{"version":"1.0.0","segments":[{"startTime":13.811,"endTime":17.491,"body":"Deirdre - Hello, welcome to"},{"startTime":13.811,"endTime":17.491,"body":"Security Cryptography Whatever."},{"startTime":17.491,"endTime":18.253,"body":"I'm Deirdre."},{"startTime":19.173,"endTime":19.673,"body":"David - I'm David."},{"startTime":20.325,"endTime":22.321,"body":"Thomas - I'm Thomas and I'm"},{"startTime":20.325,"endTime":22.321,"body":"going to"},{"startTime":22.321,"endTime":23.285,"body":"good minute in this podcast."},{"startTime":24.105,"endTime":24.885,"body":"Deirdre - That's Thomas."},{"startTime":25.926,"endTime":29.452,"body":"We have a returning special"},{"startTime":25.926,"endTime":29.452,"body":"guest today,"},{"startTime":29.452,"endTime":29.966,"body":"Peikert."},{"startTime":30.336,"endTime":31.086,"body":"How are you, Chris?"},{"startTime":32.018,"endTime":32.697,"body":"Chris - I am great."},{"startTime":32.817,"endTime":34.697,"body":"Great to be with you again"},{"startTime":32.817,"endTime":34.697,"body":"tonight."},{"startTime":34.697,"endTime":37.618,"body":"Deirdre - Yeah, I think you were"},{"startTime":34.697,"endTime":37.618,"body":"with us in our first year, and"},{"startTime":37.618,"endTime":40.058,"body":"now we're very happy to have you"},{"startTime":37.618,"endTime":40.058,"body":"come back."},{"startTime":40.697,"endTime":43.618,"body":"And now we have you on camera"},{"startTime":40.697,"endTime":43.618,"body":"for the first time."},{"startTime":44.597,"endTime":47.118,"body":"There's been a lot of news in"},{"startTime":44.597,"endTime":47.118,"body":"lattices."},{"startTime":47.798,"endTime":53.133,"body":"And so we had to reach out to, I"},{"startTime":47.798,"endTime":53.133,"body":"think it's fair to say, our"},{"startTime":53.133,"endTime":57.473,"body":"fattest favorite lattice"},{"startTime":53.133,"endTime":57.473,"body":"cryptographer to ask him"},{"startTime":57.473,"endTime":62.717,"body":"questions, especially about new"},{"startTime":57.473,"endTime":62.717,"body":"proofs about closest vector"},{"startTime":62.717,"endTime":67.148,"body":"problem, new proofs about"},{"startTime":62.717,"endTime":67.148,"body":"shortest vector problem,"},{"startTime":67.148,"endTime":72.302,"body":"something called dihedral coset"},{"startTime":67.148,"endTime":72.302,"body":"problem and how it affects"},{"startTime":72.302,"endTime":73.118,"body":"lattices."},{"startTime":73.217,"endTime":76.037,"body":"And also Classic McEliece,"},{"startTime":73.217,"endTime":76.037,"body":"because why not?"},{"startTime":76.225,"endTime":81.47,"body":"So to intro, OpenAI unleashed"},{"startTime":76.225,"endTime":81.47,"body":"their, I"},{"startTime":81.47,"endTime":81.986,"body":"model."},{"startTime":82.106,"endTime":83.486,"body":"And I forget the name of it,"},{"startTime":82.106,"endTime":83.486,"body":"Astra."},{"startTime":84.146,"endTime":84.665,"body":"David - Astral."},{"startTime":84.826,"endTime":89.066,"body":"Deirdre - They all have a cute,"},{"startTime":84.826,"endTime":89.066,"body":"whimsical, powerful name or"},{"startTime":89.066,"endTime":89.725,"body":"whatever."},{"startTime":90.146,"endTime":93.564,"body":"And they targeted it at a bunch"},{"startTime":90.146,"endTime":93.564,"body":"of just pure math problems, it"},{"startTime":93.564,"endTime":94.405,"body":"appeared to be."},{"startTime":94.405,"endTime":97.903,"body":"And they put out this paper that"},{"startTime":94.405,"endTime":97.903,"body":"was like, OpenAI's 10 math"},{"startTime":97.903,"endTime":98.326,"body":"proofs."},{"startTime":98.445,"endTime":103.93,"body":"and one of the 10 was like a new"},{"startTime":98.445,"endTime":103.93,"body":"result"},{"startTime":103.93,"endTime":106.106,"body":"closest vector problem."},{"startTime":107.646,"endTime":110.221,"body":"And when I saw this, I was like,"},{"startTime":107.646,"endTime":110.221,"body":"\"Oh, that's interesting, and"},{"startTime":110.221,"endTime":111.466,"body":"maybe I will actually go look"},{"startTime":111.485,"endTime":115.433,"body":"at the proof.\" But I think you"},{"startTime":111.485,"endTime":115.433,"body":"read it first, and you're like,"},{"startTime":115.433,"endTime":117.505,"body":"\"Actually, this is kind of"},{"startTime":115.433,"endTime":117.505,"body":"nice.\""},{"startTime":118.545,"endTime":119.945,"body":"Can you tell us your take?"},{"startTime":120.849,"endTime":124.732,"body":"Chris - Yeah, so I think the"},{"startTime":120.849,"endTime":124.732,"body":"first character of my skeet"},{"startTime":124.732,"endTime":128.969,"body":"tweet thread on this was the"},{"startTime":124.732,"endTime":128.969,"body":"exploding head emoji, like, wow."},{"startTime":130.289,"endTime":131.029,"body":"And it's held up."},{"startTime":131.099,"endTime":133.989,"body":"Like, the result itself is this"},{"startTime":131.099,"endTime":133.989,"body":"new proof."},{"startTime":134.208,"endTime":137.663,"body":"So it's about the closest vector"},{"startTime":134.208,"endTime":137.663,"body":"problem on lattices and actually"},{"startTime":137.663,"endTime":140.849,"body":"approximating the closest vector"},{"startTime":137.663,"endTime":140.849,"body":"problem on lattices, right?"},{"startTime":141.008,"endTime":144.485,"body":"So the closest vector problem is"},{"startTime":141.008,"endTime":144.485,"body":"I give you a lattice and I give"},{"startTime":144.485,"endTime":146.748,"body":"you a target point somewhere out"},{"startTime":144.485,"endTime":146.748,"body":"in space."},{"startTime":147.568,"endTime":150.069,"body":"And the goal is follow a lattice"},{"startTime":147.568,"endTime":150.069,"body":"point that's as close as"},{"startTime":150.069,"endTime":151.409,"body":"possible to that target point."},{"startTime":152.729,"endTime":155.759,"body":"And that's the exact, like you"},{"startTime":152.729,"endTime":155.759,"body":"have to follow exactly the"},{"startTime":155.759,"endTime":157.708,"body":"closest lattice vector to the"},{"startTime":155.759,"endTime":157.708,"body":"target."},{"startTime":158.328,"endTime":160.243,"body":"And then there's this"},{"startTime":158.328,"endTime":160.243,"body":"approximate version which says,"},{"startTime":160.243,"endTime":162.049,"body":"oh, you don't have to give me"},{"startTime":160.243,"endTime":162.049,"body":"exactly the closest."},{"startTime":162.229,"endTime":166.052,"body":"You can give me a point which is"},{"startTime":162.229,"endTime":166.052,"body":"within some factor of the"},{"startTime":166.052,"endTime":166.589,"body":"closest."},{"startTime":167.109,"endTime":167.248,"body":"Okay."},{"startTime":167.289,"endTime":169.068,"body":"So that's like the approximation"},{"startTime":167.289,"endTime":169.068,"body":"factor."},{"startTime":170.029,"endTime":174.299,"body":"And for a long time, we've known"},{"startTime":170.029,"endTime":174.299,"body":"that the closest vector problem"},{"startTime":174.299,"endTime":176.469,"body":"is NP-hard in that exact"},{"startTime":174.299,"endTime":176.469,"body":"version."},{"startTime":176.828,"endTime":180.855,"body":"Like that goes back to the 80s."},{"startTime":176.828,"endTime":180.855,"body":"That's classic stuff. And then"},{"startTime":180.855,"endTime":184.684,"body":"in the 90s, people showed that"},{"startTime":180.855,"endTime":184.684,"body":"increasing the approximation"},{"startTime":184.684,"endTime":188.447,"body":"factor, which can make the"},{"startTime":184.684,"endTime":188.447,"body":"problem easier, right? Like you"},{"startTime":188.447,"endTime":191.748,"body":"have more possible answers. It's"},{"startTime":188.447,"endTime":191.748,"body":"an easier problem."},{"startTime":192.808,"endTime":196.452,"body":"But even then, if you increase"},{"startTime":192.808,"endTime":196.452,"body":"the approximation factor to like"},{"startTime":196.452,"endTime":199.92,"body":"any constant, 100, a billion, a"},{"startTime":196.452,"endTime":199.92,"body":"Google, whatever, it's still"},{"startTime":199.92,"endTime":203.035,"body":"NP-hard, right, to even get"},{"startTime":199.92,"endTime":203.035,"body":"approximately close to the"},{"startTime":203.035,"endTime":203.448,"body":"factor."},{"startTime":204.089,"endTime":208.381,"body":"And then even if you go to"},{"startTime":204.089,"endTime":208.381,"body":"factors like n to the 1 over log"},{"startTime":208.381,"endTime":211.268,"body":"log n, right, so not quite a"},{"startTime":208.381,"endTime":211.268,"body":"polynomial."},{"startTime":211.479,"endTime":213.188,"body":"n is the dimension here, by the"},{"startTime":211.479,"endTime":213.188,"body":"way, dimension."},{"startTime":214.168,"endTime":218.593,"body":"So not quite polynomial, but"},{"startTime":214.168,"endTime":218.593,"body":"merely i-ish,"},{"startTime":218.593,"endTime":220.848,"body":"close-ish is still NP-hard."},{"startTime":221.569,"endTime":225.244,"body":"Okay, so that was like the last"},{"startTime":221.569,"endTime":225.244,"body":"word that we had on the NP"},{"startTime":225.244,"endTime":229.177,"body":"hardness. And it was from around"},{"startTime":225.244,"endTime":229.177,"body":"1998. I think maybe there's a"},{"startTime":229.177,"endTime":233.045,"body":"follow up journal version in"},{"startTime":229.177,"endTime":233.045,"body":"2003. So more than 20 years. And"},{"startTime":233.045,"endTime":236.849,"body":"then this hadn't budged, like"},{"startTime":233.045,"endTime":236.849,"body":"nobody had improved upon that."},{"startTime":236.849,"endTime":240.072,"body":"And that result used like this"},{"startTime":236.849,"endTime":240.072,"body":"heavy PCP machinery,"},{"startTime":240.072,"endTime":243.489,"body":"probabilistically checkable"},{"startTime":240.072,"endTime":243.489,"body":"proofs and all this stuff."},{"startTime":243.489,"endTime":245.168,"body":"Technical, doesn't matter."