle. As Yeah. So, like Yeah. Yeah. Which Well, even that struggle though is That is actually work. Right? That's the actual and work is how you get good at life. Yeah. Right? But, you know, the ability to get through that struggle and to understand not like, oh, this is something I just shouldn't do because it doesn't make sense. It's more that this is like, okay. I know my you know, it's pretty useful in those moments to know your math is good so that you're not questioning that, and then you're just like, oh, I'm just having a I don't know what's going on making this code work. I don't get it.
[00:15:33] Unknown:
Yeah. Right?
[00:15:35] Unknown:
Yeah. You know what I'm talking about because you're an implementer. That is just you know, that is, like, the in my mind, the core struggle. Right? Absolutely. Yeah. If you're wondering if you feel like that you don't know like, if you feel that you have some type of inferiority complex around math, you're gonna have a hard time getting through those moments. He's like, that's why so, you know, having the math down enables you to take those moments and just focus on
[00:16:04] Unknown:
pushing through, and that's what building Yeah. Because otherwise, you have to side quest to go like, oh, well, like, this Euclidean algorithm, like, is this is this right? Does this work? How does it how does it know? And then it also goes to, though, you know, we're all we're building on the shoulders of giants. So it's it's like a balance, man. It's it's always I always go back and forth. Right? Because there's there's the there's the, I don't know what you call it, the implementer. Right? So it's like doing doing the thing. And I don't know if this is a lower high time preference idea, but it's like, you know, how what is the what is the trade off? Right? There's no solutions. There's only trade offs. So it's like, what is the trade offs with having it all nailed down versus knowing how it works, validating that it works, and then having some reference point to touch on Yeah. For a working implementation.
[00:17:05] Unknown:
And I I I think you want you wanna have it all. It's like if you think that the see, the the risk is you take the you think the implementation is the object of the game. And it's like another quote. I I think it's the opening quote of the mathematicians lament. Literally, the opening quote says, if I wanna build a boat, instead of finding a bunch of people who understand how to hammer and nails, just train a bunch of people that yearn to be at sea. Yeah. Okay. Yep.
[00:17:35] Unknown:
I butchered that, but you get the No. Yeah. And I've heard I've heard that quote before. Not quiz. Yeah. It's yeah.
[00:17:43] Unknown:
Yeah. You get but but but but you must know the fundamentals of what you're doing. Right? You can't just hire you can't just bring a bunch of dreamers who think they can ignore the, you know, the underpinnings. Right? Right. Right. Right. So that's and I think it's a good that it's the struggle. That's the struggle. Right? The and we talked about this last week with the generalists. The generalist lament. Right? Specialists versus gen I mean, you just you know, the thing is you I what's it's going to take longer doing it the right way, and that's where the time your your time preference comes in. If you don't have the time preference, I don't I I don't like moralizing it. But I'd I one of the reasons I like time preference because it's it's a trade off. It doesn't moralize it. It just says, you know what? If you want it, you know, if you want an ashtray, if you want you you know, you can make one. Right? It's kinda like if I, you know, if I take an obese person and they wanna lose weight, I'm like, I can cut off one of your legs.
Right. And we can get that, you know, we can get the job done. Weight down. Yeah. Yeah. Yes. We can get the job done more as opposed to, you know, am I building something great? That just takes a lower time preference and be and it's slower. It's just slower because you really need to be you have at least toll gates, which is like, am I doing the right thing all the way that need to be governed? Yeah. Okay. Right? And so the the so I think coding, right, and particularly cryptography, maybe not so much the kind of cryptography that protects your passwords, but the type of cryptography that protects value.
[00:19:27] Unknown:
How are they different?
[00:19:28] Unknown:
Because I think when they protect value, it is, that we have skin in the game. It matters more. It just, you know, it just matters. I think it just matters a lot more.
[00:19:43] Unknown:
Yeah. I guess in my mind, I was getting very pedantic of, like, well, I mean, your passwords are some somehow protecting some amount of value.
