Exponential Got Less Exponential

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Created: 11/1/2026 7:58:12 PM
Duration: 4170.841
Channels: 1
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Alright. Welcome,
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and hello
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to the Magic Internet Math podcast.
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I am Brian fundamentals.
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And I'm Rob Hamilton.
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Yes.
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Our all good. Introductions.
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Yeah. I get our Totally good. Introductions upfront.
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Well, just for the clinic person and just Yeah. We can kinda move on. But,
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yeah, man. It's been a
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three weeks,
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and,
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you were you were at Lugano.
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You've been CEO of Bitcoin.
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My my shit has been ramping up.
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It's been... You know, like, think ideally, we'd like to do two weeks, but we... It's just week three. But but I'm... This is all to say, dude. So much has happened. Like, we thought we were kinda, like, on top of things
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three weeks ago.
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You know? We were we we were red teaming Bitcoin's cryptography.
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That's right. And we thought we had a nice stopping point
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to say, okay. This is... Oh, and you and I are gonna be in Amsterdam. I'm flying out tomorrow.
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We're gonna be in Amsterdam next week, and we're doing the panel called red teaming
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Bitcoin cryptography.
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And we... Right? But three... A lot of it's happened in the last three weeks. It's like,
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what do we do?
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That's right. That's right. Fast moving space.
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Yeah. I... I'm pulling up the papers now. There were some,
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observations around elliptic curve.
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Well, I guess we go to the
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the ETH hypothesis,
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which is not Ethereum as everyone initially thought.
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I really thought it was. I read, like, when you when you you sent that thing to me, and I'm like, what the hell is this? And,
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wow, poor ETH.
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I was like thinking, oh, man. What a sad day for ETH. And I I think it took me forty five minutes to figure out it wasn't about ETH.
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Yeah. That's right.
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My bad.
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So that ETH is the exponential time hypothesis. For about a day, we all... Like, people were,
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pretty hyped that
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this thing called p
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equals n q is gonna be solved.
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P equals n Can't
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forget. P... What is it?
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P equals n p? Yeah. P equals n p. One of the one of the holy grails,
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which I'll be honest, I'm like,
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like, I get the concept of it. I'm not really that embedded into why...
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Into what its implications are.
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Well, just looking at it from any any
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problem that could be solved to be able to trivially... Any problem that can be trivially verified, you could trivially solve. Right? That's like the... And maybe for those of, I know we got a lot of new listeners to the podcast.
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I was out, in Lugano evangelizing the name. Like, the...
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A lot of people are like, oh, you should start a podcast. I was like, well, I already have one.
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I already do have a podcast,
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and it is magic Internet math. And You're welcome for my great marketing of my podcast. Right. And I mean, like, the... And and the vibe of this podcast
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is,
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you know, when you're at a bar
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after the event, after the conferences, and you just wanna have a little bit of a conversation and you wanna learn more about the math. This is definitely more of a bridge to people who don't have a background or expertise in math to start getting a familiarity with the fundamentals,
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the tooling,
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foundation
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of all of these things we take for granted, right? So
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we're gonna stumble our way through this, and hopefully, those of you who are looking to learn more,
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you know, pick up a thing or two. And those of you who know way more than us, you could correctly chat us so we can update our mental model. I find that just,
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learning is just speaking in public and just on the Internet waiting to bait people into,
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correcting you, and then you learn. Yeah. It's... And it's absolutely, like,
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like, the whole point is, like, when you turn on sports radio
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and
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the first story is like, oh, this coach should be fired because he didn't call a time out in,
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you know, in this situation. And for some reason, you have people who are not technical experts in the game of football, but they know exactly what they're talking about, and they they can engage.
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You know, they can have an opinion. They can call in and, you know, they can call in and say, oh, you know, I think he's... I agree with why he didn't do that. Or we want people to have opinions about what's happening
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because
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we're kind of on a collision course with a time where
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there are going to... Like, things are gonna happen
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and we are either going to be able to have opinions about what we're being told about it or we're just gonna have to accept what we're being told about it. That's right. Right? So the whole point is to have us be able to engage
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and have some competency.
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Now maybe it takes a little more
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in the math area, a little more
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to, you know, go tell... Say that a coach should be fired.
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Right? But
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I don't think... I... You mean, I... That... That's why we're doing the podcast. Yeah. That's why we invented this so that there would be a way, a bridge. Right. A thousand percent. Right? And,
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the
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conversation where we kinda left it was
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we mapped out, like, these five or six different, like, abstract ways that if you were to try
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and wrestle with the complexities of Bitcoin and could... Not from a quantum computer, but from just a classical mathematical perspective,
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break elliptic curve cryptography,
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what would you need to do? You mean nonfiction?
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Yeah. Like, the the... Yeah. Right? Because the the genesis of this was that Justin Drake post, which was just vague posting, but not saying anything.
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Right?
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And so this actually ties the red teaming. This is the one where...
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I'm trying to... I can't get these all straight, but the Justin Drake post was that
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Bunker mode.
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Yes.
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Bunker mode.
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The Ethereum Foundation researcher,
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who changed his title to Bitcoin security researcher and then started vague posting and it went super viral.
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Think this is why Joe Lubin started following you and I recently?
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Maybe. Yeah. That's right. Last night, Joe Lubin followed both of us, which I thought was very funny. Like, almost at the same time. Like, we both asked each other, is Joe Lubin following you? He just followed me. Yeah. Yeah. Yeah. It was, like, in passing at the same time. Yeah. Yeah. Yeah.
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Welcome to Magic Internet Math, Joe Lubin. Yes. So
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Take a seat right next to Jonas Nick.
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Yes. Jonas Jonas,
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is now a subscriber to the podcast.
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It was actually just before we even get into the exponential time hypothesis. It was absolutely devastating. The one talk I wanted to listen to, like, the most was Jonas's one about
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shrinks and quantum, like, proof signatures.
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And
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I was on at the same exact time,
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and for some reason, I had the main stage. That that probably should have been flipped. As flattered as I was for the offer,
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to have a main stage slot at Lugano,
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I actually made a point specifically in my talk,
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because I I I do a little bit of glazing of the core devs and sec p and kind of the foundation of Bitcoin when you compare
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the events of this summer and the resilience of code.
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Libsec p two fifty six k one, that foundational library, all the signatures run on in Bitcoin,
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is,
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so far ahead of any other software related to Bitcoin.
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And I think this is something that you you would take for granted until all software just starts breaking down.
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And that was an amazing takeaway we got from
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from the... Of course, in events this summer. And
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it's one of the things we're here to try to have an opinion... To try to get us to have a competent... Have the competency to have an opinion on. Yeah. I I, I had a whole slide dedicated to my libsecp memes, which I heard was very well received by all of the maintainers and developers on the libsecp project that they were very proud of that. And I'm... I am happy that I was able to do a small contribution of showing gratitude and trying to make libsecp sexy because
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incredibly important,
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but,
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you know, everyone takes it for granted.
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It's just... It's the foundation of every single Yeah. HSM,
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of every single hardware wallet, of Bitcoin Core.
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It is the foundation of all of it. Right? And so
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You could say it's the sun. It's like the sun.
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It really is. And I'm happy under my my leadership now, obviously, as the CEO of Bitcoin that I'm able to kind of, you know, pivot away from the marketing
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hype engine of everything and get back to the basics and just talking about how awesome elliptic curve cryptography is and all of the effort and work that goes into that. Are you, like,
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are you,
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close enough to the YouTube from Lugano to know if they're out yet, and we can put that in at least in the show notes? I, tweeted it out. Jonas' talk? Let me see if Jonas' talk is out.
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If you got... If they gave you yours, Jonas Mine... Well, they didn't give it to me. Mainstage
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goes out first. Right? Well, we just ripped it from the stream.
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I just literally ripped it from the stream, but I'm gonna see if his talk is out. I think it's on Rumble. It was all livestreamed on Rumble.
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Okay. Plan b We should be able to get that.
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Yeah. Plan b
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twenty twenty six. Because, I mean, you may you may or may not like shrinks, but we we we need to have an opinion. We need to get ramped up so that we can know. Like, we may or may not like, isogenies.
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We talk about it on... We talked about isogenies on the podcast because
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we did enough foundational work to do so. That's right.
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That's right.
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I'll go look for it afterwards. I'm pretty I'm pretty sure both stages... The plan b form. Here we go. Plan b form, Lugano, WAGME stage,
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day one Who knew Isogenes was gonna get caught up in controversy
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with,
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that was just the stupid joke about isogenies sounding like misogyny.
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We
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will,
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I only see the main stage that may have been livestreamed. So if so, the other ones are gonna be coming out. They'll be coming. Once we're... Once we get it, we will make it available, and maybe we'll do... I mean, it looks like we're on a collision course with having Jonas on the show at some point. Inevitably. Right? Yes.
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You can only tease that out so much. We've been teasing it probably for close to a year. Yeah, yeah, yeah, yeah. That's right.
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But we're getting there. We're getting there. So let's... So it's like exponential time hypothesis, right? So this is one of those things that changed in the past three weeks where
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in short, this was an understanding
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of that certain
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problems,
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in this case,
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going from a public key to a private key, would always require exponentially growing computation as the space grew. So having two to the two fifty six keys...
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I'm sorry. 200... Two to the two fifty six bits of,
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256 bits of entropy that to be able to walk backwards was basically gonna get so computationally complex, your only best shot was really to brute force it. And And this... Just to get... Just to jump in real quick. Yeah.
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A review
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of...
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We have a private key
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that... And we... Then there's this generator
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point. It's a multiplier that everybody knows.
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So the private key is multiplied by this number, which means we do point addition on itself,
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big g times. So this amount... Number of times. And,
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you know, when you add... Like, when you go... Let's think of a number line. If you, like, add one plus one plus one, you can kinda see it just increment, go from one to two to three to four to five. But when you're in an elliptic curve,
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you can't really
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you can't really into it how point addition is taking it from one point to the next. You can from one edition. You can see
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the process.
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It's a bit more involved, right? So doing
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point addition,
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what we do know is that the
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answer is always going to be on the curve no matter how many times we add it, right? As a closed group.