},{"startTime":245.769,"endTime":251.264,"body":"And then OpenAI shows up on"},{"startTime":245.769,"endTime":251.264,"body":"August 1st and is like, hey, we"},{"startTime":251.264,"endTime":256.949,"body":"show that actually polynomial"},{"startTime":251.264,"endTime":256.949,"body":"approximation, CVP, is NP-hard."},{"startTime":257.988,"endTime":260.309,"body":"And their polynomial is n to the"},{"startTime":257.988,"endTime":260.309,"body":"1 over 400."},{"startTime":262.089,"endTime":265.288,"body":"Deirdre - I was wondering what"},{"startTime":262.089,"endTime":265.288,"body":"that term really was."},{"startTime":265.288,"endTime":266.468,"body":"Chris - And so, yeah."},{"startTime":266.468,"endTime":266.469,"body":"Deirdre - That's good."},{"startTime":268.629,"endTime":270.788,"body":"Chris - And so that's a fixed"},{"startTime":268.629,"endTime":270.788,"body":"polynomial, right?"},{"startTime":270.848,"endTime":271.788,"body":"N to the 1 over 400."},{"startTime":271.928,"endTime":274.548,"body":"That's the first term in the"},{"startTime":271.928,"endTime":274.548,"body":"title of the paper."},{"startTime":276.849,"endTime":277.889,"body":"CVP is NPR."},{"startTime":279.369,"endTime":282.028,"body":"But what's exciting is that it's"},{"startTime":279.369,"endTime":282.028,"body":"some fixed polynomials end to a"},{"startTime":282.028,"endTime":282.408,"body":"constant."},{"startTime":283.989,"endTime":287.073,"body":"And then I quickly noticed not"},{"startTime":283.989,"endTime":287.073,"body":"making any intelligent"},{"startTime":287.073,"endTime":290.691,"body":"observation whatsoever, but it's"},{"startTime":287.073,"endTime":290.691,"body":"like, why end of the one over"},{"startTime":290.691,"endTime":290.929,"body":"400?"},{"startTime":291.308,"endTime":292.969,"body":"Like, is there something"},{"startTime":291.308,"endTime":292.969,"body":"intrinsic there? Is there"},{"startTime":292.969,"endTime":293.648,"body":"something important?"},{"startTime":294.508,"endTime":297.394,"body":"And so you run to your model,"},{"startTime":294.508,"endTime":297.394,"body":"you run to your favorite cloud"},{"startTime":297.394,"endTime":298.568,"body":"or your chat or whoever."},{"startTime":299.089,"endTime":302.12,"body":"You say, can you improve this?"},{"startTime":299.089,"endTime":302.12,"body":"And it says, oh, yeah, actually,"},{"startTime":302.12,"endTime":304.76,"body":"I can get you like end of the"},{"startTime":302.12,"endTime":304.76,"body":"one over 28 without doing"},{"startTime":304.76,"endTime":307.109,"body":"anything but like improving the"},{"startTime":304.76,"endTime":307.109,"body":"bookkeeping here."},{"startTime":307.308,"endTime":309.516,"body":"Like I didn't change anything"},{"startTime":307.308,"endTime":309.516,"body":"about the proof. I just used"},{"startTime":309.516,"endTime":310.369,"body":"better numbers. Right."},{"startTime":311.949,"endTime":315.885,"body":"So I found it really interesting"},{"startTime":311.949,"endTime":315.885,"body":"that like Astra didn't try to"},{"startTime":315.885,"endTime":316.208,"body":"even."},{"startTime":317.419,"endTime":321.008,"body":"Deirdre - Well, we're not even"},{"startTime":317.419,"endTime":321.008,"body":"really sure how they queried it"},{"startTime":321.008,"endTime":323.009,"body":"or what they asked it, but it"},{"startTime":321.008,"endTime":323.009,"body":"does."},{"startTime":323.009,"endTime":323.01,"body":"Chris - This polynomial. Yeah."},{"startTime":323.029,"endTime":327.314,"body":"Deirdre - Seem that you can come"},{"startTime":323.029,"endTime":327.314,"body":"up with a impressive attacks"},{"startTime":327.314,"endTime":330.029,"body":"with very simple queries with"},{"startTime":327.314,"endTime":330.029,"body":"not a lot"},{"startTime":330.029,"endTime":335.109,"body":"of detail about what you're"},{"startTime":330.029,"endTime":335.109,"body":"asking the model to do. So"},{"startTime":335.109,"endTime":339.328,"body":"driving down that factor from"},{"startTime":335.109,"endTime":339.328,"body":"one or driving."},{"startTime":339.328,"endTime":339.329,"body":"Chris - Exactly."},{"startTime":339.349,"endTime":343.736,"body":"Deirdre - Up that factor from"},{"startTime":339.349,"endTime":343.736,"body":"one of one over 400 to one over"},{"startTime":343.736,"endTime":346.808,"body":"128 or whatever. So how so that"},{"startTime":343.736,"endTime":346.808,"body":"is bringing"},{"startTime":347.308,"endTime":350.806,"body":"the closer and closer to the"},{"startTime":347.308,"endTime":350.806,"body":"actual closest vector problem as"},{"startTime":350.806,"endTime":352.789,"body":"opposed to like this"},{"startTime":350.806,"endTime":352.789,"body":"approximation."},{"startTime":352.828,"endTime":354.308,"body":"bound, right?"},{"startTime":354.308,"endTime":356.572,"body":"Chris - No well it's making it's"},{"startTime":354.308,"endTime":356.572,"body":"taking you farther away from the"},{"startTime":356.572,"endTime":357.068,"body":"exact version."},{"startTime":357.188,"endTime":358.349,"body":"Deirdre - The other way around."},{"startTime":357.188,"endTime":358.349,"body":"Okay, yeah, yeah."},{"startTime":358.349,"endTime":361.948,"body":"Chris - Farther away yep yeah"},{"startTime":358.349,"endTime":361.948,"body":"because like we know yeah."},{"startTime":361.948,"endTime":361.949,"body":"Deirdre - Cool. And that's"},{"startTime":361.948,"endTime":361.949,"body":"attractive"},{"startTime":361.949,"endTime":362.808,"body":"because you can do more"},{"startTime":363.049,"endTime":364.948,"body":"efficient cryptography if you"},{"startTime":363.049,"endTime":364.948,"body":"have more"},{"startTime":365.229,"endTime":366.029,"body":"space, kind of?"},{"startTime":366.511,"endTime":372.467,"body":"Chris - Well, for the CVP,"},{"startTime":366.511,"endTime":372.467,"body":"actually, crypto is not in this"},{"startTime":372.467,"endTime":373.931,"body":"regime at all."},{"startTime":374.191,"endTime":376.809,"body":"So this is like purely a"},{"startTime":374.191,"endTime":376.809,"body":"complexity, computational"},{"startTime":376.809,"endTime":377.772,"body":"complexity result."},{"startTime":379.571,"endTime":381.592,"body":"So, yeah, I just want to put"},{"startTime":379.571,"endTime":381.592,"body":"that out there."},{"startTime":381.892,"endTime":386.159,"body":"But there is this one half or n"},{"startTime":381.892,"endTime":386.159,"body":"to the one half barrier, like"},{"startTime":386.159,"endTime":390.426,"body":"square root of n barrier that's"},{"startTime":386.159,"endTime":390.426,"body":"known, where we know that the"},{"startTime":390.426,"endTime":394.551,"body":"square root n approximate CVP is"},{"startTime":390.426,"endTime":394.551,"body":"in the class called co-NP,"},{"startTime":394.811,"endTime":396.392,"body":"the complement of NP problems."},{"startTime":396.571,"endTime":396.772,"body":"Deirdre - Yeah."},{"startTime":397.531,"endTime":399.931,"body":"Chris - And because of that,"},{"startTime":397.531,"endTime":399.931,"body":"it's highly unlikely."},{"startTime":400.191,"endTime":402.931,"body":"Okay, so this would cause some"},{"startTime":400.191,"endTime":402.931,"body":"major collapse"},{"startTime":403.041,"endTime":404.71,"body":"in the polynomial time"},{"startTime":403.041,"endTime":404.71,"body":"hierarchy,"},{"startTime":405.371,"endTime":408.051,"body":"dogs and cats living together,"},{"startTime":405.371,"endTime":408.051,"body":"like chaos everywhere, right?"},{"startTime":408.631,"endTime":411.45,"body":"So we do not have any reason to"},{"startTime":408.631,"endTime":411.45,"body":"make,"},{"startTime":411.621,"endTime":415.611,"body":"we very much do not expect"},{"startTime":411.621,"endTime":415.611,"body":"square root n to be NP hard."},{"startTime":417.09,"endTime":419.97,"body":"But now we have like, oh, n to"},{"startTime":417.09,"endTime":419.97,"body":"the 1 over 400 is,"},{"startTime":420.27,"endTime":421.791,"body":"n to the one over 28 is,"},{"startTime":422.26,"endTime":424.65,"body":"n to the one over eight is with"},{"startTime":422.26,"endTime":424.65,"body":"like other people"},{"startTime":424.85,"endTime":426.47,"body":"kind of pushing and prodding on"},{"startTime":424.85,"endTime":426.47,"body":"the models"},{"startTime":426.731,"endTime":427.611,"body":"to like improve this thing."},{"startTime":428.91,"endTime":431.91,"body":"And as of just a few days after"},{"startTime":428.91,"endTime":431.91,"body":"that,"},{"startTime":432.491,"endTime":434.95,"body":"somebody who goes by the name of"},{"startTime":432.491,"endTime":434.95,"body":"Mira on Twitter,"},{"startTime":435.001,"endTime":436.15,"body":"I don't even know who it is,"},{"startTime":436.97,"endTime":439.551,"body":"poked the models long enough to"},{"startTime":436.97,"endTime":439.551,"body":"get them to prove,"},{"startTime":439.811,"endTime":441.791,"body":"oh yeah, I can get any n to the"},{"startTime":439.811,"endTime":441.791,"body":"half"},{"startTime":442.041,"endTime":443.41,"body":"minus any tiny constant."},{"startTime":443.9,"endTime":446.45,"body":"So like arbitrarily close to"},{"startTime":443.9,"endTime":446.45,"body":"square root n basically"},{"startTime":447.291,"endTime":448.491,"body":"is still NP hard."},{"startTime":449.231,"endTime":452.31,"body":"So now we have this like total"},{"startTime":449.231,"endTime":452.31,"body":"phase change, you know,"},{"startTime":452.631,"endTime":456.191,"body":"up to square root n, but not"},{"startTime":452.631,"endTime":456.191,"body":"quite is NP"},{"startTime":457.11,"endTime":458.011,"body":"at square root n and beyond."},{"startTime":458.711,"endTime":460.651,"body":"You have, you know, very good"},{"startTime":458.711,"endTime":460.651,"body":"reason to think"},{"startTime":460.701,"endTime":461.49,"body":"it's not NP-hard."