[00:19:50] Unknown:
I I get it. But, like, it's just, you know, when it's being used to protect value, It meant it in my opinion value is it protecting? Right? That that's the other question. In in well, in some ways, it matters more because it's now costly to it's costly to, like, replicate and attack. When you're just protecting a password, right, you can probably you can print a lot of money and attack this thing a lot easier than if it's protecting value. And it's, you know, so it it has to be slower. It has to be slower, and that's this is I mean, maybe the whole my my entire, like, life's work right now around math is trying to convince people that this thing matters because of what we're actually you know, because of what we're protecting matters so much that, you know, we might have gone through life not thinking it really mattered
[00:20:47] Unknown:
to So what is the what is the
[00:20:50] Unknown:
yearn for the sea here? Like, what is the what what is the yearn for, when it comes to motivating the math? Right? Like, what is the It's true. It's the true, sovereignty promise. The sovereignty. Yeah. That's the prompt the the you know, which the sovereignty associated with being able to protect value behind cryptography, behind and cryptography is just a shallow word for, like, a human being's ability to keep his own secret. And that appeals to people because it's something people are capable of doing, presumably. Right?
It seems to be something Yeah. It's not. Like, it's something you get almost endowed by God, like an ability to just keep your own secret. But you've never but the ability to truly protect your value and protect, you know, to protect, sorry, to protect value behind it, you know, and the the the sovereignty promise that that offers and that we've seen a a history of humanity suffer under the inability to do that.
[00:21:51] Unknown:
When when you say I mean, in in the idea of keeping our own secrets too, that that that in and of itself is privacy. Right? Like, it's the the ability to selectively reveal oneself.
[00:22:02] Unknown:
That is It's literally that of the the word ability. You know? It's Yeah. The ability to do that because we don't you know, that's not like, it's not endowed. You have to ongoingly, claim it and exercise it. It's not something you just have that static forever. You have to it's something that you have to Right. Actively,
[00:22:27] Unknown:
What's the whole concept of rights are are taken and defended? They're not they're not given. But free speech is actively
[00:22:34] Unknown:
actively you no one gives it to you. Right. You defend it ongoingly forever, and this is you know, maybe this is an extension of free speech. Yeah. But you like, in order to keep a secret, it takes active like, a lifetime of eternal vigilance and active work. Right? And I guess I'm here to say that I think that leveling up in math is gonna be an essential part of that. I don't think you're gonna make it. I think some people maybe are special enough that will, but most people need to upgrade their math ability to be to be that sovereign and to really see this dream. I, you know, I got infected by the dream. You know, my whatever I got into Bitcoin, I got infected by all the dreaming.
[00:23:16] Unknown:
Yeah. Well, there it it gives you there's an escape hatch. Right? Like, there's this this parallel system that is and this is something that keeps myself motivated on a number of fronts is, like, there is there is greatness to be had in this new world on a Bitcoin standard. And with how early we are in it, the the things, the initiatives, the the projects that we create have the potential of of going in perpetuity.
[00:23:50] Unknown:
Right? They do. But I I see people sell that dream out so easily. Yeah. It hurts. And sometimes there's this risk of demoralization where it's like, oh my god. No one's really gonna wanna do this. And I know better. I know it's possible. And I know that, you know, sort of maintaining that dream and commitment is of vital importance. But I do see pea it is discouraging to see people so easily give up on that dream. Right? Because I think most people see it. And then some people like, well, it's not practical. I can't really. It's not, you know, it's too hard. Blah blah blah. And I I and so then I think, like, well, maybe it's only too hard because you don't have the skills. You just there's certain core skills you don't have. And so Yeah.
There's a lot of people that say you need to be more fit to keep a secret, and I think they'd be right. Maybe some people would say you need to read a lot to keep a secret, and I think they'd be right. You need to But, yeah, no but nobody's gonna do all the things. Right? And that's the that's the no solutions, only trade offs. Right? Like, there's not I don't see anybody telling people you need to level up in math, and I'm I believe that's Yeah. So that's why that's why I that's what I that's who I see myself as in the world.
[00:25:05] Unknown:
Well and and I and I wonder too, like, what does, you know, if it's if it's just us and Dan and April that that continue this motivation on math, is that sufficient? Like, what is the what is the critical mass of of of people that need, you know, mathematical sovereignty? Acknowledging that we will not like, acknowledging that no matter how much you might motivate, there there are just gonna there's a huge group of people out there that will just delegate everything. It doesn't have to be everybody.
[00:25:41] Unknown:
Yeah. It only has to be people who yearn to be free, and that's probably gonna be a small minority of people anyway, but it's enough.