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But you can imagine taking your private key, adding it to itself G times,
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and then you find yourself somewhere on the curve as the public key. And now what... Now Rob is saying is what we what we talked about weeks ago was
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trying to now... If you know the public key, it's sort of like, you know, come and get it. Come and take it if you think you can go backwards. Even though you know how many times you have to go backwards, you know the exact amount of times that you need to go backwards.
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And yet,
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it's still... There's still hardness for the system. Since this is not just like regular edition, right? It's modular arithmetic, right? So you can't just trivially
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subtract the number and just get your answer. Like, there's the... With modular, it's not as straightforward.
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Correct. It's not... It... And it's just not that straightforward.
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It is. We call it addition, but it's a process. It's just that the addition isn't... This is how As defined by the group. It's the beauty of abstract algebra is that addition can mean almost...
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It just can mean almost anything as long as it preserves these certain properties. So the name for it is point addition.
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It's just, again, it's
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not like linear. It's not like the thing you can we can intuit from what we're familiar with. So that's why when you try to go backwards, even though you know the exact amount of times you have to do it, it's computationally
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really, really expensive to the point where Satoshi's Satoshi's
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coins are still,
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you know, those are the most barest. Right? The straight p to p k, the ones that everyone knows is quantum vulnerable
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modulo
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game theory of,
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you know, the game theory of whether someone would actually expose that they could crack them. Yep.
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They're still there.
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So, like, after all this time and all these attacks, those are still there. It's it's come and take it thing. Right? So this is why we say it's very hard to go backwards in time. This is when I get tripped up mathematically with this p equals n p concept because I feel like we have a process in Bitcoin that's trivial, easy to verify, but almost impossible to go back in time. It's
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like the basis of cryptography,
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right? Correct.
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Yeah. That concludes my interruption.
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Quite okay, right? And so we had, and I'm just pulling up the slides here.
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We're kind of...
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You'll have to all indulge us listeners where... Since we have a panel
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later Are you sharing your screen and redoing this on YouTube? Not sharing my screen. Okay. I could. I'm just pulling up.
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Do do we,
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should we do that? Let me rearrange my screens real quick. I'm wearing a stupid hoodie, but whatever.
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I love it. I love this hoodie. Let me Looks stupid.
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Let me pull this up here
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and
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present
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slide format.
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How do I... Oh, I just hit the slideshow button. Here we go.
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As I'm pulling this up, I shut out now. Yeah. Oh, entire screen. I'm I'm gonna have to... Oh, no.
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Wait. Let me see if I just do a window then. Can I just share a Chrome tab? Perfect. Okay.
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I have had... So I have done this before with a GitHub. Well, was gonna do the entire screen, it requires a different setting. Right?
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Yeah. Yeah. So I just... I'm just sharing this one's tab and then we're good. Perfect. You're able to see my
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Cool.
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So
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this was the original draft. We're gonna have to update this now,
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because I think the exponential time hypothesis is relevant to it because it's actually something pointing to
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the general understanding of this. But OpenAI prompting my clanker as you speak when you say it. Perfect. Yeah. Yeah. Right? That that... We're just gonna feed the podcast transcript into the clanker to make a new version of this. Right? So the initial event was all of these, papers that came out with new mathematical proofs.
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And everyone's,
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observation was, wait a second.
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There's nothing really cryptography related in any of this. It's kind of like, what the hell is going on there? Like,
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which everyone kind of viewed the absence of any cryptography stuff as proof there was cryptography work being done. That could be a time. It's just a matter of time. Right. It just... We love to extrapolate,
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especially in this AI game. It's been going on since, like,
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since,
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you know, the last two and a half years.
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Yeah. This like, oh, you know, we show these massive improvements and only so that we can extrapolate and say, well, guess what then? Wait till you see the, you know, the next.
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Watch out for this progress.
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Right. And so it was kind of annoying.
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I got I got annoyed by people talking about the cryptography breaking, but no one was actually talking to, like, what means and mechanisms
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would actually be tied into that. Right? And so we wanted to kinda harden up a little bit. So we got our our our buddy here, libsecp,
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secp two fifty six k one. And I know we may have some audio only listeners. We're just going through some basic slides. You're not missing too much,
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of why we use this curve.
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We
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mentioned that it's a cobblets curve.
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And
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one of the hypothetical ways that this could be weakened is that because it's a cobblets curve allowing for faster verification, in a world with faster verification, does it actually allow you to quicker walk backwards to break the curve itself? Mhmm. And,
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we talk about Pollard's row, which is kind of like the naive way if you were to be able to,
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optimally with an algorithm kinda find a more efficient path, the best you could do today is a square root, which is still a 128 bits of entropy, which is still very, very strong.
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And the Just in contrast in contrast, the Yeah. Like, just in contrast, the Call Card m k fours are well below that, and those have still not been moved.
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I think they're just starting to get moved. Right. Like, as of as of the past, like, week or something. I'm hearing people a... Just a a tangible way to kind of
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see what takes. The MK four was somewhere or somewhere between fifty and seventy. I never went and did the final, like, backwards, like, final math. But,
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the difference between that and, like, the But we're three months away from an already triggered, already signaled attack, and yet... And they're only now Right. And they're only now Because the original ones were, like, 20 to 32 bits. Right? So just talk... Go from 20 to 32 to go to 50 to 70 is, like, you're talking like, okay.
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It's gonna take a lot of extra time. Right? Let alone if you do that again and again and again because every bit is a doubling of the space,
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it meaningfully gets, like, complicated.
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And then we had kind of, like, these six high level
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pieces
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of the puzzle for red teaming it. Right?
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Being able to do some basic point factoring. Could you look at this curve itself and find ways to factor to break it down to kinda go faster?
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This doesn't really have any much related to...
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For the... You know? This... The two... I I see you're struggling with two. I would just say two, the... What you call the miner's attack. Oh, the miner's attack. Yeah.
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This was being able to find minor matrices
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being able to...
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Basically, if you could find it through the miners where you could find... What was it? The determinant was zero, which meant that it it wasn't ortho... Like, wasn't orthogonal. If you're talking about linear algebra, if you were able to find a minor matrices of the points in which you were able to basically collapse the complexity,
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it'd be a way to kind of further accelerate your way of doing it. Because if the determinant is zero,
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for whatever n dimensional space you have for your matrix, If the determinant is zero, it means that it's actually expressible as a smaller form.
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Right. I would basically collapse that out. I was gonna say, like, I would look at that similar to I would... The way I would look at low entropy
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where Yeah. Right? We thought this thing had
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the full dimensionality
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set of Correct. Like its design, but it turned out it didn't. It... Right? This would be if the existence of miners
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would tell you that
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we... I don't have 256...
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Two to the two fifty six dimensions,
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orthogonal dimensions. Right? I have maybe a lot less. I got a lot of questions in the last three weeks
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Yeah. Of this nature of
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is...
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Like, what is AI actually doing in these attacks? Like, is that... You know? Right? So... Because people want Yeah. There's this collapsing
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of concepts like that AI is going to actually break the cryptography
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Or what is the division of labor here?
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Right? May... Maybe it's AI finds the weak underbelly of... Finds the blubber in the way... You know, in the whale's underbelly. Mhmm. And then it's still up to compute.
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It's still up to compute. It's like, we have Shor's algorithm. We don't need... We don't even need AI to crack it. Right? Right. Well, Shor's needs quantum computers. Right? Correct. So... But we don't... Like, so, like... And this goes back to our conversation with Riordan where there's a math, physic... Physics, and engineering problem.
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Right. Where is AI... Like, you know, is AI strictly still in the math realm? I think AI is explicitly
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ruthlessly
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checking every single mathematical hypothesis
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in the cathedral of our total sum human knowledge and finding out where there's gaps in there. Like, for, like, exponential time hypothesis,
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there's been hundreds of papers written and published on, like, computer science and theory assuming that it's true. Yeah.
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Right? So, like, this is basically doing, a leg sweep on one of those foundational bricks and being like, maybe it's not. Right? Maybe for the exponential time hypothesis, it's like it's
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it's sub exponential,
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but it's not polynomial
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time yet.
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So this is one of these things where
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we're seeing that there is a point lower than the assumption. The question is is how far down is it gonna collapse and go? We don't know yet. We actually saw
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a version of this.
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I think we've seen a couple versions of this with... That was it with linear
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multiplication,
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like, three... Like, a month ago when the linear... Like, we were able to find efficiencies in linear multiplication.
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It was, like, a fractional hair less than the assumption. And then over the coming weeks, it kept getting beaded down lower and lower and lower because you start finding, like, new ways to break through.
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I think we're going through some of... Something similar to that right now with exponential time hypothesis,
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where we don't know where the floor is.
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It's still hard.
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It's not polynomial
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base time. If it was polynomial time, then, like, this all falls apart.
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Okay.
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Yeah.
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Beating the generic bounds was we had, like, the third door.
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This is probably the one that's most straightforwardly linked to the exponential time hypothesis, if you could just find a more generic way to be able to degrade the security of the curve.
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You know, Schoop's bound remains valid for generic algorithms.
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Right. We have to kind of go outside our own knowledge and assumptions right now for how that works.
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And
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to disprove it... Not to disprove it, it has to still beat existing no knowledge around discrete log methods, which we don't have anything yet there.
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You were alluding... Yep. Sorry. What you were alluding to before is that if there's a faster way to get to the brute force
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Yeah.
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That's...
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And I think that's what people seem to be worried about with AI, but it's good to distinguish
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that. I I like to think of it a... Like, AI identified
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the weakness, the entropy weakness that allowed the cold heart attack hap... To happen, but it didn't do it. It still had to grind still had to grind. There still was an amount of work that had to be done.
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The question is, is if you were to get reduced security, how much grinding is done? Right? We have two fifty six bits,
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you know, with... It's like It's heat seeking, it's more of the
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radar, it's not the payload.
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Yeah. And so, like, with Shukesh Bound, we already have a square root of it. We're already at one twenty eight, and we've been totally fine with that for
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Which... And I think which... And I think you said because, like, there's...
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There are many algorithms that get us to one twenty eight.
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Mhmm. Right? There's the Paul Droe.
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There's, you know, the birthday paradox. There's, Shanks.
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Yeah.
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And there's Shoops.
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Right. I feel like the Moops.