},{"startTime":462.571,"endTime":464.85,"body":"And so we went from like this"},{"startTime":462.571,"endTime":464.85,"body":"huge unknown gap"},{"startTime":465.001,"endTime":468.47,"body":"to like completely closed gap in"},{"startTime":465.001,"endTime":468.47,"body":"a matter of a few days"},{"startTime":468.73,"endTime":470.191,"body":"with just miles poking on"},{"startTime":468.73,"endTime":470.191,"body":"things."},{"startTime":470.401,"endTime":471.251,"body":"I mean, that's insane."},{"startTime":472.251,"endTime":475.001,"body":"David - So I want to go back to"},{"startTime":472.251,"endTime":475.001,"body":"that a little bit to make sure"},{"startTime":475.001,"endTime":477.391,"body":"like I'm kind of understanding"},{"startTime":475.001,"endTime":477.391,"body":"that like what changed."},{"startTime":478.011,"endTime":482.744,"body":"So, like, in general, even if"},{"startTime":478.011,"endTime":482.744,"body":"it's not, like, directly related"},{"startTime":482.744,"endTime":487.71,"body":"to the things that we ultimately"},{"startTime":482.744,"endTime":487.71,"body":"ended up making cryptography on,"},{"startTime":487.71,"endTime":492.133,"body":"like, we like the idea of the"},{"startTime":487.71,"endTime":492.133,"body":"problem remaining complexity"},{"startTime":492.133,"endTime":496.789,"body":"theory hard for worse and worse"},{"startTime":492.133,"endTime":496.789,"body":"approximations, as opposed to"},{"startTime":496.789,"endTime":501.289,"body":"over time to keep it hard,"},{"startTime":496.789,"endTime":501.289,"body":"having to make the approximation"},{"startTime":501.289,"endTime":503.775,"body":"slowly approach the real"},{"startTime":501.289,"endTime":503.775,"body":"problem."},{"startTime":504.155,"endTime":507.187,"body":"because if the approximation"},{"startTime":504.155,"endTime":507.187,"body":"remains hard at arbitrarily"},{"startTime":507.187,"endTime":508.235,"body":"large sized things,"},{"startTime":508.496,"endTime":511.556,"body":"then we can feel better about"},{"startTime":508.496,"endTime":511.556,"body":"how hard everything is overall."},{"startTime":512.316,"endTime":514.467,"body":"Chris - Yeah, you got it. I"},{"startTime":512.316,"endTime":514.467,"body":"mean, it's kind of a vibes"},{"startTime":514.467,"endTime":516.335,"body":"thing. It's not like a formal"},{"startTime":514.467,"endTime":516.335,"body":"result, but like,"},{"startTime":516.696,"endTime":520.137,"body":"let's take away CVP precisely."},{"startTime":516.696,"endTime":520.137,"body":"Let's drop that problem and just"},{"startTime":520.137,"endTime":520.915,"body":"take a kind of"},{"startTime":521.566,"endTime":524.548,"body":"other lattice problems like"},{"startTime":521.566,"endTime":524.548,"body":"shortest vector problems and"},{"startTime":524.548,"endTime":526.175,"body":"things. We can do cryptography"},{"startTime":526.975,"endTime":530.832,"body":"from those problems with"},{"startTime":526.975,"endTime":530.832,"body":"approximation factors that are"},{"startTime":530.832,"endTime":533.475,"body":"like n or n to the 1.5 you know"},{"startTime":530.832,"endTime":533.475,"body":"things"},{"startTime":533.475,"endTime":536.78,"body":"like that or n squared right so"},{"startTime":533.475,"endTime":536.78,"body":"like very small polynomials"},{"startTime":536.78,"endTime":538.775,"body":"approximation factors give us"},{"startTime":536.78,"endTime":538.775,"body":"crypto"},{"startTime":539.326,"endTime":543.687,"body":"from certain lattice problems"},{"startTime":539.326,"endTime":543.687,"body":"and now we're saying oh well n"},{"startTime":543.687,"endTime":546.496,"body":"to that nearly one half for cp"},{"startTime":543.687,"endTime":546.496,"body":"at least"},{"startTime":546.876,"endTime":552.462,"body":"is np hard so it it seems like"},{"startTime":546.876,"endTime":552.462,"body":"not a big jump from this np hard"},{"startTime":552.462,"endTime":554.895,"body":"regime and we you know that"},{"startTime":554.915,"endTime":558.722,"body":"should kind of gives us a little"},{"startTime":554.915,"endTime":558.722,"body":"more confidence you know if you"},{"startTime":558.722,"endTime":560.656,"body":"feel like I mean by contrast"},{"startTime":558.722,"endTime":560.656,"body":"the—"},{"startTime":560.656,"endTime":560.657,"body":"Deirdre - Yeah."},{"startTime":560.836,"endTime":565.455,"body":"Chris - Best algorithms we have"},{"startTime":560.836,"endTime":565.455,"body":"to attack these problems in like"},{"startTime":565.455,"endTime":568.315,"body":"efficiently in polynomial time"},{"startTime":565.455,"endTime":568.315,"body":"they only"},{"startTime":568.375,"endTime":571.582,"body":"get like exponentially bad"},{"startTime":568.375,"endTime":571.582,"body":"approximation factors like"},{"startTime":571.582,"endTime":574.235,"body":"nearly two to the n so you got"},{"startTime":571.582,"endTime":574.235,"body":"to go all the"},{"startTime":574.315,"endTime":577.747,"body":"way out to like these huge"},{"startTime":574.315,"endTime":577.747,"body":"factors in order to solve these"},{"startTime":577.747,"endTime":579.916,"body":"problems efficiently and so this"},{"startTime":577.747,"endTime":579.916,"body":"kind"},{"startTime":579.916,"endTime":582.816,"body":"of gives us a belief that okay"},{"startTime":579.916,"endTime":582.816,"body":"these small polynomial factor"},{"startTime":582.816,"endTime":584.095,"body":"problems are probably hard"},{"startTime":584.115,"endTime":586.916,"body":"like that that that's a good"},{"startTime":584.115,"endTime":586.916,"body":"good warm and fuzzy feeling"},{"startTime":586.916,"endTime":587.171,"body":"yeah."},{"startTime":587.591,"endTime":592.597,"body":"David - Yeah, because like,"},{"startTime":587.591,"endTime":592.597,"body":"previously, like, 1 over log log"},{"startTime":592.597,"endTime":598.027,"body":"n, like, at extremely large n is"},{"startTime":592.597,"endTime":598.027,"body":"basically just like, n to the 0,"},{"startTime":598.027,"endTime":598.791,"body":"right, n."},{"startTime":598.791,"endTime":599.27,"body":"Chris - Yeah kind of yeah."},{"startTime":599.471,"endTime":602.81,"body":"David - But to get out there"},{"startTime":599.471,"endTime":602.81,"body":"with one over the end of 400,"},{"startTime":603.01,"endTime":605.77,"body":"you need to be able to end of"},{"startTime":603.01,"endTime":605.77,"body":"the E to the E to the 400."},{"startTime":605.83,"endTime":610.23,"body":"Chris - Yeah right right if"},{"startTime":605.83,"endTime":610.23,"body":"something like that yeah yeah."},{"startTime":610.23,"endTime":610.231,"body":"David - Or something like that"},{"startTime":610.23,"endTime":610.231,"body":"for it to cross over."},{"startTime":610.231,"endTime":611.411,"body":"So it's like, all these numbers"},{"startTime":610.231,"endTime":611.411,"body":"are fake."},{"startTime":611.411,"endTime":614.134,"body":"Chris - Yeah. Yeah. And I think,"},{"startTime":611.411,"endTime":614.134,"body":"I think the other thing that's"},{"startTime":614.134,"endTime":615.137,"body":"cool about this,"},{"startTime":616.417,"endTime":619.777,"body":"I don't think anybody expected"},{"startTime":616.417,"endTime":619.777,"body":"it or would have bet on it."},{"startTime":620.677,"endTime":624.377,"body":"Like if you had asked me last"},{"startTime":620.677,"endTime":624.377,"body":"Friday is small, you know,"},{"startTime":624.598,"endTime":628.848,"body":"tiny polynomial approximate or"},{"startTime":624.598,"endTime":628.848,"body":"hard NP hard, like probably not."},{"startTime":628.848,"endTime":629.397,"body":"I don't,"},{"startTime":629.637,"endTime":633.781,"body":"I don't think that's, that's"},{"startTime":629.637,"endTime":633.781,"body":"going to be even true, much less"},{"startTime":633.781,"endTime":634.818,"body":"do I expect it."},{"startTime":635.358,"endTime":639.216,"body":"And then, so it just completely"},{"startTime":635.358,"endTime":639.216,"body":"changed our understanding of"},{"startTime":639.216,"endTime":640.198,"body":"these problems."},{"startTime":641.218,"endTime":644.732,"body":"Deirdre - One other thing that"},{"startTime":641.218,"endTime":644.732,"body":"you mentioned when you were"},{"startTime":644.732,"endTime":647.198,"body":"skeeting, posting about this on"},{"startTime":644.732,"endTime":647.198,"body":"Blue Sky,"},{"startTime":647.527,"endTime":651.489,"body":"was that the proof is actually"},{"startTime":647.527,"endTime":651.489,"body":"quite elegant and uses novel"},{"startTime":651.489,"endTime":654.017,"body":"techniques, which is like"},{"startTime":651.489,"endTime":654.017,"body":"wonderful to"},{"startTime":654.177,"endTime":658.325,"body":"see because even humans"},{"startTime":654.177,"endTime":658.325,"body":"sometimes have a hard time"},{"startTime":658.325,"endTime":661.458,"body":"giving a grokkable, nice proof"},{"startTime":658.325,"endTime":661.458,"body":"of some"},{"startTime":662.108,"endTime":666.525,"body":"either, you know, something that"},{"startTime":662.108,"endTime":666.525,"body":"they're trying to establish or"},{"startTime":666.525,"endTime":668.877,"body":"that, you know, a lemma is"},{"startTime":666.525,"endTime":668.877,"body":"correct"},{"startTime":668.958,"endTime":669.938,"body":"or something like that."},{"startTime":670.547,"endTime":671.657,"body":"Can you explain that a little"},{"startTime":670.547,"endTime":671.657,"body":"bit?"},{"startTime":673.738,"endTime":675.098,"body":"Chris - A couple of things about"},{"startTime":673.738,"endTime":675.098,"body":"this."