[00:25:48] Unknown:
Well, Well, this to me, this is the same question of, like, the whole, like, not your keys, not your coin thing. Right? Like, there's there's there's some people I know that just, like, no way in hell that they will ever have the desire, to to hold their own keys. And if they did, they would they would flub it completely. I mean yeah. But I I
[00:26:06] Unknown:
I did okay. Look. I'm sympathetic to that argument. But I see if you take any one of those people and you hand them a circumstance Mhmm. There is I say there exists a circumstance where that will be untrue. There exists a situation if they, you know, somebody if, you know, all of a sudden the bank steals all their fucking money, they're gonna they they are going to flip. So it's a think all of those people just have not income encountered the use case. Right? They Well, and, also, I think the They live in the illusion. They, you know, they continue to live in the illusion that their money is safe, and,
[00:26:47] Unknown:
they don't get it. And that's When I think I think also in in my mind when I made the statement, and and I wanna correct it, and probably in your mind, like, you were thinking of, like, an adult. And I think that's probably the misconception here is because, you know, once you're in adulthood and you're developed and everything, there's not a lot of people with the neuroplasticity to sort of, like, adjust their worldviews and stuff. And that's more and more people have. Don't get me wrong. Buy that either. I think that well, I think the fund like, I think that, like, the next generation
[00:27:15] Unknown:
As a 50 year old, I don't that I don't who you know? How many in your peer group, though? Now or or three years ago?
[00:27:25] Unknown:
Sure. Yeah. I mean, it Okay. Okay. Alright. I'll concede yeah. I'll see that. Yeah. Yeah. But what I was getting at is more of, like, the, having it a fundamental curriculum.
[00:27:37] Unknown:
Oh, and by the way, not to just not to interrupt you from Yeah. But neuroplasticity, if, first of all, if anyone if we really buy into what that means. Okay. Let's assume that this neuroplasticity argument is true. Spending a couple hours in the morning doing math, I think, is a is likely a great way to, ensure ensure that you have the neuroplasticity to do anything you want.
[00:28:06] Unknown:
That's good. Interesting. I wonder, like, I the the idea just jumped in my mind, so I'm gonna say it out loud. I think about, like, those daily calendars that you'd like to peel off calendars. Yeah. And it's like there should be, you know, the the fundamentals of cryptography daily calendar of, like, a math problem to to solve. And I imagine something like that might already exist, but it's it's an idea.
[00:28:31] Unknown:
Yeah. That's cool. I would just like a daily calendar that just says, don't quit. Just keep going.
[00:28:38] Unknown:
Don't quit. That's it. Like, you can request the one message. Over and over again. It's just the same message. That's probably Fundamentals will call will will find your brain
[00:28:47] Unknown:
and fuck you up if you quit.
[00:28:51] Unknown:
That sounds really aggressive.
[00:28:56] Unknown:
Don't do that. Don't get demoralized.
[00:28:59] Unknown:
I didn't. I looked at snore signatures this morning. So I didn't do math. I didn't do any math by hand, but I I did I did ask about snore signatures and that sort of, like, their linearity property.
[00:29:14] Unknown:
And then You know, I'd feel better about Schnorr signatures if it didn't have such a goofy name. What do you wanna call them? I don't know. I I I don't know. I'm gonna I accept it. I I I do accept it. Okay. It's like, it's kinda like I was saying yesterday, like, the name Lutnick does not inspire confidence and, like, the name, like, Lutnick is like the kind of guy that gets splashed by a cab who gets you know, every day, the second he walks by this puddle, a cab just splashes him with water.
[00:29:43] Unknown:
Okay.
[00:29:45] Unknown:
But I'll accept Schnorr for what it is.
[00:29:48] Unknown:
The signature is as defined in BIP three forty, which just rolls off the tongue.
[00:29:54] Unknown:
Yeah. BIP three forty. And, you know, one of these days I one of these days, I'm gonna commit to going through this BIP. It's right here. Something that I like, before I got into a math rabbit hole Yeah. I was, I used to just pair print out the BIPs and go through them character by character. I did it with all the lighting, the bolts up to 11. And, Really? Yeah. So, like, right literally all the fields mapping together. Like, it was Yeah. You know, commitment to understand these things. So three forty was never something that was on my in my radar nowadays.
[00:30:28] Unknown:
You should definitely do it because there's, like, a wall of numbers at one point, and there's a bunch of math equations.
[00:30:36] Unknown:
I love the thing you said the, the set p GitHub that you sent me that was written in Python. Did you go through that one? I scanned through it. I think that would be a cool thing for us to, do together potentially with crew with a group.
[00:30:52] Unknown:
Well, in the code review. Like a like a code like a code review. Yeah. Yeah. Yeah. Well, in the the the implementation, right, was, like, experimentation, education, and prototyping. And that that education piece just stuck out to me. I was like, oh, this like, I need to send this fundamentals because Very cool.