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Right.
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And then we got There's the shores.
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Shores and then there's shoops. There's a bunch of different ways. That's right. That's right.
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We gotta get the Seinfeld... We gotta get the guy making those Seinfeld videos to do one of those. Yeah. Shores and shoops. Yeah. Shores and shoops. Oh, that'd be a good one. Yeah. Yeah. Yeah. Next,
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we have the cobblets curve symmetry, which I talked about already. We've talked about during our sec p 10 episode miniseries about,
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a cobblets curve where,
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the fact that a is zero in the
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curve for sec p two fifty six k one. That's why it's just y squared equals x cubed plus seven. There is no a squared or anything in there.
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A zero meaning it's really... Like, y squared is a x cubed plus b x squared plus c x plus d.
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Yep.
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Sorry. I can't screw that up. Yeah. But there is no x squared factor. That's The wire stress
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version now has x... It's x cubed plus now,
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like an a x squared plus b x.
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There you go. So, anyway, not to get... Not to actually add that too much, but you... The whole point is it's x... There's no coefficient around an x squared term, and there's no coefficient
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around an x term. It's just x cubed plus seven.
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Yeah.
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Correct. And
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then
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one we have smooth curve lifting mapping the problem to a different field. Before you move on smooth curve lifting, which I just, you know, you
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bring in sort of... You start bringing in lean in the Cobbler's curve symmetry I see here.
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Do I start bringing lean in?
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Or at least my clientele did. Oh,
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Yeah.
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I think your clanker did. So someone did a proof that basically,
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in theory, I think the efficiency that's gained from a cobblets curve,
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that it it it preserves both ways, basically. That it being a cobble... The the efficiency and computation survives both ways in theory.
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We... Maybe we could round out these. We could talk a little bit about lean because there's a couple of lean topics to bring up next. Yep.
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Smooth curve lifting. Right?
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I'm pulling up my article now because I went into this a little bit in there.
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The
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the idea behind lifting
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is that we usually picture elliptic curves as smooth curves over the real numbers. Cryptography uses a finite set points across that finite field.
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Could we connect that finite field problem to another arithmetic setting with better tooling?
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So the strategy is around lifting the corresponding curve points of rationals or the number field,
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and preserving all of that data. And the hope is that we'd be able to,
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by basically removing...
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By changing the field in which we're evaluating the problem by doing a transposition,
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would we be able to use,
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other
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fields of math, whether it's,
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geometry or whatever else, to be able to evaluate this in a way that we could actually find
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reductions. Basically, by changing the domain in which we evaluate the problem, can we find shortcuts elsewhere and then push it back to the finite field to basically accelerate computation.
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To which I think isogenies
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is in the same family of that. It is. Yeah. And so like an isogenies, like a cousin curve almost
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where
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you'd be able to look at a different curve and find reductions there. The thing is though, is for it to actually apply, you can't, you have to kind of maintain all of the security properties of the cousin curve for it to actually be useful.
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But that would be the same. A curve as we know is nothing more than a representation of finite field.
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Yeah. Modulo p. Right. And just that you can't, like, switch it out for a curve that has, like, a much smaller,
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factor group. Right? You can't, like, shortcut it No. That It has to be isomorphic.
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Right? Exactly. Exactly.
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Or it has to be something morph. It has to be something morphic.
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Not sure it has to be isomorphic,
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but it probably does.
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Yeah. Yeah.
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This is where we need this is where we need Jonas and people of that ilk to bridge... Just help us bridge the gap. Help us understand that. Yeah. I I just jumped over to the next slide.
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Yep.
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One way functions, which in this case we talk about are usually hashing algorithms
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Yep.
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Fall into a little bit of a different
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domain
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than
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elliptic curves.
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Yep.
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It's another thing to continue to distinguish that there are two... There's two cryptographic primitives to worry about. Not... They're not... You know?
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Bitcoin relies on two cryptographic primitives. If you... People view... Tend to view it as a single point of failure, this thing called cryptography,
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this library called sec p, but there are really two primitives.
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Yep. One operates the Bitcoin network and the other really kind of operates
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humans keeping a secret.
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That's right. So you have elliptic curve cryptography for basically the private,
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the property ownership within Bitcoin.
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And then you have SHA two fifty six, which is for the proof of work and maintenance of the Byzantine Generals Problem Solution,
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Nakamoto Consensus,
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as the general thing. You also do hash addresses
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when you put them on chain. So you actually,
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in some ways, get a little bit of protection there.
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And then we have our final defense here, p versus n p,
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as the ultimate backstop. So with the exponential time hypothesis,
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platform three is the one at the moment. We're seeing a little bit of,
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I wouldn't even say shaky or instability, but just open questions now of where that ultimately ends up.
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So with... Yeah. Without fully really understanding
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the distinction between
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three and two,
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like, there... In my mind, you know, my stupid brain is looks like, well,
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we can't go... I always had it like, oh, we can't go backwards, but mostly because of discrete log hardness.
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Right. But this p versus n p is sort of a new player. Discrete log problem is part of the p versus n p, p equals n p p n p problems. There are many problems that Right? Are PNP
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Yeah. And so the discrete log problem is in that bucket of things that are PNP hard. So when P... If if...
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Okay.
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Yeah. Okay. So the question though is in the... In this mathematical arena, what is being argued? You know, what is,
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like, what is at stake with this PE versus NP?
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You know what mean? Basically, mean, it's like every... Like, think of like, they're just fundamental problems that are seen to be so complex that for you to be able to find the optimal solution that it requires exponentially more and more amounts of compute. A very simple one would be the traveling salesman problem.
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Right?
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You are traveling... Have you heard of the traveling salesman problem? Nope.
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Yeah. Perfect. So, traveling salesman problem
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is this idea that you have a list of cities and distances between each pairs of the cities, and what's the possible... Shortest possible route of visiting each city once
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and returning to the starting city.
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Now for three cities, that may be okay. For 10 cities, that's okay. Or for a 100 cities, you may be able to figure it out. But once you get larger and larger and larger, the actual computational overhead
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to solve this is
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PNP hard.
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I see. I see.
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But now the idea though is that if you were able to
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show that P equals
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NP, that any problem... That would be like the most extreme. Like in polynomial time,
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anything that you could trivially verify
409
00:31:55.855 --> 00:31:58.175
is something that you would be able to
410
00:31:58.519 --> 00:31:59.559
actually prove,
411
00:31:59.799 --> 00:32:01.399
that you'd be able to compute the answer,
412
00:32:02.120 --> 00:32:14.645
that is ultimately what we're talking about. Is that anything that could be verified can also be computed and figured out in real time. So we're banking on them not equaling. We're banking on this asymmetry. I mean Yeah. Like whole cryptography.
413
00:32:14.645 --> 00:32:15.205
If
414
00:32:15.765 --> 00:32:19.445
we're living in a post P equals NP world,
415
00:32:19.765 --> 00:32:20.164
like
416
00:32:20.645 --> 00:32:29.789
everything changes, like the ability to like do a cure to cancer. Because if you can verify, oh, I've cured cancer, then you should be able to trivially actually solve the cure to cancer.
417
00:32:30.910 --> 00:32:33.470
Right? Like everything, like that is like the
418
00:32:34.750 --> 00:32:37.070
post abundance AI space communism,
419
00:32:38.965 --> 00:32:41.125
everything is just We don't need cryptography
420
00:32:41.125 --> 00:32:46.325
because we live in such a wonderful world that Yeah. Like it Everything is infinite. Right. And so
421
00:32:46.885 --> 00:32:58.559
what we're seeing right now is just an initial, it may not be as hard. It doesn't mean that everything goes straight to P equals NP. You could still have them. Right. It hadn't clicked for me that P equals NP means the end
422
00:32:58.880 --> 00:33:00.720
of cryptography. Like that now
423
00:33:00.880 --> 00:33:03.599
clicks. It's the asymmetry that
424
00:33:04.640 --> 00:33:05.440
we rely on.
425
00:33:06.184 --> 00:33:06.985
Yeah,
426
00:33:06.985 --> 00:33:08.105
like that's
427
00:33:08.585 --> 00:33:11.065
a way of thinking about it. And I think also though,
428
00:33:11.385 --> 00:33:16.424
there are certain things like a hashing function where you collapse everything down to,
429
00:33:16.665 --> 00:33:18.424
you know, two fifty six bits
430
00:33:18.960 --> 00:33:23.999
that if you can collapse anything down to two fifty six bits, you're not gonna be able to fully reverse engineer
431
00:33:24.480 --> 00:33:26.239
the entire hashing function
432
00:33:26.400 --> 00:33:29.919
because it's just the amount of, like, raw space compute would just be
433
00:33:30.240 --> 00:33:32.640
too complicated. But in in a way, though,
434
00:33:33.455 --> 00:33:36.735
I even saw in the past week that SHA-two 56
435
00:33:37.695 --> 00:33:38.495
regularly
436
00:33:38.815 --> 00:33:42.174
gets like updates of people finding weaknesses around like
437
00:33:42.895 --> 00:33:45.774
the multiple rounds that happen in the hashing algorithm,
438
00:33:45.935 --> 00:33:46.815
they find weaknesses
439
00:33:47.510 --> 00:33:53.910
like, within the middle of that, right, that can kind of, like, accelerate and make things go faster. We're nowhere near reverse engineering all
440
00:33:54.390 --> 00:34:05.534
of the hashes. But it might make sense... So the... I'm gonna I'm gonna attempt to thread a needle here, but given how much work we've done on this podcast. But, like, when we talk about, again, the two primitives,
441
00:34:05.535 --> 00:34:06.654
ECDSA
442
00:34:06.735 --> 00:34:14.415
and hashing functions. Right? And we've said that ECDSA is intentionally... Has to be an isomorphism because the inverse isn't necessary
443
00:34:15.119 --> 00:34:16.000
necessary
444
00:34:16.079 --> 00:34:23.599
to be able to find your private key from a public key. Right? Very Yeah. Super, super important words. A hash function is the opposite. A hash function,
445
00:34:23.760 --> 00:34:24.960
it's a semigroup.
446
00:34:24.960 --> 00:34:26.160
There's no inverse,
447
00:34:27.039 --> 00:34:29.039
and, it's not an isomorphism.