},{"startTime":675.238,"endTime":678.628,"body":"So the, you know, the prior best"},{"startTime":675.238,"endTime":678.628,"body":"result that goes back to the"},{"startTime":678.628,"endTime":679.137,"body":"late 90s,"},{"startTime":679.578,"endTime":682.358,"body":"using this like really heavy"},{"startTime":679.578,"endTime":682.358,"body":"machinery, this PCP machinery,"},{"startTime":682.537,"endTime":684.037,"body":"and all this like"},{"startTime":682.537,"endTime":684.037,"body":"self-composition,"},{"startTime":685.137,"endTime":685.877,"body":"really complicated."},{"startTime":687.057,"endTime":688.358,"body":"It's pretty hard to follow."},{"startTime":690.297,"endTime":693.417,"body":"It's a great result, but it's"},{"startTime":690.297,"endTime":693.417,"body":"like pretty quiet run."},{"startTime":695.098,"endTime":696.257,"body":"Why can't be there."},{"startTime":697.598,"endTime":698.998,"body":"And then this result,"},{"startTime":699.218,"endTime":701.657,"body":"it just like shoots straight at"},{"startTime":699.218,"endTime":701.657,"body":"the target."},{"startTime":701.897,"endTime":704.738,"body":"I mean, it gives this direct"},{"startTime":701.897,"endTime":704.738,"body":"reduction."},{"startTime":704.998,"endTime":706.557,"body":"I know you all remember from"},{"startTime":704.998,"endTime":706.557,"body":"undergrad,"},{"startTime":706.797,"endTime":708.157,"body":"like to prove a problem and be"},{"startTime":706.797,"endTime":708.157,"body":"hard,"},{"startTime":708.377,"endTime":712.118,"body":"you give a reduction from 3SAT"},{"startTime":708.377,"endTime":712.118,"body":"to your problem."},{"startTime":712.118,"endTime":713.897,"body":"Deirdre - Yeah yeah sure we all"},{"startTime":712.118,"endTime":713.897,"body":"remember from undergrad."},{"startTime":713.897,"endTime":716.537,"body":"Chris - So you guys do these in"},{"startTime":713.897,"endTime":716.537,"body":"your sleep still."},{"startTime":717.098,"endTime":719.598,"body":"So that's what this did."},{"startTime":719.777,"endTime":724.698,"body":"It just went straight from 3SAT"},{"startTime":719.777,"endTime":724.698,"body":"to a CVP problem,"},{"startTime":725.098,"endTime":726.177,"body":"this approximate CVP problem."},{"startTime":727.017,"endTime":730.698,"body":"And it did so with really just"},{"startTime":727.017,"endTime":730.698,"body":"elegant,"},{"startTime":731.838,"endTime":735.397,"body":"algebraic encoding of the 3SAT"},{"startTime":731.838,"endTime":735.397,"body":"formula."},{"startTime":735.397,"endTime":736.797,"body":"You have to take a 3SAT formula"},{"startTime":736.818,"endTime":739.649,"body":"and translate it to a CVP, a"},{"startTime":736.818,"endTime":739.649,"body":"lattice and a target point,"},{"startTime":739.649,"endTime":739.958,"body":"right?"},{"startTime":740.517,"endTime":742.238,"body":"And satisfying certain"},{"startTime":740.517,"endTime":742.238,"body":"properties."},{"startTime":743.017,"endTime":745.277,"body":"And it just did it straight."},{"startTime":745.427,"endTime":748.91,"body":"It took like, oh yeah, we're"},{"startTime":745.427,"endTime":748.91,"body":"going to encode these whole"},{"startTime":748.91,"endTime":749.417,"body":"formulas"},{"startTime":749.728,"endTime":752.198,"body":"as a Reed Solomon code, a Reed"},{"startTime":749.728,"endTime":752.198,"body":"Solomon code word."},{"startTime":752.407,"endTime":754.421,"body":"And we're going to take each"},{"startTime":752.407,"endTime":754.421,"body":"clause and encode it in a"},{"startTime":754.421,"endTime":755.257,"body":"slightly different way"},{"startTime":755.387,"endTime":757.897,"body":"as a Reed Solomon code word and"},{"startTime":755.387,"endTime":757.897,"body":"put constraints."},{"startTime":758.088,"endTime":761.417,"body":"And these constraints give you a"},{"startTime":758.088,"endTime":761.417,"body":"CVP instance."},{"startTime":761.917,"endTime":764.317,"body":"Actually, it gives you this, the"},{"startTime":761.917,"endTime":764.317,"body":"side effect is it gives you"},{"startTime":764.338,"endTime":767.557,"body":"this nearest code word problem"},{"startTime":764.338,"endTime":767.557,"body":"instance, actually."},{"startTime":768.017,"endTime":769.958,"body":"So it goes by two steps."},{"startTime":770.178,"endTime":771.718,"body":"First, it goes to the nearest"},{"startTime":770.178,"endTime":771.718,"body":"code word problem."},{"startTime":772.377,"endTime":775.637,"body":"And then there's a very simple"},{"startTime":772.377,"endTime":775.637,"body":"prior known reduction"},{"startTime":775.897,"endTime":777.698,"body":"from nearest code word problem"},{"startTime":775.897,"endTime":777.698,"body":"to CVP."},{"startTime":778.777,"endTime":782.198,"body":"So the interesting novelty is in"},{"startTime":778.777,"endTime":782.198,"body":"that step"},{"startTime":782.357,"endTime":784.538,"body":"to nearest code word, which is"},{"startTime":782.357,"endTime":784.538,"body":"quite cool."},{"startTime":785.857,"endTime":788.438,"body":"And it's just unlike anything"},{"startTime":785.857,"endTime":788.438,"body":"I've ever seen."},{"startTime":788.458,"endTime":791.418,"body":"I asked some people around, and"},{"startTime":788.458,"endTime":791.418,"body":"they hadn't seen it either."},{"startTime":791.678,"endTime":794.489,"body":"I asked the people who would"},{"startTime":791.678,"endTime":794.489,"body":"like work in the coding"},{"startTime":794.489,"endTime":795.757,"body":"complexity and like all"},{"startTime":795.757,"endTime":798.992,"body":"these polynomial code coding"},{"startTime":795.757,"endTime":798.992,"body":"problems. And they're like,"},{"startTime":798.992,"endTime":799.757,"body":"yeah, I mean,"},{"startTime":799.897,"endTime":803.418,"body":"I've seen some stuff with"},{"startTime":799.897,"endTime":803.418,"body":"shadows and whatever,"},{"startTime":803.737,"endTime":807.557,"body":"but nothing nearly quite like"},{"startTime":803.737,"endTime":807.557,"body":"this. So really original, really"},{"startTime":807.557,"endTime":808.058,"body":"elegant,"},{"startTime":808.058,"endTime":808.059,"body":"Deirdre - Yeah."},{"startTime":808.558,"endTime":808.958,"body":"Chris - Very beautiful."},{"startTime":810.058,"endTime":813.692,"body":"David - And to just like confirm"},{"startTime":810.058,"endTime":813.692,"body":"I know we all know this from"},{"startTime":813.692,"endTime":816.418,"body":"undergrad but to confirm um what"},{"startTime":813.692,"endTime":816.418,"body":"we definitely"},{"startTime":816.538,"endTime":819.682,"body":"learned in ECS 376, like when"},{"startTime":816.538,"endTime":819.682,"body":"you're"},{"startTime":819.682,"endTime":821.798,"body":"there, the goal is to say, look,"},{"startTime":819.682,"endTime":821.798,"body":"3SAT,"},{"startTime":821.838,"endTime":825.232,"body":"we all agree, you know, is NP"},{"startTime":821.838,"endTime":825.232,"body":"hard. So if"},{"startTime":825.232,"endTime":826.958,"body":"problem, or you can take a 3SAT"},{"startTime":827.078,"endTime":830.354,"body":"instance, convert it into"},{"startTime":827.078,"endTime":830.354,"body":"another problem, solve that"},{"startTime":830.354,"endTime":832.938,"body":"problem, and then convert it"},{"startTime":830.354,"endTime":832.938,"body":"back, we must"},{"startTime":833.097,"endTime":836.097,"body":"know that that other problem is"},{"startTime":833.097,"endTime":836.097,"body":"at least as hard as 3SAT. So in"},{"startTime":836.097,"endTime":837.597,"body":"this case, we took an arbitrary"},{"startTime":837.918,"endTime":841.536,"body":"3SAT instance, and we turned it"},{"startTime":837.918,"endTime":841.536,"body":"into, I don't want to solve that"},{"startTime":841.536,"endTime":843.317,"body":"problem, instead I'll solve CVP"},{"startTime":844.857,"endTime":849.146,"body":"directly and then therefore had"},{"startTime":844.857,"endTime":849.146,"body":"we done that it must be at least"},{"startTime":849.146,"endTime":851.257,"body":"as hard now which way does the—"},{"startTime":851.257,"endTime":854.877,"body":"Chris - Exactly a plus yeah yeah"},{"startTime":851.257,"endTime":854.877,"body":"yeah yeah."},{"startTime":854.877,"endTime":854.878,"body":"David - Inequality get rid see"},{"startTime":854.877,"endTime":854.878,"body":"this was the thing that always"},{"startTime":854.878,"endTime":855.218,"body":"confused me I would always get"},{"startTime":854.878,"endTime":855.218,"body":"backwards"},{"startTime":855.277,"endTime":857.834,"body":"I never remembered which"},{"startTime":855.277,"endTime":857.834,"body":"direction of the reduction was"},{"startTime":857.834,"endTime":859.777,"body":"which is that three sat less"},{"startTime":857.834,"endTime":859.777,"body":"than or three"},{"startTime":859.997,"endTime":861.617,"body":"sat greater than CVP."