[00:31:08] Unknown:
Yes. This is this is it. If I had seen this first and not the other one, I might not be here.
[00:31:14] Unknown:
Well, that's kind of a that's a big assertion.
[00:31:17] Unknown:
I'm just saying I might not have panicked and decided I needed to learn all this math two and a half years ago or when
[00:31:24] Unknown:
Well, I'm glad that you did, first of all. I would have been like, oh, this is the answer. Okay. No problem. I get this. Okay. One end of end of finalize, it's it's it's titled sec p two fifty six k one lab, and that's the organization name and the repository name. And it just has, like, low level sec p k one field and group arithmetic,
[00:31:45] Unknown:
which is, like, things we've been talking about. I'm just kidding. Be not to beat a dead horse.
[00:31:49] Unknown:
Beat it away.
[00:31:51] Unknown:
It's through validation that you realize you don't you find the thing you don't have the aptitude for or you don't the current aptitude for it. Oh, yeah. Failure is the best way to success. And that you know? And so I'm pretty sure I would have found myself here regardless one way or the other.
[00:32:07] Unknown:
Yeah. Like, failure repeated failures, how do you get to ultimate success? So alright. But there's snore shining and verification according to BIP three forty, so you could get the BIP out and go directly into this. And then it lift elliptic curve, DV helmet key exchange Yes. Which is important for other math that I'm into, like blinded signatures.
[00:32:33] Unknown:
And here's a question. Here's a question, I guess, you I'll ask you to sit with. Okay. If we had started with Schnorr, would it ever even matter? Would would there ever be a reason to have to learn ECDSA? If we just started with Schnorr, is it even, you know, is it even relevant? It Schnorr feels like a much a more general it's just a question to sit with. Is that, like, would we even if Schnorr was there first, would we even would anybody even know what ECDSA is? Does it add Probably probably did not. Does it add any like, that's so it's just a question I would say Yeah. Does it add anything to, like, the corpus of knowledge?
Because Schnorr feels like the answer we always wanted to get to.
[00:33:21] Unknown:
Yeah. But there was stupid intellectual property things.
[00:33:24] Unknown:
It's just anyway anyway, it's just stuff I like to sit with.
[00:33:28] Unknown:
Yeah. I mean, I don't I don't think it would be a yeah. Just off the cuff, it seems like nothing that would be widely like, what other unless you were into, like, security research. Right? Like, the info infosec
[00:33:41] Unknown:
information. I mean, this is a different type of elliptic curve signature. It's a different formula. Right? Yeah. But I'm saying I mean, it's just because it doesn't it doesn't call itself elliptic curve digital signature algorithm. It it is a elliptic curve digital signature algorithm. You know? Yeah. It it is that. So I guess that maybe that's the thing I will will put a pin in. So let's so what do you have in mind here?
[00:34:11] Unknown:
Just we we talked, you had made the observation that because of the way that you can do, batch verification and, like, these the the multisignature
[00:34:24] Unknown:
things. That it's closed under the it's like closed like, it's like the group axiom. It's closed under the operation of the signature. That's what we that's what we had observed the last time, and then we were like, okay. Is that is it does that mean is, you know, is it a group? Right? Is it Yeah. Is that what it did? Does it is it, like, literally leveraging the properties of a group to
[00:34:49] Unknown:
be more, you know, to be as powerful as it is? And and the answer that at least reading through this made sense was, like, it depends
[00:34:58] Unknown:
sort of thing. That's, like, pretty cool. So it's not a no. Yeah. It's it's not it's it's the because it did feel that way. And then I, you know, I I hear about, this nomenclature in Monero called ring signature, which maybe I've I've heard of that as well. Yeah. Something worth looking into as well. Well, what's a ring? Right? Yep. Like, I never thought about it. I never associated the word ring with the algebraic structure until
[00:35:23] Unknown:
recently. Right? Until, like Oh, yeah. Yeah. Okay.
[00:35:27] Unknown:
Right? And but that's it seems as though maybe it's very similar. I mean, ring is this is is just a, slightly, modified version of a group, right, where you have addition and multiplication. You have all the group properties for addition, not necessarily for multiplication.
[00:35:44] Unknown:
Yeah. But, like, what is the what is the key contextual piece that makes something a ring?
[00:35:50] Unknown:
Close well, so closed under, you know, all the group axioms under addition. Mhmm. And then it's also closed under multiplication and associative under multiplication, and thereby you have the distributed property. That is what make that is, like, the technical definition of a rank.