448
00:34:29.205 --> 00:34:32.485
Right? It's Mhmm. A different type of morphism. And so
449
00:34:33.205 --> 00:34:37.365
p equals n p may really crush isomorphisms
450
00:34:37.365 --> 00:34:37.845
without
451
00:34:38.405 --> 00:34:40.325
having the same impact on
452
00:34:41.045 --> 00:34:42.645
whatever kind of morphism
453
00:34:42.645 --> 00:34:43.685
a hash function is.
454
00:34:45.180 --> 00:34:46.060
Meaning,
455
00:34:46.060 --> 00:34:53.820
if the... An inverse exists, it's gonna be... P equals m p is gonna crush it. It's right per... Perhaps. Whereas may... It may be not as
456
00:34:54.300 --> 00:34:55.260
ruthless
457
00:34:55.260 --> 00:34:56.060
on
458
00:34:56.875 --> 00:34:59.515
on a hash function where there is no inverse.
459
00:35:01.995 --> 00:35:11.755
Stuff from my clanker maybe to sort through. And and have it chew on. Yeah. But, I mean, this whole thing, we say p equals n p. What is the scope of that? So there's...
460
00:35:12.155 --> 00:35:16.930
I think it's actually important to call out because we actually, on the previous slide, we had something... A little shout out to the
461
00:35:17.329 --> 00:35:20.530
generalized Riemann hypothesis, right? And so these
462
00:35:20.530 --> 00:35:27.329
are related, but they are different, right? So exponential time coming from, like, the computational complexity of a problem. And the question is, is,
463
00:35:28.105 --> 00:35:34.265
being able to solve these logic problems, can they hap... Like, the three set problem. Have you seen actually the...
464
00:35:34.665 --> 00:35:37.705
Damn. I should have started here. This feels like graph theory...
465
00:35:38.425 --> 00:35:42.105
Kind of standard graph theory stuff. I'm not... I have not studied graph theory,
466
00:35:42.265 --> 00:35:49.500
but Kayla's studying it right now, so we talk about it. But there's this... Like, the, like, the three color problem or the four color problem. Yeah.
467
00:35:49.980 --> 00:35:51.260
That... Did you see...
468
00:35:51.900 --> 00:35:53.580
I I should have linked this to you ahead of time.
469
00:35:56.454 --> 00:35:57.255
The...
470
00:35:57.575 --> 00:36:03.175
Basically, like, the idea of, like, a three set problem and how that's related to the exponential time.
471
00:36:04.694 --> 00:36:07.895
I have not. I should have sent you this. Yeah. So,
472
00:36:09.660 --> 00:36:15.500
like, if you take... I'm trying to think the best way to do this on a podcast with a lot of audio listeners.
473
00:36:18.220 --> 00:36:23.995
Is ripping. Because look If you have, like... If you have a super basic set of A or B or C,
474
00:36:25.035 --> 00:36:29.035
right, that's pretty... You could look at it. It's pretty quick to figure out and verify,
475
00:36:29.115 --> 00:36:33.035
right? But if you expand and What's that? Sorry. What's quick to verify? Like,
476
00:36:33.435 --> 00:36:35.435
what conditions make it true and satisfiable?
477
00:36:35.710 --> 00:36:37.310
A or B or C.
478
00:36:37.710 --> 00:36:44.350
Okay. Like, that's pretty quick. You have any three sets and you can verify... You can answer that question. Pretty quickly. Right? That's pretty straightforward.
479
00:36:44.750 --> 00:36:49.390
But what if you had A or B or C and not A or D or E?
480
00:36:50.694 --> 00:36:52.775
It's gonna take a little bit more effort. It starts
481
00:36:53.335 --> 00:36:55.494
to get a little more hairy, but it
482
00:36:56.295 --> 00:36:57.494
feels manageable.
483
00:36:57.494 --> 00:37:03.734
And then you get to A or B or C and not A or D or E and not C or F or G.
484
00:37:04.590 --> 00:37:12.190
Right. Starts to... It starts getting more and more complicated to be able to find a true equation, right? And so that's basically
485
00:37:12.590 --> 00:37:14.030
what we're talking about
486
00:37:15.150 --> 00:37:19.630
with this trivial ability to go one way or both ways. Because you can basically structure a lot of problems
487
00:37:20.395 --> 00:37:21.515
in that format.
488
00:37:22.395 --> 00:37:25.915
It's the most abstract end of it, right, but a three set problem.
489
00:37:26.315 --> 00:37:32.235
And that's what they were finding out with these proofs that they were able to actually... Following proofs that were able to solve this stuff in sub exponential time.
490
00:37:32.475 --> 00:37:34.555
It's not polynomial time, but it's sub exponential.
491
00:37:36.170 --> 00:37:40.970
And it's about finding general faster computer algorithms. And just, again, for the generalists
492
00:37:40.970 --> 00:37:44.730
out there, exponential time is bigger than polynomial
493
00:37:44.730 --> 00:37:48.089
time. Yes. Right? Polynomial time is sort of linear.
494
00:37:48.825 --> 00:37:57.145
It's not quite linear. It's more... It's not... Well, in one dimension, it's linear. In two dimensions, it's quadratic. Like two to the end. Two to the end. Right?
495
00:37:57.545 --> 00:38:02.025
So... But then, yeah, exponential just about what powers are doing in polynomial
496
00:38:02.025 --> 00:38:04.810
time. Polynomial time is like book powers. So
497
00:38:05.609 --> 00:38:13.369
what we had though, like with this, what they were able to find was that in some... It went from two to the n to like 1.3 to the n. So it's still exponential,
498
00:38:13.369 --> 00:38:27.255
but like it's a smaller base that you're exponent on top of. So it's... And very... How quickly does two to the n versus 1.3 to the n, how quickly do those start diverging in their sizes? And that's the thing. So, like, the the the thing I just thought about was the
499
00:38:27.895 --> 00:38:28.775
harmonic series.
500
00:38:30.000 --> 00:38:35.280
Right? There's... You guys know what harmonic series is? It's the sum of one over n where n is,
501
00:38:35.760 --> 00:38:38.240
you know, zero, one, two, three, four, and
502
00:38:38.720 --> 00:38:41.520
that series is known to diverge.
503
00:38:41.600 --> 00:38:45.440
Right? That series is known to diverge very slowly. But then the question is,
504
00:38:46.505 --> 00:38:49.305
what if you raised end to a certain power?
505
00:38:50.185 --> 00:38:51.385
Right? Yeah.
506
00:38:51.705 --> 00:38:59.545
It it then converges. I mean, it's so slowly, like, could never ever observe it. But it's like there is a moment. There is a power
507
00:39:00.030 --> 00:39:18.955
where... And it's on... Like, this is where math gets into some funny areas where it's not so straightforward because it almost looks like... Like, I look at it like, asymptote crossing. There's just some, like... It's weird. It's almost like there's, like, some touch of god going on where the whole fucking state changes. Yeah. Whole state of the world changes. Yeah. Yeah.
508
00:39:19.915 --> 00:39:32.160
I... And just because I know we have a... Our dozens of listeners who I I accidentally misspoke. It was not 1.3 to the end. I was looking at a different example. It went from two to the end to... It's now two to the n divided by log of n.
509
00:39:33.760 --> 00:39:38.720
Right. Sorry, the square root of log n. Square root of the log of the n. So
510
00:39:38.960 --> 00:39:41.760
we've gone from two to the n, just pure exponential,
511
00:39:42.234 --> 00:39:44.475
to two to the n
512
00:39:44.555 --> 00:39:45.835
divided by
513
00:39:46.155 --> 00:39:47.915
the square root of log n.
514
00:39:48.315 --> 00:39:48.955
Okay.
515
00:39:49.115 --> 00:39:51.595
So it's still... It's like
516
00:39:52.635 --> 00:40:01.610
sub exponential because it's not just a straight exponent, but like still linear polynomial. It's on the side of the asymptote that it's still essentially It's
517
00:40:01.610 --> 00:40:05.930
basic. It might as well be exponential. It as be exponential because it's... That's where...
518
00:40:06.410 --> 00:40:12.905
Like, the world hasn't changed. That's the whole thing. There is this... The question we're worried about is asymptote
519
00:40:12.905 --> 00:40:13.625
jumping.
520
00:40:14.105 --> 00:40:19.545
Going to the other side. Yeah. And we go from something that... Yes. That that just completely...
521
00:40:21.305 --> 00:40:26.100
This this thing of convergence versus divergence is one of those things where it's like
522
00:40:26.580 --> 00:40:27.540
everything
523
00:40:27.620 --> 00:40:30.260
you knew about the world does change. Right.
524
00:40:31.620 --> 00:40:36.020
That's It's like zero to one or one to zero. It's an infinite it's got the infinite
525
00:40:36.135 --> 00:40:38.855
to finite. It's basically an infinite to finite
526
00:40:39.415 --> 00:40:40.615
Right. Transformation.
527
00:40:41.335 --> 00:40:42.055
Right.
528
00:40:43.815 --> 00:40:47.335
That's what we're saying. Like... So what the news is
529
00:40:49.210 --> 00:40:50.010
exponential
530
00:40:50.250 --> 00:40:52.570
got less exponential. It's still exponential.
531
00:40:52.570 --> 00:40:54.090
It's
532
00:40:54.090 --> 00:40:56.890
gotten closer to the asymptote, but okay.
533
00:40:57.370 --> 00:40:57.930
Right?
534
00:41:00.490 --> 00:41:05.815
Yes. It's still in orbit. It's still doing what, like, it's supposed to be doing.
535
00:41:06.694 --> 00:41:11.575
That's right. We don't know is if we get closer and closer to this asymptote,
536
00:41:11.895 --> 00:41:14.135
is something gonna happen where we actually jump it?
537
00:41:14.934 --> 00:41:15.575
Right.
538
00:41:15.974 --> 00:41:16.454
Right.
539
00:41:17.310 --> 00:41:18.750
And it...
540
00:41:18.750 --> 00:41:40.535
In this question, I think it's correct for there to be a large number of people in the world to say, don't wanna take that chance. I wanna figure I wanna figure this out. I wanna I wanna prepare the world as though that's gonna happen because I'm worried that that's... You know, I can I can respect that completely? And I'm kind of like, that's part of why I want to continue to have this conversation, right? I want to be able to understand
541
00:41:40.535 --> 00:41:41.815
people that
542
00:41:42.454 --> 00:41:43.974
want to prepare for that world.