},{"startTime":861.617,"endTime":864.73,"body":"Chris - It's 3SAT less than or"},{"startTime":861.617,"endTime":864.73,"body":"equal"},{"startTime":864.73,"endTime":866.357,"body":"saying like the difficulty"},{"startTime":866.818,"endTime":870.649,"body":"of the three set problem is no"},{"startTime":866.818,"endTime":870.649,"body":"more than the difficulty of of"},{"startTime":870.649,"endTime":872.437,"body":"the cvp problem but you know"},{"startTime":872.458,"endTime":876.467,"body":"the inequality aside, you have"},{"startTime":872.458,"endTime":876.467,"body":"it exactly right. And the"},{"startTime":876.467,"endTime":879.237,"body":"interesting thing, like we're"},{"startTime":876.467,"endTime":879.237,"body":"trying to"},{"startTime":879.418,"endTime":883.568,"body":"prove that not CVP is NP-hard,"},{"startTime":879.418,"endTime":883.568,"body":"but"},{"startTime":883.568,"endTime":885.678,"body":"what you have to do is actually"},{"startTime":885.958,"endTime":890.379,"body":"design a reduction that maps"},{"startTime":885.958,"endTime":890.379,"body":"this formula to a CVP instance,"},{"startTime":890.379,"endTime":893.078,"body":"but you need to kind of like"},{"startTime":890.379,"endTime":893.078,"body":"polarize"},{"startTime":893.237,"endTime":897.328,"body":"it in some way. So if the"},{"startTime":893.237,"endTime":897.328,"body":"formula is satisfiable, you need"},{"startTime":897.328,"endTime":899.697,"body":"to generate a CVP instance that"},{"startTime":897.328,"endTime":899.697,"body":"is"},{"startTime":900.438,"endTime":903.927,"body":"a yes instance, like the target"},{"startTime":900.438,"endTime":903.927,"body":"point is pretty close to the"},{"startTime":903.927,"endTime":905.938,"body":"lattice. But if the formula was"},{"startTime":903.927,"endTime":905.938,"body":"not"},{"startTime":906.158,"endTime":909.878,"body":"satisfiable, target point has to"},{"startTime":906.158,"endTime":909.878,"body":"be like much farther away from"},{"startTime":909.878,"endTime":911.558,"body":"the lattice by this n to the"},{"startTime":911.558,"endTime":915.064,"body":"1 over 400 factor or whatever"},{"startTime":911.558,"endTime":915.064,"body":"the factor is. So you need to"},{"startTime":915.064,"endTime":916.938,"body":"kind of generate these like two"},{"startTime":917.617,"endTime":921.195,"body":"very different situations from"},{"startTime":917.617,"endTime":921.195,"body":"merely the fact that this"},{"startTime":921.195,"endTime":923.538,"body":"formula is either satisfiable or"},{"startTime":921.195,"endTime":923.538,"body":"not."},{"startTime":924.018,"endTime":927.04,"body":"And you don't know whether it is"},{"startTime":924.018,"endTime":927.04,"body":"your reduction just transfers"},{"startTime":927.04,"endTime":928.577,"body":"its satisfiability to these two"},{"startTime":928.597,"endTime":933.538,"body":"conditions. So that's why it's"},{"startTime":928.597,"endTime":933.538,"body":"super intricate and tricky to"},{"startTime":935.418,"endTime":937.078,"body":"some approximation proofs."},{"startTime":937.578,"endTime":942.724,"body":"Deirdre - Yeah. This kind of"},{"startTime":937.578,"endTime":942.724,"body":"jumped out at me when we were"},{"startTime":942.724,"endTime":947.419,"body":"analyzing this because we've"},{"startTime":942.724,"endTime":947.419,"body":"seen other proofs, other"},{"startTime":947.419,"endTime":949.497,"body":"algorithms from models."},{"startTime":951.018,"endTime":953.325,"body":"We especially care about how"},{"startTime":951.018,"endTime":953.325,"body":"they're applicable to"},{"startTime":953.325,"endTime":953.938,"body":"cryptography."},{"startTime":954.087,"endTime":957.221,"body":"And this is sort of a hop, skip"},{"startTime":954.087,"endTime":957.221,"body":"and a jump away from how hard"},{"startTime":957.221,"endTime":960.459,"body":"are some of the lattice problems"},{"startTime":957.221,"endTime":960.459,"body":"that we build our cryptography"},{"startTime":960.459,"endTime":960.617,"body":"on."},{"startTime":961.298,"endTime":965.239,"body":"But sometimes, like we've seen"},{"startTime":961.298,"endTime":965.239,"body":"some papers come out that are"},{"startTime":965.239,"endTime":968.912,"body":"basically driven by some of"},{"startTime":965.239,"endTime":968.912,"body":"these large language models,"},{"startTime":968.912,"endTime":973.12,"body":"such as"},{"startTime":968.912,"endTime":973.12,"body":"ones that of Anthropic,"},{"startTime":973.12,"endTime":976.927,"body":"obviously kept it up to date"},{"startTime":973.12,"endTime":976.927,"body":"with the latest literature in"},{"startTime":976.927,"endTime":977.597,"body":"the field."},{"startTime":978.257,"endTime":981.447,"body":"And you saw all the pieces, you"},{"startTime":978.257,"endTime":981.447,"body":"were able to keep it all in your"},{"startTime":981.447,"endTime":984.536,"body":"context, and you were able to"},{"startTime":981.447,"endTime":984.536,"body":"put the pieces together and then"},{"startTime":984.536,"endTime":986.158,"body":"kind of draw the rest of the"},{"startTime":984.536,"endTime":986.158,"body":"owl."},{"startTime":986.398,"endTime":991.154,"body":"And like the result is a result"},{"startTime":986.398,"endTime":991.154,"body":"and it's meaningful and it's"},{"startTime":991.154,"endTime":994.137,"body":"useful, but it's also not very"},{"startTime":991.154,"endTime":994.137,"body":"clever."},{"startTime":994.938,"endTime":998.964,"body":"I don't think the words elegant"},{"startTime":994.938,"endTime":998.964,"body":"or, you know, interesting or,"},{"startTime":998.964,"endTime":1003.192,"body":"you know, any of the things that"},{"startTime":998.964,"endTime":1003.192,"body":"you used to describe this proof"},{"startTime":1003.192,"endTime":1004.737,"body":"would be used for that."},{"startTime":1004.808,"endTime":1008.684,"body":"But now this is apparently fully"},{"startTime":1004.808,"endTime":1008.684,"body":"powered by yet another model"},{"startTime":1008.684,"endTime":1012.495,"body":"with a different way it was"},{"startTime":1008.684,"endTime":1012.495,"body":"grown or a different way that it"},{"startTime":1012.495,"endTime":1014.757,"body":"was targeted or something like"},{"startTime":1012.495,"endTime":1014.757,"body":"that."},{"startTime":1015.997,"endTime":1019.224,"body":"and it's it's very interesting"},{"startTime":1015.997,"endTime":1019.224,"body":"to see and we we might be"},{"startTime":1019.224,"endTime":1021.278,"body":"reaching the point because I've"},{"startTime":1019.224,"endTime":1021.278,"body":"been"},{"startTime":1021.457,"endTime":1025.364,"body":"sort of trying to keep my ear"},{"startTime":1021.457,"endTime":1025.364,"body":"out for do"},{"startTime":1025.364,"endTime":1027.857,"body":"moment when it comes to"},{"startTime":1025.364,"endTime":1027.857,"body":"mathematics or"},{"startTime":1028.018,"endTime":1031.401,"body":"cryptography or anything like"},{"startTime":1028.018,"endTime":1031.401,"body":"that where"},{"startTime":1031.401,"endTime":1033.818,"body":"doing something that to the"},{"startTime":1031.401,"endTime":1033.818,"body":"human experts"},{"startTime":1034.497,"endTime":1038.922,"body":"seems different or notable or I"},{"startTime":1034.497,"endTime":1038.922,"body":"would never think of that or"},{"startTime":1038.922,"endTime":1041.698,"body":"alien because sometimes these"},{"startTime":1038.922,"endTime":1041.698,"body":"you know"},{"startTime":1041.717,"endTime":1044.362,"body":"Go grandmasters would describe"},{"startTime":1041.717,"endTime":1044.362,"body":"the moves that AlphaGo would"},{"startTime":1044.362,"endTime":1045.457,"body":"take and they'd be like,"},{"startTime":1045.977,"endTime":1049.711,"body":"it's like someone came down to"},{"startTime":1045.977,"endTime":1049.711,"body":"Earth and was playing some crazy"},{"startTime":1049.711,"endTime":1051.518,"body":"alien version of Go with moves"},{"startTime":1051.658,"endTime":1057.04,"body":"that I would never even think"},{"startTime":1051.658,"endTime":1057.04,"body":"of. And this smells something in"},{"startTime":1057.04,"endTime":1060.217,"body":"that ballpark. So yeah, I don't"},{"startTime":1057.04,"endTime":1060.217,"body":"know."},{"startTime":1061.318,"endTime":1064.581,"body":"Chris - Yeah I I I kind of agree"},{"startTime":1061.318,"endTime":1064.581,"body":"with everything you just said I"},{"startTime":1064.581,"endTime":1066.757,"body":"mean I don't want to minimize"},{"startTime":1064.581,"endTime":1066.757,"body":"anything from"},{"startTime":1066.757,"endTime":1070.329,"body":"the previous results they're"},{"startTime":1066.757,"endTime":1070.329,"body":"super impressive but like you"},{"startTime":1070.329,"endTime":1072.837,"body":"say like the for the most part"},{"startTime":1070.329,"endTime":1072.837,"body":"people say"},{"startTime":1072.918,"endTime":1077.211,"body":"like okay yeah you took like"},{"startTime":1072.918,"endTime":1077.211,"body":"very uh expertly put together a"},{"startTime":1077.211,"endTime":1079.977,"body":"lot of different pieces and put"},{"startTime":1077.211,"endTime":1079.977,"body":"them in"},{"startTime":1080.198,"endTime":1082.912,"body":"in in different ways but like"},{"startTime":1080.198,"endTime":1082.912,"body":"the dominoes were kind of all"},{"startTime":1082.912,"endTime":1084.457,"body":"there lined up we didn't quite"},{"startTime":1082.912,"endTime":1084.457,"body":"see"},{"startTime":1084.477,"endTime":1087.69,"body":"how to knock over you know the"},{"startTime":1084.477,"endTime":1087.69,"body":"first one or whatever and then"},{"startTime":1087.69,"endTime":1089.137,"body":"you know the model found it"},{"startTime":1089.168,"endTime":1093.175,"body":"and then everything falls falls"},{"startTime":1089.168,"endTime":1093.175,"body":"and and it comes out great and"},{"startTime":1093.175,"endTime":1095.278,"body":"like that's super useful uh"},{"startTime":1093.175,"endTime":1095.278,"body":"super"},{"startTime":1095.438,"endTime":1099.409,"body":"interesting but I think this is"},{"startTime":1095.438,"endTime":1099.409,"body":"the first one you know where I"},{"startTime":1099.409,"endTime":1101.558,"body":"can you know from my own"},{"startTime":1099.409,"endTime":1101.558,"body":"knowledge"},{"startTime":1101.837,"endTime":1105.904,"body":"and experience confidently say"},{"startTime":1101.837,"endTime":1105.904,"body":"like oh this is really original"},{"startTime":1105.904,"endTime":1108.038,"body":"like this is it's not alien math"},{"startTime":1108.137,"endTime":1111.4,"body":"because it's all known stuff"},{"startTime":1108.137,"endTime":1111.4,"body":"it's like these read solomon"},{"startTime":1111.4,"endTime":1113.557,"body":"things or whatever right but"},{"startTime":1111.4,"endTime":1113.557,"body":"they were"},{"startTime":1114.298,"endTime":1118.791,"body":"the whole path that it took was"},{"startTime":1114.298,"endTime":1118.791,"body":"like extremely different from"},{"startTime":1118.791,"endTime":1121.038,"body":"anything you know I'm aware of"},{"startTime":1121.257,"endTime":1125.665,"body":"and anyone I've talked to is"},{"startTime":1121.257,"endTime":1125.665,"body":"aware of so that is that's why I"},{"startTime":1125.665,"endTime":1128.237,"body":"think you know the Mythos Hawk"},{"startTime":1125.665,"endTime":1128.237,"body":"break"},{"startTime":1128.237,"endTime":1132.215,"body":"and everything I was like oh"},{"startTime":1128.237,"endTime":1132.215,"body":"that's really"},{"startTime":1132.215,"endTime":1134.798,"body":"was like wow like whoa this is"},{"startTime":1132.215,"endTime":1134.798,"body":"really."