[00:36:08] Unknown:
Right. So I wonder maybe we should look at those signatures to, like, understand what that is. Because in this one, the, like, the ultimate conclusion was it's not necessarily it's not closed under not not generally, like, closed under group, but with, like, certain conditions. And that that's where these, like, multisignature protocols. So it's you're basically putting additional constraints on it to get something that is
[00:36:40] Unknown:
close like, has closure. Yeah. So that's what the tech so the technique act
[00:36:45] Unknown:
The the technique of Schnorr Schnorr itself
[00:36:48] Unknown:
doesn't have this property, but it it the techniques of Musig and Frost are able to somehow manipulate them in a way to make them groups so that they can have these so that they can be used in this way. Is that correct?
[00:37:05] Unknown:
I believe so. Yes. Yeah. Yeah. It's it's only under controlled settings. So, like, you have to, like, put additional, like, guardrails, which that's the that was one of the things of, like, the group itself is is, like, you have to define it as what the real was it real numbers or whatever? Or there's, like, a certain it's it's all about setting the definition of what the box is that you're operating within Yeah. Yeah. For saying if this is a group or not.
[00:37:32] Unknown:
Right. And, like, as in, like, specifying the operation. Yeah. Okay. I think what I'm I think what you are referring to is when we talked about the integers, the set of integers under, like, multiplications, not a group, but it is under addition. Because under addition, you have an the identity elements there with zero and you have an inverse, which is the integer minus, you know, plus the negative of the, you know, the negative of that number is the inverse. Whereas the multiplication, you don't have that because you would need a fraction to multiply back to the identity.
Right. Right. Right. Yeah. That was yeah. That's that's that specification. But I think it's interesting that Schnorr in and of itself may not be actually what's useful. Schnorr, you Well, let's talk about it. By Musig or Frost.
[00:38:22] Unknown:
Well and it's not it's not even that. Like, the Musig and the the Multisig protocols is, like, it offers closure, but it's not, like, a general group closure for, like, all of the signatures.
[00:38:36] Unknown:
Okay. I think I'm gonna have to really read this spec. The spec is are are you in bit is this what I'm looking at? Three BIP three forty, or is it well, there's a yeah. There's a few I think this is an article that This is BIP three forty. But I will send you Yeah. Okay. Yeah. I will send I will send all these things. When I'm looking at, there are headings like group closure. Yeah. And that's not in the BIP. No. No. No. No. Yeah. Not at all.
[00:39:03] Unknown:
But, yeah, it's it's worth it. And there's this this Aline Tamescu, which I don't know. It was something that came up in in the search, but it was titled shore signatures, everything you wanted to know but were afraid to ask. And it goes into, like, batch verification and some other things. It also goes into some, like, mistakes that you can make, like pitfalls, which I think are some of these are pretty common, like reusing nonces, which again allow you to, like, mathematically back up Yep. Back out of a signature into a private key.
[00:39:34] Unknown:
Universal a universal law, it seems, do not reuse nonces.
[00:39:40] Unknown:
Yes. Oh, and look at that. Look at the you you in the conclusion of this, it says why you should prefer Schnorr over ECDSA. So it could even, potentially ask, you know, it it sort of summarizing the findings, as to why.
[00:39:57] Unknown:
So You wanna just provide a a highlight of what they're saying? Just
[00:40:03] Unknown:
Yeah. It's, I guess, I didn't read this part. I just literally just saw the link as we were discussing it. So, one is the threshold is thresholdizable, it says, which that's an interesting thing. Weird word. You well, it you can't do threshold signatures. Right? So frost is a threshold variation using Schnorr, but you can't do that with eCDSA because you don't have the linearity to combine the different
[00:40:28] Unknown:
pieces. So threshold meaning
[00:40:32] Unknown:
Threshold meaning Multi sig.
[00:40:34] Unknown:
A number of have it being able to set a number of Yes. That are needed.
[00:40:39] Unknown:
Three out of five multi sig sort of thing or two out of three or x or t out of m is just how I've often seen it displayed.
[00:40:48] Unknown:
And I think isn't the re so Schnorr is presents a multisig as make makes it look identical to o single sig because of this closure. Right? Because the signature is the signature itself is closed under the operation of addition, whereas in ECDSA, the signature itself is not. And so you have to you have to show all three SIGs in the and then list them in the pub key. Whereas what you see under snore, it seems it looks like it looks identical to a single SIG because that's what it because it has closure. Right?