543
00:41:44.454 --> 00:41:46.535
For sure. Let's change it up a little bit.
544
00:41:47.990 --> 00:41:51.670
So I was talk... I was chatting with, Jonas in Lugana,
545
00:41:51.750 --> 00:41:53.430
and he showed me this sig.golf
546
00:41:53.430 --> 00:41:54.390
website.
547
00:41:54.869 --> 00:41:58.150
Okay. And so there's a team of Ethereum researchers right now,
548
00:41:58.549 --> 00:41:59.590
which are doing,
549
00:42:00.869 --> 00:42:01.670
shrink
550
00:42:01.829 --> 00:42:02.390
based
551
00:42:02.635 --> 00:42:07.275
hash based signatures on Ethereum while they're exploring Is Koblit one of these people?
552
00:42:07.595 --> 00:42:08.875
You know, Neil Koblit? Because
553
00:42:09.275 --> 00:42:13.115
Koblit is at the Ethereum Foundation. That's a good question. Yeah. I don't know offhand.
554
00:42:13.595 --> 00:42:17.915
In collaboration with the Ethereum Foundation. So if he's at the Ethereum Foundation,
555
00:42:18.740 --> 00:42:22.420
very fast. Cobblets starts following us, that's when I think we start
556
00:42:22.980 --> 00:42:24.980
That's when we made it. Yeah. Okay. We made
557
00:42:25.780 --> 00:42:26.260
Yeah.
558
00:42:27.940 --> 00:42:28.820
And so,
559
00:42:30.260 --> 00:42:38.485
Jonah showed this to me because what... The way this works, like, it's a competition, right, for making these hash based signatures smaller and cheaper to verify.
560
00:42:39.765 --> 00:42:44.885
K. It's trying to basically leverage these AI tools, which are really good at grinding and finding efficiencies
561
00:42:45.285 --> 00:42:52.300
and being able to get outcomes. And I think this is where a year ago... I think I think the term slop
562
00:42:52.700 --> 00:42:55.260
is gonna be a dated term for a moment in time.
563
00:42:56.060 --> 00:42:58.140
Slop was a transitionary point
564
00:42:58.300 --> 00:43:02.460
of the ability of these models to do interesting, powerful things. And
565
00:43:03.035 --> 00:43:06.315
with the rate of accelerated improvement we keep on getting with these,
566
00:43:07.515 --> 00:43:26.200
we're at a point where a year from now, I think slop is gonna be... Slop is just gonna be the fact that you didn't even put any effort into thinking about how to guide the models. It's not because the models are slop. Right? The slop will become you because you're not actually steering this stuff. I actually... You and I... I'm sure you're gonna agree with me on this, but I think this idea of
567
00:43:26.440 --> 00:43:32.119
figuring out how much we can do without putting any thought or effort into it is an important stage.
568
00:43:33.355 --> 00:43:40.475
Yeah. Oh, for sure. It's an interesting check on the strength of the tooling itself. Right? Like, what... At what level is it autonomously
569
00:43:40.475 --> 00:43:41.595
always correct
570
00:43:41.755 --> 00:43:53.250
without having to worry about, having to monitor and, like like, shepherd the model and steering on. It's Good to understand the baseline of what anyone in the world can do with, you know, a computer and enough
571
00:43:53.650 --> 00:43:55.970
KYC to get a AI subscription.
572
00:43:56.210 --> 00:43:57.490
Right. Right.
573
00:43:58.290 --> 00:43:59.890
And so this
574
00:44:00.355 --> 00:44:01.955
this tool basically
575
00:44:01.955 --> 00:44:12.755
are everyone's grinding over the existing proofs. And basically when you post a new proof that's more efficient, everyone gets to see it. So everyone gets to kind of like keep on charging forward in the progress of this.
576
00:44:13.779 --> 00:44:16.260
So it's like a bit of open source where...
577
00:44:18.579 --> 00:44:21.140
I think in the terms of the velocity of training
578
00:44:21.539 --> 00:44:26.500
the model, it accelerates it greatly because you can stand on shoulders real much quicker.
579
00:44:27.705 --> 00:44:28.345
That
580
00:44:29.625 --> 00:44:32.105
you're getting... Assuming that like the quality
581
00:44:32.425 --> 00:44:39.065
of these proofs is improving as we continue to work on it. Yeah. This reminds me of like... Have you ever heard of Kaggle competitions?
582
00:44:39.465 --> 00:44:53.400
Yeah. Yeah. Yeah, where everyone would get an open source dataset and you wanted to see how well you'd score based on a blinded test set? And the reason why I mentioned that is when I first started thinking about this, you obviously can keep on grinding and get incremental improvements, but you can see the curve here. It's kind of plateaued.
583
00:44:53.975 --> 00:45:01.175
I openly wonder, just looking at this, like, right here. Like, we basically had a... Like, every, like, five seconds, we were getting a new improvement, getting a new improvement.
584
00:45:01.415 --> 00:45:03.815
And then, like, we got one on the
585
00:45:04.455 --> 00:45:06.535
20 you the models, think. The nineteenth.
586
00:45:06.615 --> 00:45:09.580
Yeah. On the nineteenth, the twenty second, the twenty fifth,
587
00:45:09.820 --> 00:45:14.380
we got a burst overnight, actually. On the thirty first to the first, we got a small little burst update.
588
00:45:14.540 --> 00:45:19.660
It makes me wonder, though, is this kind of current efficiency, is this like a local minima?
589
00:45:19.965 --> 00:45:22.365
And if you actually took a huge step
590
00:45:22.685 --> 00:45:24.765
back, could you find a more efficient
591
00:45:25.245 --> 00:45:29.325
local min... An actual optimal maximal minima elsewhere?
592
00:45:29.405 --> 00:45:47.145
If you're just... Because everyone's kind of looking at the most recent result and trying to iterate on that. If you're thinking about, like, multidimensional space and, like, the efficiencies you can gain, are we, like, in a local rut with this specific one where if you just kind of, like, tear everything apart and start it from the beginning again, could you actually find a different better path? That's just, a random thought looking at this. But Or
593
00:45:47.705 --> 00:45:50.985
is this like... Do do... Are academics now gonna monitor
594
00:45:50.985 --> 00:45:51.625
these
595
00:45:52.025 --> 00:45:56.745
and say, okay. This is now... Now it's time for me to... Oh, look. You're in there.
596
00:45:57.305 --> 00:45:57.945
Like,
597
00:45:58.265 --> 00:46:04.520
you know, now you look at you Hey. Look. I am in there. With with DeepSeek v four. Look at that.
598
00:46:04.760 --> 00:46:05.800
Look at that.
599
00:46:06.119 --> 00:46:08.360
Wasn't using DeepSeek v four.
600
00:46:08.599 --> 00:46:11.799
That was a good little... Let's see. Where where am I on the twenty seventh?
601
00:46:13.734 --> 00:46:14.695
There's me.
602
00:46:16.454 --> 00:46:19.255
Look at that. I did it with DeepSeek too. That's great.
603
00:46:20.055 --> 00:46:27.494
This this is not me learning on the podcast because I set a clanker to just autonomously do this with, like, many sub agents, and then I left my computer on and walked away.
604
00:46:28.320 --> 00:46:40.160
But... So, like, I mean, I wonder if somebody like Neil Kobla, somebody who... The the... Some... These grand poo bars, somebody like Jonas is like, they they do these... They want these things. They want people to participate. And then they're like,
605
00:46:40.825 --> 00:46:48.665
once it gets to a certain level and the public can't approve it anymore, really, that's when I'm gonna stand on its shoulders and really beat the shit out of this.
606
00:46:49.465 --> 00:46:55.625
Yeah. Well, I I think it's interesting. Right? And so for Bitcoin, one, as a point of pride, it'd be awesome if
607
00:46:56.330 --> 00:47:11.530
a Bitcoiner won this competition in the end just just because he could. Think that... I think that's a great place What's winning? What is the goal here? Well, how is... Oh, this is this is interesting. Right? So the scoring works here. You're trying to get the lowest score possible, and it's taking two different things. It's taking the size of a signature,
608
00:47:12.974 --> 00:47:14.095
and it's taking,
609
00:47:14.815 --> 00:47:17.215
the amount of computation to verify.
610
00:47:21.055 --> 00:47:35.920
My memory of Jonas's presentation at OVNEXT, which is now a long time ago, is is that that... Yes. Now I'm remembering what Trinx does. Any ordinary instruction is one cycle. Multiplication and division is four cycles. Hashing is eight,
611
00:47:36.560 --> 00:47:47.125
which, to be honest, I don't... I think that's a little bit of a shortcut. I think it takes more... More than eight CPU cycles to run a hash, but this is their rules and how they set things up. So it actually probably... You're gonna get,
612
00:47:47.605 --> 00:47:49.365
answers that have a lot more hashing
613
00:47:50.900 --> 00:47:52.820
because you're not properly
614
00:47:52.820 --> 00:47:58.020
gauging the cost of doing This the is like the witness discount now. Yeah, yeah, yeah.
615
00:47:58.340 --> 00:47:58.900
And
616
00:48:00.980 --> 00:48:11.935
and there's also one cycle for every two fifty six bytes of verification, right? And so this was something Jonas showed to me, thought it was pretty cool. I got, I'm currently, I should turn on the clankers again.
617
00:48:13.295 --> 00:48:15.215
Look at this, deep seek thing for...
618
00:48:15.934 --> 00:48:17.215
Yeah, I'm just looking at it.
619
00:48:17.694 --> 00:48:18.015
Nice.
620
00:48:19.080 --> 00:48:22.600
That's okay and what... And it has like a nice little brief on like
621
00:48:23.640 --> 00:48:25.880
everything that's being done for part of this.
622
00:48:34.955 --> 00:48:37.115
Anyway, So sorry I'm just looking through now.