},{"startTime":1135.698,"endTime":1136.387,"body":"Deirdre - Yeah. All right."},{"startTime":1135.698,"endTime":1136.387,"body":"Anyone have anything else before"},{"startTime":1136.387,"endTime":1136.756,"body":"we we pivot? No. Cool. Awesome."},{"startTime":1136.866,"endTime":1139.415,"body":"You mentioned that there were"},{"startTime":1136.866,"endTime":1139.415,"body":"some you mentioned before we"},{"startTime":1139.415,"endTime":1142.099,"body":"started recording that there"},{"startTime":1139.415,"endTime":1142.099,"body":"were some other results that had"},{"startTime":1142.099,"endTime":1142.905,"body":"come out recently."},{"startTime":1143.106,"endTime":1147.062,"body":"not the closest vector problem,"},{"startTime":1143.106,"endTime":1147.062,"body":"but the shortest vector problem"},{"startTime":1147.062,"endTime":1148.785,"body":"that jumped out to you that"},{"startTime":1148.785,"endTime":1149.986,"body":"we had completely missed."},{"startTime":1150.295,"endTime":1152.905,"body":"Do you want to share with that"},{"startTime":1150.295,"endTime":1152.905,"body":"with the"},{"startTime":1153.526,"endTime":1156.903,"body":"Chris - Sure. Yeah. I mean, it"},{"startTime":1153.526,"endTime":1156.903,"body":"was over a span of maybe three"},{"startTime":1156.903,"endTime":1157.185,"body":"days."},{"startTime":1157.915,"endTime":1161.43,"body":"We had three different papers"},{"startTime":1157.915,"endTime":1161.43,"body":"posted to ePrint, which is like"},{"startTime":1161.43,"endTime":1163.305,"body":"the cryptography preprint"},{"startTime":1161.43,"endTime":1163.305,"body":"server,"},{"startTime":1164.825,"endTime":1169.139,"body":"all getting more or less the"},{"startTime":1164.825,"endTime":1169.139,"body":"same result, which the result is"},{"startTime":1169.139,"endTime":1170.146,"body":"the following."},{"startTime":1171.185,"endTime":1173.57,"body":"The shortest vector problem, so"},{"startTime":1171.185,"endTime":1173.57,"body":"that is you're just given a"},{"startTime":1173.57,"endTime":1174.886,"body":"lattice, there's no target"},{"startTime":1173.57,"endTime":1174.886,"body":"point,"},{"startTime":1175.366,"endTime":1179.891,"body":"and you want to follow the exact"},{"startTime":1175.366,"endTime":1179.891,"body":"shortest non-zero vector in the"},{"startTime":1179.891,"endTime":1180.466,"body":"lattice."},{"startTime":1180.525,"endTime":1180.846,"body":"Deirdre - Mm-hmm."},{"startTime":1181.146,"endTime":1183.586,"body":"Chris - So zero is always in"},{"startTime":1181.146,"endTime":1183.586,"body":"there, that's shortest,"},{"startTime":1183.586,"endTime":1184.065,"body":"obviously,"},{"startTime":1184.146,"endTime":1186.726,"body":"but you want the shortest"},{"startTime":1184.146,"endTime":1186.726,"body":"non-zero vector in the lattice."},{"startTime":1187.486,"endTime":1192.086,"body":"So the state-of-the-art for the"},{"startTime":1187.486,"endTime":1192.086,"body":"exact SVP is from 2015,"},{"startTime":1193.165,"endTime":1194.586,"body":"And it's basically a two to the."},{"startTime":1195.896,"endTime":1199.085,"body":"So exponential time with a nice"},{"startTime":1195.896,"endTime":1199.085,"body":"clean n in the exponent, right?"},{"startTime":1199.486,"endTime":1201.705,"body":"And with a little extra, let's"},{"startTime":1199.486,"endTime":1201.705,"body":"worry about that."},{"startTime":1202.276,"endTime":1205.386,"body":"So basically two to the n, and"},{"startTime":1202.276,"endTime":1205.386,"body":"then these new papers,"},{"startTime":1206.925,"endTime":1208.726,"body":"you can get something like two"},{"startTime":1206.925,"endTime":1208.726,"body":"to the point"},{"startTime":1209.026,"endTime":1212.026,"body":"seven, two something something"},{"startTime":1209.026,"endTime":1212.026,"body":"times."},{"startTime":1212.906,"endTime":1215.205,"body":"So they improve the constant in"},{"startTime":1212.906,"endTime":1215.205,"body":"the exponent"},{"startTime":1215.315,"endTime":1218.606,"body":"from like just one times n to"},{"startTime":1215.315,"endTime":1218.606,"body":"0.7 something times n."},{"startTime":1219.866,"endTime":1223.34,"body":"And they all came out like"},{"startTime":1219.866,"endTime":1223.34,"body":"within a couple days of each"},{"startTime":1223.34,"endTime":1223.726,"body":"other."},{"startTime":1224.266,"endTime":1226.366,"body":"And they all use the same basic"},{"startTime":1224.266,"endTime":1226.366,"body":"technique."},{"startTime":1227.045,"endTime":1231.386,"body":"And some of the papers admit"},{"startTime":1227.045,"endTime":1231.386,"body":"that like AI came up with this"},{"startTime":1231.585,"endTime":1235.305,"body":"and other ones, we kind of got a"},{"startTime":1231.585,"endTime":1235.305,"body":"little"},{"startTime":1235.386,"endTime":1237.886,"body":"And some of them don't comment"},{"startTime":1235.386,"endTime":1237.886,"body":"at all on other AI games."},{"startTime":1239.185,"endTime":1242.445,"body":"But in any case, it's pretty"},{"startTime":1239.185,"endTime":1242.445,"body":"clear that AI"},{"startTime":1242.526,"endTime":1244.606,"body":"was the force multiplier."},{"startTime":1245.726,"endTime":1248.493,"body":"And so, you know, that's the"},{"startTime":1245.726,"endTime":1248.493,"body":"result"},{"startTime":1248.654,"endTime":1250.333,"body":"that hadn't been improved in 11"},{"startTime":1248.654,"endTime":1250.333,"body":"years."},{"startTime":1250.554,"endTime":1253.934,"body":"It uses the same core component"},{"startTime":1254.753,"endTime":1255.713,"body":"behind the prior test results,"},{"startTime":1256.574,"endTime":1257.394,"body":"but does some extra"},{"startTime":1259.133,"endTime":1260.593,"body":"in a more efficient way."},{"startTime":1262.373,"endTime":1263.594,"body":"It doesn't seem to have any"},{"startTime":1262.373,"endTime":1263.594,"body":"effect"},{"startTime":1263.854,"endTime":1266.153,"body":"on the security of Datis crypto,"},{"startTime":1266.734,"endTime":1267.974,"body":"as far as anyone can tell,"},{"startTime":1268.153,"endTime":1272.653,"body":"because it's attacking this"},{"startTime":1268.153,"endTime":1272.653,"body":"exact worst SVP."},{"startTime":1272.834,"endTime":1274.574,"body":"So if the algorithm has to"},{"startTime":1272.834,"endTime":1274.574,"body":"provably work,"},{"startTime":1274.834,"endTime":1284.993,"body":"and it's already has a nice"},{"startTime":1274.834,"endTime":1284.993,"body":"shape to it and everything."},{"startTime":1285.543,"endTime":1287.454,"body":"And so kind of heuristically,"},{"startTime":1287.604,"endTime":1289.353,"body":"we know how to do much better"},{"startTime":1289.533,"endTime":1291.334,"body":"than the 2^{0.7 whatever n}."},{"startTime":1292.694,"endTime":1293.873,"body":"So it doesn't really change"},{"startTime":1294.184,"endTime":1297.094,"body":"as far as we can tell any of the"},{"startTime":1294.184,"endTime":1297.094,"body":"security estimates,"},{"startTime":1297.283,"endTime":1298.393,"body":"but it is like, again,"},{"startTime":1298.594,"endTime":1300.153,"body":"like as a pure complexity"},{"startTime":1298.594,"endTime":1300.153,"body":"result,"},{"startTime":1301.054,"endTime":1302.594,"body":"it's a big step forward."},{"startTime":1303.433,"endTime":1307.475,"body":"Deirdre - I wonder, I'm the fact"},{"startTime":1303.433,"endTime":1307.475,"body":"that we had like three that came"},{"startTime":1307.475,"endTime":1309.813,"body":"out very close to each other."},{"startTime":1307.475,"endTime":1309.813,"body":"And they"},{"startTime":1309.813,"endTime":1313.551,"body":"were very similar. I'm very"},{"startTime":1309.813,"endTime":1313.551,"body":"curious how they were querying"},{"startTime":1313.551,"endTime":1315.913,"body":"or what they were querying. And"},{"startTime":1313.551,"endTime":1315.913,"body":"like,"},{"startTime":1316.872,"endTime":1320.523,"body":"I'm just I'm, I'm very curious,"},{"startTime":1316.872,"endTime":1320.523,"body":"because I have a feeling they"},{"startTime":1320.523,"endTime":1322.532,"body":"all kind of went in the same"},{"startTime":1320.523,"endTime":1322.532,"body":"path."},{"startTime":1323.073,"endTime":1325.966,"body":"And they finessed it into, you"},{"startTime":1323.073,"endTime":1325.966,"body":"know, something that they, you"},{"startTime":1325.966,"endTime":1327.413,"body":"know, they put out themselves."},{"startTime":1329.071,"endTime":1329.131,"body":"Well, yeah, this is,"},{"startTime":1329.131,"endTime":1332.346,"body":"Chris - And this is one where"},{"startTime":1329.131,"endTime":1332.346,"body":"like all the techniques used are"},{"startTime":1332.346,"endTime":1332.991,"body":"kind of well"},{"startTime":1333.251,"endTime":1338.251,"body":"established and it was put"},{"startTime":1333.251,"endTime":1338.251,"body":"together in a way,"},{"startTime":1338.251,"endTime":1338.252,"body":"Deirdre - All right."},{"startTime":1338.971,"endTime":1341.87,"body":"Chris - But it wasn't like, Oh"},{"startTime":1338.971,"endTime":1341.87,"body":"my gosh,"},{"startTime":1342.171,"endTime":1344.791,"body":"this is some brand new alien"},{"startTime":1342.171,"endTime":1344.791,"body":"math or anything like that."},{"startTime":1344.791,"endTime":1345.39,"body":"Deirdre - Yeah, okay."