[00:41:32] Unknown:
Yeah. Yeah. Yeah. Because you end up with another point on the same cur like, you end up Yeah. Still within the same Like, a signature plus a signature is another something is a signature. Correct. Yes. Yes. True in ECDSA.
[00:41:45] Unknown:
Yeah. And that goes into the whole, like, batch verification thing. A point plus a point is a the points have closure, but the signature does not. That was an under e under ECDSA. Right? The points are a group are an abelian group. Right? So they a point plus a point is a point.
[00:42:03] Unknown:
Yes. But when you put it through the signature algorithm is not does not have that property.
[00:42:08] Unknown:
In Schnorr, it does. That's what and that that's really well, that's why it looks like a single sig. Well, that's the linearity piece of it is That's called that they're called that's otherwise known as linearity. Right? Yeah. That makes sense. I would say otherwise known as closure under the operation of, you know, the signature is closed has closure under the operation of addition. The same way the point does.
[00:42:36] Unknown:
Right. Right. Right. Yeah. Right. Because you can you can combine the things and still stay within the thing. But once again, in ECDSA,
[00:42:43] Unknown:
the signature does not have that property. Yeah. Right? So you have this clunky you have to list them all out. It's not that it's clunky. It's that it docks as the purpose. You don't get to Schnorr has the very powerful ability to abstract the fact that you're using a multisig. It's really powerful. I mean, you know, a multisig is, much less secure if somebody finds a key and knows it's part of the multisig.
[00:43:15] Unknown:
Right? Well and it's interesting though because there there's, like, again, no no solutions, only trade offs though. Because to a certain degree, though, if I'm making a signature with a quorum of people, maybe I do wanna know, like, okay. Who didn't sign? Sure. Or who didn't participate? Or if there were some sort of can do that. Malfeasance.
[00:43:35] Unknown:
You're you're nothing's stopping like, nothing's stopping somebody from doing from displaying those things. Maybe you don't have to display it to the to the whole chain, though, potentially. Right? Right. Right. Yeah. You don't have to let the world know.
[00:43:50] Unknown:
That's true. That's true. Yeah. It would be it would be sort of out of band from, it it'd be in the signing protocol, not in the actual Bitcoin protocol where Docking docksing lightning.
[00:44:02] Unknown:
Sorry. Doxing lightning channels because, you know, two zero two multisig is clearly is, you know, almost always gonna be a lightning channel. So you don't snore abstracts that so that you don't dox a lightning channel. But, also, I mean yeah. I mean, the the key if if if a person if an attacker doesn't know it's in a multisig, then, you know, it's it's a world of difference than if they do.
[00:44:33] Unknown:
You know? Yeah. It's it's the fog of war. Right? Like, in in the event of an attacker, the fog of war is, is this a single sig? Is this multi sig? You know, if I'm even if I'm going to hit you with a $5 well, it's a $15 wrench now. But a $15 wrench attack, even if I show up at your house, if I see that you have some multisig set up on chain, now I know how many keys I'm looking for. That's right. And if I show up, and I have no, I mean, I have no idea how many keys I'm looking for, there's some plausible deniability there,
[00:45:05] Unknown:
where maybe If you don't know that if you think your mission is over, right, and that you just hit a dead end Yeah. Yeah. And even if you don't like, let's say you're smart and you're like, I'm this isn't working. I know this is a multisig. You better, you know he doesn't know what the quorum is. He doesn't know if it's two or three, a three or five. He doesn't know how he doesn't know what he doesn't know. That's the that's the key. You don't know what you When the other the other interesting thing that I just thought of is there's, like, a way
[00:45:39] Unknown:
so in, like, a frost quorum, you can add additional keys to to the quorum, like, using math. You're you're just, like, finding additional points, but that doesn't invalidate all the previous, key shares that you used. Right? So or the keys. Right? So if you had, like, a three out of five and then all of a sudden, you know, you get you get robbed or whatever. I I wonder about just like, you know, two of your key or your your three keys are are taken of your five or whatever, but maybe you still have the data, to add additional keys. And so you can't change the threshold, but you can change, like, the the keys that are valid within the threshold.
And so you can make it like a three six or three seven or three of eight. And now it's a race between you and the attacker to go, like, sign and broadcast something. Something that just came to mind. So, like, let's not, let's not quote me on that. You still need all the x bugs and all that to be able to use do you still need all That's what I'm not concrete on. Yeah. I think you're you're gonna need there's, like, a certain level of knowledge that you still need because you're you're essentially you're you're adding I I I don't wanna say it the wrong way, but in my mind, I wanna say you're adding another coefficient to, like, the polynomial that is the the the frost quorum.