623
00:48:39.675 --> 00:48:43.835
It's a new kind of like interesting world where we all can kind of take our distributed
624
00:48:43.835 --> 00:48:48.395
compute. This is almost like the, folding at home protein experiment but it's actually
625
00:48:48.849 --> 00:48:51.810
very deliberately targeting this stuff. And so there
626
00:48:52.050 --> 00:48:54.130
are lean proofs on the backend.
627
00:48:56.450 --> 00:49:00.610
Which I guess we We have to should talk a little bit about now. That's I was trying to do.
628
00:49:01.255 --> 00:49:16.650
So you have to submit Yeah. People probably happy we're doing this on a different chain, right? People get all I think it's a great place to start. Well, I mean, like it's not even really happening yet, right? This is just the Ethereum Foundation doing research for asset it's based a test bed. This is a good, but it's like, some of these other chains might be...
629
00:49:16.970 --> 00:49:24.330
Now that we just went through all this hullabaloo of people doing things on Bitcoin that we don't want them to or whatever, maybe
630
00:49:24.970 --> 00:49:27.130
there is use for some of these other chains here.
631
00:49:27.714 --> 00:49:41.795
Yeah. Well, that was always the case with Bitcoin, right? The idea was that you'd be able to use other chains as experimentation playgrounds. But so there's lean proofs that specifically check the submitted proofs against the organizers definitions and establishing that all the proofs were generating signatures honestly for verification,
632
00:49:42.200 --> 00:49:47.720
that verification stays within the claimed cost and that the scheme satisfies the defined security requirements,
633
00:49:48.040 --> 00:49:50.920
and the program respects resource limits and terminates.
634
00:49:51.320 --> 00:49:55.480
So like, it's just a... They're using LeanProofs almost as like an auto... Like a Scantron autograder,
635
00:49:55.775 --> 00:50:00.015
where you submit your answer and then it goes through their proof system to validate that it's correct or not.
636
00:50:00.655 --> 00:50:06.175
Okay. And yeah, one of these days it would be nice to go through a very simple example of a lean proof.
637
00:50:08.660 --> 00:50:10.020
We should do that Yes, auto
638
00:50:11.780 --> 00:50:12.740
we should do that.
639
00:50:14.180 --> 00:50:15.860
We absolutely should do that.
640
00:50:16.660 --> 00:50:22.100
But can we do a lean proof on the square root of two is irrational or something like that? Oh, we should definitely do that.
641
00:50:24.105 --> 00:50:30.425
That would be in... That... Yeah. That'd be on brand for us. Yeah. Yeah. Very nice. Yeah. I agree. We should probably...
642
00:50:30.745 --> 00:50:33.625
I don't know. We we have a lot of, like, open items that we wanna discuss.
643
00:50:34.425 --> 00:50:39.280
Hashing functions we wanted to do. Maybe we just turn into a shrinks miniseries.
644
00:50:39.359 --> 00:50:46.640
We could do, like, a two, three episode shrinks thing and then bring Jonas on. Like, there's probably a couple of things we could do to just, like, go through this.
645
00:50:49.040 --> 00:50:53.359
But I guess maybe I should pull up... Let me set up my computer here.
646
00:50:54.585 --> 00:50:55.625
I started,
647
00:50:58.744 --> 00:51:02.585
yeah. Here we go. I started just... I had access to a bunch of compute.
648
00:51:03.145 --> 00:51:06.265
I just had access to a bunch of bunch of compute. And
649
00:51:06.700 --> 00:51:11.580
so what I did was I wanted to think about things that would be generally useful for anyone
650
00:51:11.580 --> 00:51:16.620
as a common good. So the IMIT license this. This is, BTC lean.
651
00:51:16.860 --> 00:51:27.005
I also did l... I did Lightning lean, LN lean, and I did Nut Lean for Cashew. And I just started taking all of, like, the consensus code and starting to map it out into different things.
652
00:51:28.365 --> 00:51:52.724
I gotta get this on the website. Gotta get this on the Magic Internet Math website. And so, like, a lot of people met like, Rob, what are your ambitions? Like, what do you wanna do with this? And I'm like, I I don't know. I just had a bunch of compute, so I just spun up hundreds of sub agents to start grinding this out as a community good. I don't... I've never written a Lean Proof before. You know, like, I'm I'm I'm far from an expert in it. Since these clankers are really good at it, was like, let me put it out there. Because there's, like, there's Hornet node. There is,
653
00:51:54.325 --> 00:51:55.285
what's his name?
654
00:51:55.845 --> 00:51:56.565
Adrian.
655
00:51:56.724 --> 00:52:04.325
I think it's Adrian, who's also working on lean proof stuff. Like, there's a couple of people. I think one hundred beats was doing some work on lean proof stuff. It was just more of, like,
656
00:52:05.150 --> 00:52:07.070
wanted to throw this in there. I actually,
657
00:52:07.710 --> 00:52:10.030
I met, Antoine Riyard,
658
00:52:11.310 --> 00:52:16.030
and he actually had some good feedback that I need to actually go sit down and read through here.
659
00:52:17.950 --> 00:52:19.550
He had some critiques on just, like,
660
00:52:20.705 --> 00:52:25.665
the structure of it all that I need to actually go sit down and do, but I think there's areas for improvement. I also used
661
00:52:26.145 --> 00:52:26.945
DeepSeek,
662
00:52:26.945 --> 00:52:28.065
and I used,
663
00:52:30.385 --> 00:52:38.510
I used DeepSeek mostly for all of this. So I didn't even use, like, the bleeding edge, like, leading models. So I think there's probably a lot of opportunity in area to
664
00:52:38.510 --> 00:52:39.950
improve and increase this.
665
00:52:44.350 --> 00:52:45.230
So what's
666
00:52:45.470 --> 00:52:46.190
going on here?
667
00:52:48.315 --> 00:53:00.075
So this is, an example of part of the Lean Proof. Like, this is what, Antoine talked about. I had a bunch of different rules. So, like, I had a bunch of consensus rules like BLK for block rules, and there's a rule in Bitcoin consensus talking about how
668
00:53:00.635 --> 00:53:08.920
the... A node when a new block gets found, there's two bounds in which it must maintain. One, it cannot be further than two hours of your local time node.
669
00:53:09.640 --> 00:53:11.800
Right. And that's what the 7,200,
670
00:53:12.040 --> 00:53:12.920
is here.
671
00:53:13.400 --> 00:53:19.725
And you have to also do... There's a second rule of the median... It's BIP one thirteen, which is the median time passed of the past
672
00:53:20.205 --> 00:53:30.125
11 blocks. You need to take... Your timestamp for the block header has to be greater than the median time of the past 11 blocks. This basically enforces a rough alignment of keeping track of time and honesty
673
00:53:30.530 --> 00:53:48.155
Because if you can start messing with time That's right. You can start gaming a lot and breaking Bitcoin. So these are, like, kind of, like, the hard rules in there. This is the mechanism for block... Connecting block time to actual time. Yes. And the miners are the ones who do that. It's why I was like describing that Bitcoin is an entirely endogenous system of internal
674
00:53:48.474 --> 00:53:54.954
hashing functions and signature checks and everything linking back to previous blocks and transactions. The one external input
675
00:53:55.220 --> 00:54:00.099
that is required for Bitcoin to work is time itself. And that's the role that the miners have beyond constructing
676
00:54:00.819 --> 00:54:02.579
the blocks. They also have to keep OWNS,
677
00:54:03.299 --> 00:54:05.619
accounting of the tracking of time. Yep.
678
00:54:06.180 --> 00:54:08.819
Yeah. That's why the UTC time is in every...
679
00:54:09.485 --> 00:54:12.365
Is... Right? But basically every every header.
680
00:54:12.525 --> 00:54:13.565
Yeah. That's right.
681
00:54:14.125 --> 00:54:15.965
And so there's a bunch of,
682
00:54:17.165 --> 00:54:19.245
was it the spec? No. It's the spec one
683
00:54:21.085 --> 00:54:22.045
where I have,
684
00:54:25.260 --> 00:54:28.460
oh, this is the importing all of it. I'm just doing this live
685
00:54:29.180 --> 00:54:30.780
live So in real
686
00:54:32.060 --> 00:54:34.060
you have a bunch of Bitcoin proofs.
687
00:54:34.460 --> 00:54:35.020
Yeah.
688
00:54:35.340 --> 00:54:46.065
Tried just taking all of consensus and just saying basically, like, if I were to take all of consensus Can you represent them as proofs? Is that that's what you're sort of asking that question? That's a great Right. Fucking
689
00:54:48.385 --> 00:54:49.425
like I have like
690
00:54:49.665 --> 00:55:05.000
a script that's This Bitcoin store, you're creating it. You're creating it at least like the AI agents can go to the Bitcoin store if we That's right. And so it's been actually really fun. I've been going through this, and then, Reardon has been cross checking his consensus code in our Bitcoin, the Rust Bitcoin implementation.
691
00:55:05.240 --> 00:55:07.080
And he caught a couple early on.
692
00:55:07.560 --> 00:55:08.120
And,
693
00:55:09.375 --> 00:55:10.975
so what I'm trying to do now
694
00:55:11.455 --> 00:55:16.175
is I probably need to take another pass at this with some of the clankers to update,
695
00:55:16.495 --> 00:55:18.735
you know, and have this keep on building.
696
00:55:18.975 --> 00:55:20.095
So activation,
697
00:55:20.095 --> 00:55:22.975
ledger, property, small curve, theorems,
698
00:55:25.390 --> 00:55:28.350
encoding. Oh, yeah. Have a whole mini script section in here.
699
00:55:31.550 --> 00:55:32.670
The encoding
700
00:55:32.830 --> 00:55:34.510
of base 58.
701
00:55:36.605 --> 00:55:40.765
Is, like, amazing because this... I mean, I... I'll just say this reminds me
702
00:55:41.484 --> 00:55:46.365
of what I did to verify Bitcoin to begin with just looking at the Python libraries.
703
00:55:46.525 --> 00:55:57.599
Yeah. So this one right here is just talking about the base 58 encoding that Bitcoin uses for its addresses and stuff. Yep. And it's actually encoding it into, like, a mathematical proof, and this gets fed into other things. But here's Beck 32.