},{"startTime":1345.952,"endTime":1350.01,"body":"David - I was going to say, I"},{"startTime":1345.952,"endTime":1350.01,"body":"seem to recall there being a"},{"startTime":1350.01,"endTime":1353.499,"body":"proof for one of the"},{"startTime":1350.01,"endTime":1353.499,"body":"lattice-related problems that"},{"startTime":1353.499,"endTime":1357.842,"body":"the average case complexity and"},{"startTime":1353.499,"endTime":1357.842,"body":"the worst case complexity were"},{"startTime":1357.842,"endTime":1358.485,"body":"the same."},{"startTime":1359.646,"endTime":1361.646,"body":"And so does that not apply here?"},{"startTime":1361.845,"endTime":1364.354,"body":"Like you were saying, oh, it's"},{"startTime":1361.845,"endTime":1364.354,"body":"not relevant because it's worst"},{"startTime":1364.354,"endTime":1364.766,"body":"case only."},{"startTime":1365.325,"endTime":1367.521,"body":"But I thought that we had proved"},{"startTime":1365.325,"endTime":1367.521,"body":"for just about everything with"},{"startTime":1367.521,"endTime":1369.434,"body":"lattices that worst case and"},{"startTime":1367.521,"endTime":1369.434,"body":"average case have the same"},{"startTime":1369.434,"endTime":1369.825,"body":"complexity."},{"startTime":1370.745,"endTime":1371.926,"body":"So what am I misunderstanding?"},{"startTime":1371.926,"endTime":1374.466,"body":"Chris - Yeah, so we have these"},{"startTime":1371.926,"endTime":1374.466,"body":"worst case to average case"},{"startTime":1374.466,"endTime":1378.277,"body":"reductions, which is like what"},{"startTime":1374.466,"endTime":1378.277,"body":"crypto frequently relies on,"},{"startTime":1378.277,"endTime":1382.154,"body":"because you got to use random"},{"startTime":1378.277,"endTime":1382.154,"body":"instances for your crypto, but"},{"startTime":1382.154,"endTime":1385.571,"body":"you want to make sure that"},{"startTime":1382.154,"endTime":1385.571,"body":"you're using secure random"},{"startTime":1385.571,"endTime":1388.266,"body":"instances that are actually hard"},{"startTime":1385.571,"endTime":1388.266,"body":"to break."},{"startTime":1388.845,"endTime":1391.614,"body":"And the worst case hardness of"},{"startTime":1388.845,"endTime":1391.614,"body":"those kind of tells you, well,"},{"startTime":1391.614,"endTime":1394.152,"body":"you can't break the crypto"},{"startTime":1391.614,"endTime":1394.152,"body":"unless you're also capable of"},{"startTime":1394.152,"endTime":1396.046,"body":"breaking these problems in the"},{"startTime":1394.152,"endTime":1396.046,"body":"worst case."},{"startTime":1396.825,"endTime":1400.565,"body":"So the reason it doesn't kind of"},{"startTime":1396.825,"endTime":1400.565,"body":"move the needle on that, which"},{"startTime":1400.565,"endTime":1404.184,"body":"is a great question, is that"},{"startTime":1400.565,"endTime":1404.184,"body":"these worst case to average case"},{"startTime":1404.184,"endTime":1407.622,"body":"reductions usually have a blow"},{"startTime":1404.184,"endTime":1407.622,"body":"up in the dimension to some"},{"startTime":1407.622,"endTime":1408.046,"body":"amount."},{"startTime":1408.325,"endTime":1410.867,"body":"Right. So it's like, oh, it"},{"startTime":1408.325,"endTime":1410.867,"body":"starts in dimension N and it"},{"startTime":1410.867,"endTime":1413.225,"body":"goes to maybe dimension 10 N or"},{"startTime":1410.867,"endTime":1413.225,"body":"something like that."},{"startTime":1413.446,"endTime":1417.213,"body":"Right. And so, oh, if I can"},{"startTime":1413.446,"endTime":1417.213,"body":"break, well, I can break the"},{"startTime":1417.213,"endTime":1421.254,"body":"worst case in 2^0.7n, whatever"},{"startTime":1417.213,"endTime":1421.254,"body":"n, or I can break the average"},{"startTime":1421.254,"endTime":1425.432,"body":"case in 2^0.7n, whatever, 0.2,"},{"startTime":1421.254,"endTime":1425.432,"body":"something times 10n, like these"},{"startTime":1425.432,"endTime":1427.146,"body":"aren't"},{"startTime":1425.432,"endTime":1427.146,"body":"really comparable."},{"startTime":1428.506,"endTime":1431.845,"body":"So that's the, maybe the short"},{"startTime":1428.506,"endTime":1431.845,"body":"answer to that question."},{"startTime":1432.327,"endTime":1436.298,"body":"Deirdre - Okay we're gonna oh of"},{"startTime":1432.327,"endTime":1436.298,"body":"course yeah yeah yeah and"},{"startTime":1436.298,"endTime":1439.574,"body":"there's yeah and there's always"},{"startTime":1436.298,"endTime":1439.574,"body":"like especially."},{"startTime":1439.574,"endTime":1439.575,"body":"Chris - There's also"},{"startTime":1439.574,"endTime":1439.575,"body":"approximation factors in there"},{"startTime":1439.575,"endTime":1439.576,"body":"too. This is for exact SVP. So"},{"startTime":1439.575,"endTime":1439.576,"body":"there's another reason."},{"startTime":1439.595,"endTime":1442.148,"body":"Deirdre - If you're trying to"},{"startTime":1439.595,"endTime":1442.148,"body":"like, you know, the learning"},{"startTime":1442.148,"endTime":1444.254,"body":"with errors problem reduces the"},{"startTime":1442.148,"endTime":1444.254,"body":"shortest vector,"},{"startTime":1444.284,"endTime":1447.661,"body":"and there's, there's already"},{"startTime":1444.284,"endTime":1447.661,"body":"gaps in there"},{"startTime":1447.661,"endTime":1449.494,"body":"we've got gaps in here. And then"},{"startTime":1449.555,"endTime":1452.572,"body":"we've got gaps between the"},{"startTime":1449.555,"endTime":1452.572,"body":"problem that we build our"},{"startTime":1452.572,"endTime":1455.235,"body":"constructions with and all of"},{"startTime":1452.572,"endTime":1455.235,"body":"them add up into"},{"startTime":1455.394,"endTime":1459.107,"body":"what you can how expensive it is"},{"startTime":1455.394,"endTime":1459.107,"body":"to try and actually estimate any"},{"startTime":1459.107,"endTime":1460.674,"body":"of this stuff and break it."},{"startTime":1460.674,"endTime":1460.815,"body":"Chris - Break it. Yeah, exactly."},{"startTime":1461.394,"endTime":1464.674,"body":"Yeah. So the gaps always make"},{"startTime":1461.394,"endTime":1464.674,"body":"things a little easier and yeah."},{"startTime":1464.894,"endTime":1465.014,"body":"So."},{"startTime":1465.316,"endTime":1469.001,"body":"Deirdre - Okay, and more"},{"startTime":1465.316,"endTime":1469.001,"body":"lattices for"},{"startTime":1469.001,"endTime":1473.663,"body":"lattice cryptographer. There is"},{"startTime":1469.001,"endTime":1473.663,"body":"a is a is a is a quantum attack"},{"startTime":1473.663,"endTime":1474.115,"body":"paper,"},{"startTime":1474.444,"endTime":1479.634,"body":"a preliminary draft on the"},{"startTime":1474.444,"endTime":1479.634,"body":"ePrint, and they're trying to"},{"startTime":1479.634,"endTime":1482.654,"body":"attack the dihedral coset"},{"startTime":1479.634,"endTime":1482.654,"body":"problem"},{"startTime":1483.394,"endTime":1488.007,"body":"in what they say is polynomial"},{"startTime":1483.394,"endTime":1488.007,"body":"time. And this has been a bit of"},{"startTime":1488.007,"endTime":1489.794,"body":"a kerfuffle because one,"},{"startTime":1489.894,"endTime":1493.091,"body":"it's a quantum algorithm and you"},{"startTime":1489.894,"endTime":1493.091,"body":"can't just code up your quantum"},{"startTime":1493.091,"endTime":1494.715,"body":"algorithm against toy parameters"},{"startTime":1495.014,"endTime":1498.346,"body":"and just run it and see if"},{"startTime":1495.014,"endTime":1498.346,"body":"it"},{"startTime":1498.346,"endTime":1500.335,"body":"those computers yet,"},{"startTime":1498.346,"endTime":1500.335,"body":"unfortunately."},{"startTime":1501.735,"endTime":1510.035,"body":"And everyone is trying to see if"},{"startTime":1501.735,"endTime":1510.035,"body":"this paper were correct and how"},{"startTime":1510.035,"endTime":1512.934,"body":"closely it would apply"},{"startTime":1513.115,"endTime":1517.958,"body":"from the dihedral coset problem"},{"startTime":1513.115,"endTime":1517.958,"body":"to things"},{"startTime":1517.958,"endTime":1518.355,"body":"true."},{"startTime":1519.115,"endTime":1520.835,"body":"And we don't know."},{"startTime":1520.995,"endTime":1522.375,"body":"It doesn't sound like anyone"},{"startTime":1520.995,"endTime":1522.375,"body":"knows."},{"startTime":1522.654,"endTime":1523.554,"body":"Do you have an opinion?"},{"startTime":1524.995,"endTime":1527.984,"body":"David - Also, can you explain"},{"startTime":1524.995,"endTime":1527.984,"body":"what the dihedral coset problem"},{"startTime":1527.984,"endTime":1530.774,"body":"is? Because that's something we"},{"startTime":1527.984,"endTime":1530.774,"body":"all also definitely know."},{"startTime":1530.774,"endTime":1530.775,"body":"Chris - I have opinions. Yeah,"},{"startTime":1530.774,"endTime":1530.775,"body":"yeah, we should start with that."},{"startTime":1530.775,"endTime":1535.397,"body":"Indeed, indeed. Yeah. So before"},{"startTime":1530.775,"endTime":1535.397,"body":"we go to dihedral, we should go"},{"startTime":1535.397,"endTime":1540.475,"body":"to cyclic, because that's where"},{"startTime":1535.397,"endTime":1540.475,"body":"the story begins, really, like"},{"startTime":1540.475,"endTime":1541.975,"body":"30 some years ago."},{"startTime":1541.975,"endTime":1541.976,"body":"Deirdre - That too, because I"},{"startTime":1541.975,"endTime":1541.976,"body":"didn't know that one before I"},{"startTime":1541.976,"endTime":1541.977,"body":"started reading this."},{"startTime":1543.375,"endTime":1545.975,"body":"Chris - So, you know, we kind of"},{"startTime":1543.375,"endTime":1545.975,"body":"all know Shor's quantum"},{"startTime":1545.975,"endTime":1548.575,"body":"algorithm, which like breaks"},{"startTime":1545.975,"endTime":1548.575,"body":"factoring and discrete log."},{"startTime":1548.575,"endTime":1548.576,"body":"Deirdre - Yes."