[00:47:07] Unknown:
Right. And I don't know if those are the right words. Asking. Yeah. And I have a question that I guess it's good to have your own questions when you go through these things so that you know what you're searching. You know, you have the location to search for. My other question would be, how does it know it's easy to in the ECDSA, you it's easy to know the answer to the question, what is the quorum? How do you and, you know, in Schnorr, how does how does it know what the quorum actually is?
[00:47:34] Unknown:
Well, to be clear, it's Schnorr is not Schnorr is just a signature algorithm. Right. In the transact what I'm saying is Frost is the threshold quorum. The like, these are two distinct things. So that's
[00:47:46] Unknown:
What's that? That's right. So that's maybe that's also why, like, Schnorr in and of itself is just a signature, but Frost is the is the is the implementation of it. Like, where in a transaction, hex would I see the quorum itself? Or maybe you don't like, how how would one maybe you just that that's the whole key. You don't see it from the you don't see it publicly. But how would one know?
[00:48:14] Unknown:
For
[00:48:15] Unknown:
the you're talking about in the quorum? If you're using, yeah, you're using schnorr, you're using, you know, you've put a multi you put a two or three together with frost. Mhmm.
[00:48:26] Unknown:
That that's all done by the people doing the signing. It's not it's not visible on chain at all.
[00:48:33] Unknown:
I we I don't I don't know. Like, I've been These are my bosses. A long time. Yeah. Yeah. If we're gonna do, like, a code review or a BIP review Yeah. Yeah. With, people that in our audience that wanna do that, those would be some of my motivating questions to try to figure out.
[00:48:49] Unknown:
Well, in the You know? Definitely. I definitely and I don't know. I we need I I I think the next thing I'll do is I'll go and dive into Frost to see because there's a certain way of basically taking the different keys existing keys that can be used for creating snore signatures, like different s c, sec p keys, and then combining them to create this, like, shared key
[00:49:27] Unknown:
sort of thing. I feel like I need another an another base 58 class that does it on that
[00:49:34] Unknown:
uses Like, just
[00:49:36] Unknown:
oh, interesting. You know? Because that's every most of what I learned was through doing the base 58 transactions class. Yeah. Yeah. Yeah. Yeah. At least that's where I got my base. No pun intended.
[00:49:49] Unknown:
Oh, here it is. This is okay. So this is a good one from from the I see a picture of Andrew Polster. Yeah. Blackstream's glossary, Frost flexible round optimization or signature threshold signatures is a protocol that minimizes number of rounds of communication between participants in a signature scheme. So Frost is a way of, like, in the rounds or, like, how how much back and forth we have to do between us if we're doing signatures together. And so frost is is, like, way of doing that in a very, very, it well, it says maximum three rounds for signing. So So you just okay. So the actual exercise of doing the signing is now also different. So it's a different Yes. User experience. That's what I'm saying. You could you on your own with a single key can just do a Schnorr signature. Right? You don't need anybody else's participation.
Right. But if you wanna do these multisignature or threshold signature things, then you have to coordinate the mathematics and the nonces and all these other things. You have to coordinate them all together with all participants. Well, if if you're doing this in a trust minimized way, right, because I don't necessarily like, we're we're dealing with, you know, 10,000 Bitcoin in this wallet. Well, you don't want me to screw you over and somehow sweep the coins myself. So Frost is is a is a communication protocol for sort of doing a snore signature together with other people.
Right? And it does it in this, you know, minimal rounds of train like, because the more and this is a general thing in cryptography of interactive versus noninteractive.
[00:51:30] Unknown:
Yeah.
[00:51:31] Unknown:
So, like, for instance, the Bitcoin cryptography in Bitcoin is, like, noninteractive. Right? You can just you can just validate it all on your own. You do all the signature validation, everything like that. You don't need to talk to necessarily anybody else. You just need to get the data. Right? But, you know, Frost in this instance is an interact or Moosig is an interactive protocol where two parties have to communicate to exchange data, and there's sort of these rounds that happen, and each rounds have its own, like, state along the way. Uh-huh. And if you're not following a specific protocol, you know, there's a way to sort of, like, maliciously
[00:52:14] Unknown:
use certain numbers or or nonces or anything like that. In the middle attack piece. I mean and then, you know, I'm curious, curious about also, like, how MiniScript would work in this context as well. And I think that's I think this is separate. MiniScript is For multi six. I'm if it's but they're not maybe they're not using Schnorr.