704
00:55:58.079 --> 00:56:09.755
Right? So you want your addresses to be encoded reasonably. This is all of the logic that would be required for how do you encode an address. And then this proof can get fed into other things like a transaction and proving that, like, oh, I'm I'm sending two of Beck 32 address. Like,
705
00:56:09.915 --> 00:56:12.795
all of this stuff is, building blocks that build on top of each other.
706
00:56:14.475 --> 00:56:16.795
I think I have a couple here for some of the BIPs.
707
00:56:17.980 --> 00:56:20.860
Let's see here. BIPS 66 coverage.
708
00:56:21.740 --> 00:56:23.100
BIPS 66
709
00:56:23.260 --> 00:56:24.060
here.
710
00:56:24.460 --> 00:56:27.980
It's the DARE encoding, I believe. Yeah. Check sig.
711
00:56:28.140 --> 00:56:36.475
Okay. Check multisig verify. And it just goes into like the actual sig length and all of like the dimensions and the shape and size of these signatures.
712
00:56:38.075 --> 00:56:44.875
And then a couple of test examples to prove that they do work or they don't work, right? Just kind of like unit testing to kind of like get added onto it.
713
00:56:46.150 --> 00:56:48.950
Oh my God, I'm so bringing this into
714
00:56:49.510 --> 00:56:55.510
magic internet mass. I added this one Oh, as a this is gonna be great. Do you know BIP42?
715
00:56:56.310 --> 00:56:58.630
Not personally, no. BIP42
716
00:56:58.630 --> 00:57:00.070
is like my favorite BIP.
717
00:57:01.535 --> 00:57:02.735
What do we got here?
718
00:57:03.135 --> 00:57:06.015
Fundament monetary. So it was proposed on
719
00:57:06.415 --> 00:57:08.735
04/01/2014.
720
00:57:09.375 --> 00:57:10.015
So
721
00:57:10.415 --> 00:57:11.935
everyone would think it was a joke?
722
00:57:12.495 --> 00:57:13.375
It's
723
00:57:14.735 --> 00:57:15.455
technically real.
724
00:57:17.400 --> 00:57:19.240
And it's technically a soft fork.
725
00:57:19.560 --> 00:57:27.000
They had updated so that the total supply was only 21,000,000 because otherwise it would wrap back around and start doing 50 Bitcoin block subsidies again. Oh.
726
00:57:31.404 --> 00:57:34.445
Why it's so much Bitcoin. It was Bitcoin,
727
00:57:35.404 --> 00:57:41.164
so I took it. This is literally, Peter Willa doing a whole bit on basically the Bitcoin total supply is 21,000,000.
728
00:57:41.164 --> 00:57:42.365
Thank you for coming to my talk.
729
00:57:45.940 --> 00:57:52.020
That's why... And imagine, like, waking up in 2014 with no AI and and saying, how do I know? Right?
730
00:57:52.420 --> 00:57:53.860
Yeah. Do we know that...
731
00:57:54.660 --> 00:57:58.420
And I guess... I'm guessing they simulated it out and saw it happen.
732
00:57:59.785 --> 00:58:00.665
Right? Yeah.
733
00:58:01.945 --> 00:58:02.665
Yeah.
734
00:58:02.745 --> 00:58:03.385
This is,
735
00:58:04.345 --> 00:58:16.820
the soft fork for this will take place on twenty two one four and permanently setting the subsidy to zero. Do you know how many blocks it is to get... Do you know off top of your head how many blocks to to the last block? Not offhand.
736
00:58:17.140 --> 00:58:18.500
For the last reward?
737
00:58:18.820 --> 00:58:20.740
Everyone talks about twenty one forty,
738
00:58:21.300 --> 00:58:22.340
but Right.
739
00:58:22.740 --> 00:58:25.860
I I know the block height offhand. There's a... It's It's every 210,000
740
00:58:25.860 --> 00:58:26.980
blocks. 210,000
741
00:58:26.980 --> 00:58:31.885
times 32, I guess, is probably really the answer, but I was curious. 2,000,000?
742
00:58:32.125 --> 00:58:39.165
Yeah. So I mean, you could do this in a reg test in like under a minute. Yeah. Yeah. Absolutely.
743
00:58:40.045 --> 00:58:41.085
Yeah. So like
744
00:58:41.325 --> 00:58:42.765
everything that touches consensus,
745
00:58:43.270 --> 00:58:51.030
I just started sending a swarm of clinkers. So cool. And so this is... So this was made without you doing any... This is all you literally did today.
746
00:58:52.150 --> 00:58:56.310
Just said spin up a 100 sub agents, start mapping out all of Bitcoin consensus as a lean proof.
747
00:58:57.025 --> 00:58:59.745
You know, it's so funny, dude. I talk a lot about how,
748
00:59:00.625 --> 00:59:03.185
let's let's not get crazy with intelligence.
749
00:59:03.265 --> 00:59:08.065
Right? But, like, man, pattern recognition is still... There is a lot.
750
00:59:08.385 --> 00:59:12.080
There's a long way to go. Yep. It's... It could do so much.
751
00:59:12.400 --> 00:59:13.120
Here's
752
00:59:13.360 --> 00:59:19.680
here's a whole lean proof on what I was just talking about BIP one thirteen with the median time pass of the past 11 blocks. Yeah. Yeah. Yeah. This
753
00:59:20.160 --> 00:59:24.880
is doing all of the math and logic around making sure that you reject blocks that
754
00:59:25.665 --> 00:59:28.145
are less than the median time passed and accept the And
755
00:59:28.705 --> 00:59:34.225
is it this simple to say, you know, when we verified Bitcoin, we went to the Python code, but now
756
00:59:34.625 --> 00:59:35.985
this is how clankers
757
00:59:35.985 --> 00:59:37.585
can verify Bitcoin? Yeah.
758
00:59:39.290 --> 00:59:42.170
And I think there's more woah that can There's a lot of work to be Is done and
759
00:59:42.810 --> 00:59:49.130
it not more important also that we know they can? This is how we know they can verify it. Right.
760
00:59:49.530 --> 00:59:51.530
I think it's important. Yeah.
761
00:59:52.090 --> 00:59:53.450
I have a bunch of audits here.
762
00:59:56.785 --> 01:00:00.305
Dot corner audit. Genesis equal empty to accept an opportunity never stored.
763
01:00:01.585 --> 01:00:08.465
So this is a pro... I mean, this is now... You... Now we're starting to get into this area where this would be a nice open source project for somebody to pick up.
764
01:00:09.130 --> 01:00:15.610
Well, that's why I made it MIT licensed. And, like, if I spent a bunch of compute on it, you can just take it from here and improve it.
765
01:00:18.330 --> 01:00:18.970
Yeah.
766
01:00:19.369 --> 01:00:20.250
That was the idea.
767
01:00:21.295 --> 01:00:22.335
Oh, this is
768
01:00:22.895 --> 01:00:31.135
SIGHASH single and find and delete. Oh, that's so good. All of this like really niche things in legacy script. All this niche stuff in legacy script and just defining all of it.
769
01:00:31.535 --> 01:00:34.015
Are you getting into BIOHASH territory with that one?
770
01:00:34.495 --> 01:00:34.815
Basically.
771
01:00:35.360 --> 01:00:38.080
I think I said... I showed this to Robin when I was in
772
01:00:40.960 --> 01:00:41.920
Lugano.
773
01:00:42.800 --> 01:00:43.280
Still
774
01:00:44.000 --> 01:00:46.880
gotta get Robin on here. We're still gonna glaze Binohash.
775
01:00:47.200 --> 01:00:47.680
Absolutely.
776
01:00:48.345 --> 01:00:49.145
Absolutely.
777
01:00:49.305 --> 01:01:00.425
Yeah. So that was like the Bitcoin BTC lean stuff. Like I've had multiple people ask me, what are your thoughts? Like, what are you gonna do with it? Like, what's next? And like, maybe I'll spend some more clanker energy on it, but I'm not trying to
778
01:01:02.025 --> 01:01:03.225
go too crazy with it.
779
01:01:04.740 --> 01:01:09.060
I feel like there's a way for me to turn those into demos
780
01:01:09.060 --> 01:01:18.180
to visualize what you're doing. We probably... You probably could. You should start putting your your clinker on it. That's what I'm... Yeah. I'm... I might have to get... Boot back my pro subscription
781
01:01:20.165 --> 01:01:24.725
to do that work. Yeah. I had I had downgraded because I'm only doing... You know?
782
01:01:25.125 --> 01:01:27.685
I'm I'm not doing that kind of work anymore
783
01:01:27.845 --> 01:01:30.245
with my clankers, but now I might have to
784
01:01:30.725 --> 01:01:38.570
I might have to do that. Yeah. I'm... Now, like, I want I want visual demonstrations of what I just saw you walk me through.
785
01:01:39.210 --> 01:01:43.370
Probably... I probably should take a a legitimate, like, frontier model and
786
01:01:43.610 --> 01:01:45.130
short... You know, polish it up a bit.
787
01:01:46.145 --> 01:01:49.905
This was all using DeepSeek 4.1 Flash ten seventeen.
788
01:01:49.905 --> 01:01:53.105
At least, yeah, take the v four through it. Right?
789
01:01:54.305 --> 01:01:55.825
I probably will take,
790
01:01:56.865 --> 01:02:01.860
maybe a little bit. I'll probably set up a, like, a nice long running gold prompt and just start getting in there with
791
01:02:02.260 --> 01:02:04.100
with Codex loaded autopilot
792
01:02:04.100 --> 01:02:05.300
with Astra or something.
793
01:02:06.260 --> 01:02:10.660
Yeah. Interesting. Bulk work is done, so now it's just gonna be, like, little whittling on polishing on the edges, I think.
794
01:02:11.825 --> 01:02:14.625
It's interesting seeing the models people were using for
795
01:02:15.345 --> 01:02:25.424
the Oh, the SIG Golf? The SIG Golf project. It was all It's all on Opus. Yeah. Opus five five, Astra, Opus five five. I'm the one DeepSeek. It's so funny. I'm the only person
796
01:02:25.850 --> 01:02:34.650
I'm the only person who didn't use the Frontier model. That's why you're the CEO. Here we go. Someone October 13 did DeepSeek v four. Oh, there's a couple DeepSeek v fours. Okay.