[00:52:37] Unknown:
I think MiniScript is more of, like, templating for a transaction. Right? So you have, like, a MiniScript for a type of transaction, and maybe that transaction is a a multisig, like, a two out of three multisig using, your standard ECDSA
[00:52:51] Unknown:
signatures or something, and that would be like a template. Yeah. So they're not and they're not they're not using this math.
[00:52:57] Unknown:
No. Not necessarily. No. It it's it MiniScript is more for the scripting aspect of Bitcoin transactions and less so for the how the signature is accomplished. So the implications of the mathematical
[00:53:08] Unknown:
breakthrough we're using here is just that a little bit of the procedure need now needs to be, managed.
[00:53:17] Unknown:
Yeah. Yeah. Right? Yep. Well, as so before the price of extraction
[00:53:21] Unknown:
is having more, maybe, it's more of the signers involvement, it seems.
[00:53:27] Unknown:
Yeah. Definitely. Because I get you know, before you could do a presigned or partially signed Bitcoin transaction where it's like a multisig and you're, like, passing this thing around. But I know like, I can give this to you, this PSBT. I can give a multisig PSBT to you with my signature already done. That's right. And you can just do your signature then and then broadcast it. Right? And everything's fine and dandy. Feels the way God intended it in some ways. But if we're doing if we're doing a frost signature or music's music signature Mhmm. At the time of the signature generation, we need to be coordinating and communicating. And that's what it that's what it refers to in these rounds of communication.
Mhmm. It's like how many times do we need to do, like, an exchange of data to finalize a signature?
[00:54:10] Unknown:
Interesting. It feels like the environment just needs to be managed the whole way.
[00:54:15] Unknown:
Yeah. And you also have to you know, if you're thinking closed literally
[00:54:19] Unknown:
like, closed doesn't just mean the math. Closed also means the entire environment that it's all being done in.
[00:54:28] Unknown:
Yes and no. Like, there that's that's one of the things. Right? Because I mean, the dev environment. I just mean the gen as a general word. Yeah. Yeah. Well, if you're doing things in a close like, if you and I go into a secure bank vault room, you know Mhmm. SCIF facility, whatever, and do key stuff, that is a lot easier. But the assumption, at least my understanding of the assumptions made with, like, Frost and Musig is, the communication may or may not, like, may or may not be public. Right? Like, you you have this, like Yeah. You have other parties involved. Right? Like, you you are involved, and you're not a part you're not me. So there's there's this, like So it's a it's more of a local versus global thing now. It's more of a local, like, the
[00:55:16] Unknown:
this multi six scheme, things need to happen locally before it goes on the global chain. Yeah. Yeah. Before it's a sort of broadcast and living in the global world.
[00:55:27] Unknown:
I totally agree.
[00:55:29] Unknown:
Also kinda cool. It feels like it feels like that is just another way of human beings want wanting to be, you know Well, and I think tool privacy tool, potentially.
[00:55:40] Unknown:
Well, and one of my within groups. Absolutely.
[00:55:42] Unknown:
Groups of people. Sorry. Not that.
[00:55:45] Unknown:
Yeah. Is it an billion group of people or it's a Bitcoin or group of people. This is, I mean, this is just this is almost like reaffirming my ongoing thesis of, like, the the hyper localization that Bitcoin is going to drive forward because you're you're gonna wanna do these key ceremonies.
[00:56:04] Unknown:
Yeah. Pre broadcast. It's like once you broadcast, you're out in the wild. But before you can do more before you broadcast, that's local.
[00:56:11] Unknown:
Yeah. Support local Bitcoin or sign sign sign local. Screw buy local. Sign local. You know? Thanks, everybody. Couple of do songs.
Introduction and Weekly Math Reflections
The Art of Teaching and Passion in Education
Challenges in Advanced Math Education
Inspiration from Dr. Payam and Joy in Math
Mathematics as a Creative Art
Critique of Traditional Math Education
The Beauty of Computer Science and Coding
The Role of Computers in Expanding Human Capability
The Struggle and Satisfaction in Coding
The Balance Between Fundamentals and Implementation
Cryptography and Protecting Value
The Dream of Sovereignty and Mathematical Skills
Neuroplasticity and Math as Mental Exercise
Exploring Schnorr Signatures
Schnorr vs. ECDSA: Advantages and Applications
The Importance of Multisignature Protocols
Frost Protocol and Signature Coordination
Hyper Localization and Bitcoin's Future