797
01:02:35.690 --> 01:02:36.650
There you go.
798
01:02:38.330 --> 01:02:42.845
I love DeepSeek v four. It's it's a... It's fast. It's cheap.
799
01:02:43.245 --> 01:02:44.525
It's pretty damn good.
800
01:02:45.325 --> 01:02:51.725
It's it's basically free for me with my... In... Like, with Hermes in my new subscription,
801
01:02:51.885 --> 01:02:53.965
and it's it's
802
01:02:54.045 --> 01:02:54.765
wildly good.
803
01:02:55.860 --> 01:02:56.580
Yeah.
804
01:02:56.660 --> 01:03:02.100
I think so. It's maybe not to do this kind of math. I don't know. Maybe it's not at that level, but, like,
805
01:03:03.860 --> 01:03:06.580
for what I needed to do, it's it's it's free.
806
01:03:11.025 --> 01:03:14.065
Yeah. I'm excited. There's a lot of fun stuff to do.
807
01:03:15.025 --> 01:03:19.825
What do we have as open items we wanna discuss on the pod today? Anything else?
808
01:03:20.625 --> 01:03:21.984
Okay. Well, okay.
809
01:03:22.704 --> 01:03:26.704
Just trying to think through in the current event space, did we really
810
01:03:28.520 --> 01:03:30.360
did we cover what we wanted here?
811
01:03:31.320 --> 01:03:32.760
I think mostly.
812
01:03:33.320 --> 01:03:34.040
Was there...
813
01:03:34.600 --> 01:03:35.880
Wasn't there something about,
814
01:03:37.640 --> 01:03:40.600
I think if we're gonna add something to the, presentation,
815
01:03:40.600 --> 01:03:43.595
it'll be something on lean proofs on on this.
816
01:03:43.915 --> 01:03:50.795
Lane proofs? Yeah. We could probably throw lane proofs in there. Because why it's important not for us to just... Not just for us to verify, but for
817
01:03:51.194 --> 01:03:53.435
us to verify that machines can verify.
818
01:03:54.875 --> 01:03:55.194
Yeah.
819
01:03:57.400 --> 01:04:01.320
Right? And somebody we need... Somebody needed to start that ball rolling.
820
01:04:04.040 --> 01:04:06.280
Yeah. I think it's also... The the
821
01:04:07.320 --> 01:04:14.325
nature of reason why lean proofs are so powerful with these AI models is that if you were running a scientific experiment in biology or chemistry,
822
01:04:14.485 --> 01:04:24.165
it could give you some new novel idea for something. But you would then need, like, a wet lab to, like, do all of the work to actually verify it. Whereas since math is just internally consistent,
823
01:04:24.565 --> 01:04:26.165
you could just abstractly
824
01:04:26.405 --> 01:04:28.085
iterate, grind, optimize
825
01:04:28.940 --> 01:04:30.060
all this stuff.
826
01:04:33.980 --> 01:04:34.940
There was...
827
01:04:35.100 --> 01:04:35.580
So
828
01:04:35.980 --> 01:04:37.100
I have it right here.
829
01:04:38.300 --> 01:04:39.660
There was a paper
830
01:04:40.220 --> 01:04:43.820
about sub exponential time algorithm for elliptic curve discrete logarithm
831
01:04:44.694 --> 01:04:46.695
from the Max Planck Institute.
832
01:04:47.175 --> 01:04:48.055
And
833
01:04:49.575 --> 01:04:50.295
it's...
834
01:04:50.775 --> 01:04:53.575
I mean, I I could send you this paper right now.
835
01:04:55.175 --> 01:04:57.015
I feel like we're just going to,
836
01:04:57.895 --> 01:04:59.494
be stumbling through it in real time.
837
01:05:00.210 --> 01:05:05.810
No. We're not... We don't need to go through this now. But it'd be cool to give it to my clanker. I I just I
838
01:05:05.810 --> 01:05:10.610
just sent it to you. I need to start doing that more, keeping my clanker up to date on all these
839
01:05:11.250 --> 01:05:19.505
Like, a little rock bot going? Well, like, I have... Like, immediately, I brought in all those a... I brought in all the lean proofs of those OpenAI problems.
840
01:05:19.905 --> 01:05:23.265
And then the next thing I brought in was the uncle Ted Kaczynski
841
01:05:23.265 --> 01:05:25.105
thing that Michael Warren put out,
842
01:05:26.710 --> 01:05:28.150
where he basically...
843
01:05:28.310 --> 01:05:32.550
He he put out lean proofs of all of Ted Kaczynski's work. So I put that on my
844
01:05:33.110 --> 01:05:34.070
That's great.
845
01:05:34.550 --> 01:05:36.950
Yeah. I put that on the site immediately.
846
01:05:37.430 --> 01:05:45.015
And so... But at least now, like, when I... You know, when the clanker goes through the podcast and starts looking at the deck, it has all of this stuff already loaded up in it. So
847
01:05:45.735 --> 01:05:48.375
I just gotta keep making sure it's up to date.
848
01:05:48.775 --> 01:05:51.895
I wanna get your lean proofs in there. I feel like that's really foundational.
849
01:05:52.055 --> 01:05:52.455
Yeah.
850
01:05:54.039 --> 01:05:57.640
So I... I'm gonna give a quick summary of this. We could throw it in.
851
01:05:58.680 --> 01:06:04.119
This is, like, a quick summary of this paper from the Max Planck Institute and Rohr University.
852
01:06:05.079 --> 01:06:05.880
Rohr.
853
01:06:07.164 --> 01:06:27.540
A sub exponential time algorithm for elliptic curve discrete logarithm. Researchers are now described how OpenEye's claimed breakthrough in the exponential time hypothesis could be applied to elliptic curve private key recovery. Instead of simply guessing keys, they can use a method called index calculus, collect mathematical relationships between curve points, and then combine those relationships to recover the secret. The new ingredient is,
854
01:06:27.859 --> 01:06:44.935
a tensor network solver to solve these relationships. Assuming OpenAI's underlying result is correct, the algorithm has sub exponential scaling. That's theoretically significant, but the authors explicitly say it offers no improved concrete attack on currently deployed curves. This is a potential change to our understanding of the long term computation hardness, not a demonstration that Bitcoin has been cracked.
855
01:06:47.270 --> 01:06:58.390
The... This index calculus method, by the way, is something that is in Koblitz's book, Number Theory and Cryptography that I talked about here. So, like... And it's it's like page four.
856
01:07:00.515 --> 01:07:01.315
Definitely
857
01:07:01.474 --> 01:07:02.275
recommend
858
01:07:02.275 --> 01:07:13.635
that book. Gotta put that in the show notes. I definitely rec... That that... It's like everything you talk about somehow, you know, it's like is in the cobblets books. Cobblets has gotta be it's gotta be working on this somehow.
859
01:07:14.410 --> 01:07:15.050
Yeah.
860
01:07:17.930 --> 01:07:26.250
Of this this white paper, it says it does not apply to current deployed curves including NIST p two fifty six, NIST p two five twenty one, and e d two,
861
01:07:26.570 --> 01:07:28.775
five five one nine. They don't mention
862
01:07:29.175 --> 01:07:30.295
SecP in there.
863
01:07:31.175 --> 01:07:33.175
Do they... I mean, is it even on their radar?
864
01:07:33.735 --> 01:07:34.215
I
865
01:07:36.055 --> 01:07:37.975
mean, e d $255.19,
866
01:07:37.975 --> 01:07:48.920
I think, is the Ethereum Solana curve, if I... Or I think it's Solana's curve. But I mean But was that... Were those... I mean, a question for you. Right? Were those forks of ZEC P or were those fucking No.
867
01:07:49.559 --> 01:07:52.680
No. They're their own thing. Is that why they're so fucked up?
868
01:07:53.079 --> 01:07:59.785
No. I mean, there's a lot of engineering decisions around those that just make and they use BLS signatures, not, ECDSA.
869
01:08:00.424 --> 01:08:02.744
They use a different signature algorithm. But
870
01:08:03.305 --> 01:08:09.224
from our, our doors we were talking about earlier on the deck between like the different ways this could be attacked, this is basically going after rows and troops.
871
01:08:09.940 --> 01:08:12.900
Basically, is there a better, is there a better than a sub,
872
01:08:13.060 --> 01:08:15.140
is there better than square root that we can do?
873
01:08:15.540 --> 01:08:17.860
And that's the kind of like the path that these are going for.
874
01:08:18.900 --> 01:08:36.545
Okay. Because I mean, know, it's still like an open puzzle of like why probably throw that into the deck. Like, this this paper being kind of, like, where this is starting to go is not more of the esoteric stuff, but just seeing if you could just buy pure computational efficiency and go lower than square root for row. Right. Right. Right. Because now you're... It's square root.
875
01:08:38.150 --> 01:08:41.670
Is square root also birthday paradox or is birth or
876
01:08:41.830 --> 01:08:43.030
is It's related.
877
01:08:44.070 --> 01:08:47.590
It's definitely related. Like the square root of time. I'm not sure.
878
01:08:48.310 --> 01:08:52.710
Related in at least conceptually in my head, they seem related, but I couldn't answer that directly offhand.
879
01:08:54.664 --> 01:09:00.104
Yeah. It's more severe than... Birthday paradox maybe is only... I think it's half, not square root.
880
01:09:00.425 --> 01:09:02.344
Yeah. Yeah. Yeah.
881
01:09:04.664 --> 01:09:07.784
Gotta keep those, you know, gotta keep those straight.
882
01:09:08.105 --> 01:09:08.425
Yeah.
883
01:09:08.949 --> 01:09:12.949
Yeah. No. So I think I think this is good. I think this is a good place
884
01:09:14.550 --> 01:09:16.709
good place to probably wrap it unless
885
01:09:16.949 --> 01:09:21.829
we got other business we wanna talk about. I think I think I think all business has been discussed.
886
01:09:22.150 --> 01:09:23.190
I think we're in a good spot.
887
01:09:23.946 --> 01:09:24.745
Alright.
888
01:09:24.826 --> 01:09:28.506
Good stuff. Magic Internet Math is In the books.
889
01:09:28.906 --> 01:09:30.026
In the books.
890
01:09:30.346 --> 01:09:30.826
Peace.