},{"startTime":1548.745,"endTime":1553.411,"body":"Chris - Right. And the way it"},{"startTime":1548.745,"endTime":1553.411,"body":"does that is by solving this"},{"startTime":1553.411,"endTime":1557.995,"body":"what's called a hidden shift"},{"startTime":1553.411,"endTime":1557.995,"body":"problem on the cyclic group,"},{"startTime":1557.995,"endTime":1558.814,"body":"basically."},{"startTime":1559.024,"endTime":1562.459,"body":"So there's cyclic groups in the"},{"startTime":1559.024,"endTime":1562.459,"body":"discrete log problem and there's"},{"startTime":1562.459,"endTime":1564.914,"body":"cyclic groups hiding in the"},{"startTime":1562.459,"endTime":1564.914,"body":"factoring problem."},{"startTime":1566.095,"endTime":1570.294,"body":"And quantum algorithms,"},{"startTime":1566.095,"endTime":1570.294,"body":"computers, Shor,"},{"startTime":1570.294,"endTime":1574.804,"body":"at solving these hidden hidden"},{"startTime":1570.294,"endTime":1574.804,"body":"hidden shift problems on the"},{"startTime":1574.804,"endTime":1575.894,"body":"cyclic groups."},{"startTime":1576.575,"endTime":1577.615,"body":"Okay, huge cyclic groups."},{"startTime":1578.674,"endTime":1583.021,"body":"So the closest thing to being a"},{"startTime":1578.674,"endTime":1583.021,"body":"cyclic group without cyclic is"},{"startTime":1583.021,"endTime":1584.375,"body":"the dihedral group."},{"startTime":1584.934,"endTime":1588.543,"body":"Okay, so the dihedral group is"},{"startTime":1584.934,"endTime":1588.543,"body":"basically cyclic, but also with"},{"startTime":1588.543,"endTime":1589.194,"body":"like flips."},{"startTime":1589.774,"endTime":1593.392,"body":"So if you think of like an"},{"startTime":1589.774,"endTime":1593.392,"body":"N-gon, a regular N-gon, a"},{"startTime":1593.392,"endTime":1597.577,"body":"triangle, a square, a pentagon,"},{"startTime":1593.392,"endTime":1597.577,"body":"et cetera, with N sides, and"},{"startTime":1597.577,"endTime":1601.054,"body":"then you can obviously rotate it"},{"startTime":1597.577,"endTime":1601.054,"body":"to itself, right?"},{"startTime":1601.284,"endTime":1603.815,"body":"And then it'll overlap with"},{"startTime":1601.284,"endTime":1603.815,"body":"itself with all the variations."},{"startTime":1604.454,"endTime":1607.676,"body":"But you can also flip it, right,"},{"startTime":1604.454,"endTime":1607.676,"body":"if it's got an even number of"},{"startTime":1607.676,"endTime":1607.994,"body":"sides."},{"startTime":1609.375,"endTime":1612.334,"body":"Flip is giving you now the"},{"startTime":1609.375,"endTime":1612.334,"body":"dihedral group."},{"startTime":1612.665,"endTime":1616.299,"body":"So this is, the dihedral group"},{"startTime":1612.665,"endTime":1616.299,"body":"is basically the symmetry of an"},{"startTime":1616.299,"endTime":1617.074,"body":"N-gon, right?"},{"startTime":1618.115,"endTime":1623.941,"body":"And for all we know, quantum"},{"startTime":1618.115,"endTime":1623.941,"body":"breaks and solves this hidden"},{"startTime":1623.941,"endTime":1627.314,"body":"shift problem on the cyclic"},{"startTime":1623.941,"endTime":1627.314,"body":"group,"},{"startTime":1628.014,"endTime":1631.355,"body":"huge cyclic groups, but it's"},{"startTime":1628.014,"endTime":1631.355,"body":"totally unable to do it on the"},{"startTime":1632.754,"endTime":1637.146,"body":"adding this one flip element"},{"startTime":1632.754,"endTime":1637.146,"body":"kind of destroys, seems to"},{"startTime":1637.146,"endTime":1639.994,"body":"destroy quantum's power to solve"},{"startTime":1637.146,"endTime":1639.994,"body":"it."},{"startTime":1641.074,"endTime":1645.334,"body":"So that's kind of a strange and"},{"startTime":1641.074,"endTime":1645.334,"body":"bizarre situation."},{"startTime":1646.374,"endTime":1647.134,"body":"But there we have it."},{"startTime":1647.815,"endTime":1651.151,"body":"And then, so people for a long"},{"startTime":1647.815,"endTime":1651.151,"body":"time have been trying to solve"},{"startTime":1651.151,"endTime":1651.374,"body":"this"},{"startTime":1652.334,"endTime":1656.046,"body":"dihedral hidden coset or"},{"startTime":1652.334,"endTime":1656.046,"body":"dihedral coset problem"},{"startTime":1656.046,"endTime":1656.854,"body":"quantumly."},{"startTime":1657.225,"endTime":1659.811,"body":"So that's what the claimed"},{"startTime":1657.225,"endTime":1659.811,"body":"result is basically to have done"},{"startTime":1659.811,"endTime":1660.035,"body":"this."},{"startTime":1676.894,"endTime":1681.084,"body":"So you can take a lattice"},{"startTime":1676.894,"endTime":1681.084,"body":"problem, transform it into this"},{"startTime":1681.084,"endTime":1683.854,"body":"hidden shift on a huge dihedral"},{"startTime":1681.084,"endTime":1683.854,"body":"group."},{"startTime":1684.455,"endTime":1687.106,"body":"And then if you can solve that,"},{"startTime":1684.455,"endTime":1687.106,"body":"that gives you a solution to"},{"startTime":1687.106,"endTime":1688.455,"body":"your original lattice problem."},{"startTime":1689.675,"endTime":1691.214,"body":"So that's what we're dealing"},{"startTime":1689.675,"endTime":1691.214,"body":"with here."},{"startTime":1691.814,"endTime":1694.31,"body":"And there's a bunch of overheads"},{"startTime":1691.814,"endTime":1694.31,"body":"involved in these reductions,"},{"startTime":1694.31,"endTime":1695.415,"body":"but they're all polynomial."},{"startTime":1696.774,"endTime":1700.795,"body":"So the claim here is polynomial"},{"startTime":1696.774,"endTime":1700.795,"body":"time"},{"startTime":1700.795,"endTime":1701.734,"body":"coset problem,"},{"startTime":1702.375,"endTime":1706.78,"body":"and therefore for all these"},{"startTime":1702.375,"endTime":1706.78,"body":"lattice problems that underlie"},{"startTime":1706.78,"endTime":1709.254,"body":"cryptography. So pretty serious."},{"startTime":1710.544,"endTime":1715.82,"body":"The good news or bad news or"},{"startTime":1710.544,"endTime":1715.82,"body":"news is that people don't seem"},{"startTime":1715.82,"endTime":1719.095,"body":"to buy the proof. They don't."},{"startTime":1715.82,"endTime":1719.095,"body":"They're"},{"startTime":1719.254,"endTime":1724.079,"body":"identified errors in the proof"},{"startTime":1719.254,"endTime":1724.079,"body":"that are pretty substantial and"},{"startTime":1724.079,"endTime":1726.294,"body":"they don't seem to be easily"},{"startTime":1726.354,"endTime":1731.65,"body":"fixable. And it's in more than"},{"startTime":1726.354,"endTime":1731.65,"body":"one place, it appears to be. So"},{"startTime":1731.65,"endTime":1733.995,"body":"the status of this claim is"},{"startTime":1734.374,"endTime":1737.514,"body":"still kind of up in the air. And"},{"startTime":1734.374,"endTime":1737.514,"body":"people are trying to figure out,"},{"startTime":1737.514,"endTime":1739.134,"body":"you know, what's actually going"},{"startTime":1737.514,"endTime":1739.134,"body":"on"},{"startTime":1739.235,"endTime":1743.067,"body":"here? Are these serious issues?"},{"startTime":1739.235,"endTime":1743.067,"body":"Are they fixable? Or is there"},{"startTime":1743.067,"endTime":1745.175,"body":"something fundamentally, you"},{"startTime":1743.067,"endTime":1745.175,"body":"know,"},{"startTime":1745.655,"endTime":1749.841,"body":"insufficient with this approach?"},{"startTime":1745.655,"endTime":1749.841,"body":"So that's where we are as of"},{"startTime":1749.841,"endTime":1752.354,"body":"August, whatever day we're"},{"startTime":1749.841,"endTime":1752.354,"body":"recording."},{"startTime":1752.354,"endTime":1753.175,"body":"Deirdre - It's just 13."},{"startTime":1753.175,"endTime":1755.835,"body":"Chris - This and by the time you"},{"startTime":1753.175,"endTime":1755.835,"body":"print we may have some"},{"startTime":1755.835,"endTime":1758.415,"body":"resolution. I know people have"},{"startTime":1755.835,"endTime":1758.415,"body":"found some"},{"startTime":1758.655,"endTime":1762.114,"body":"interesting things about this so"},{"startTime":1758.655,"endTime":1762.114,"body":"stay tuned."},{"startTime":1763.675,"endTime":1770.536,"body":"Deirdre - If this did hold, how"},{"startTime":1763.675,"endTime":1770.536,"body":"far away"},{"startTime":1770.536,"endTime":1777.512,"body":"it, and which instances of LWE"},{"startTime":1770.536,"endTime":1777.512,"body":"would be shaking in their boots"},{"startTime":1777.512,"endTime":1779.114,"body":"versus others?"},{"startTime":1779.114,"endTime":1779.115,"body":"Chris - Yeah."},{"startTime":1779.334,"endTime":1783.94,"body":"Deirdre - Because this reminds,"},{"startTime":1779.334,"endTime":1783.94,"body":"some of us are getting"},{"startTime":1783.94,"endTime":1786.895,"body":"flashbacks to Chen's paper in"},{"startTime":1783.94,"endTime":1786.895,"body":"2024,"},{"startTime":1788.715,"endTime":1791.834,"body":"which was a different quantum"},{"startTime":1788.715,"endTime":1791.834,"body":"attack."},{"startTime":1792.715,"endTime":1796.906,"body":"And it was basically going to"},{"startTime":1792.715,"endTime":1796.906,"body":"endanger a whole bunch of"},{"startTime":1796.906,"endTime":1798.614,"body":"lattice constructions,"},{"startTime":1798.624,"endTime":1803.589,"body":"but especially more complex"},{"startTime":1798.624,"endTime":1803.589,"body":"instances like"},{"startTime":1803.589,"endTime":1804.654,"body":"need for FHE"},{"startTime":1804.794,"endTime":1806.374,"body":"or the things you need for,"},{"startTime":1808.314,"endTime":1809.614,"body":"there's more space in the"},{"startTime":1808.314,"endTime":1809.614,"body":"parameters."},{"startTime":1809.645,"endTime":1812.455,"body":"I think it's between the"},{"startTime":1809.645,"endTime":1812.455,"body":"dimension and the modulus size,"},{"startTime":1812.895,"endTime":1813.655,"body":"things like that."},{"startTime":1813.685,"endTime":1815.255,"body":"And those are things that you"},{"startTime":1813.685,"endTime":1815.255,"body":"usually use"},{"startTime":1815.374,"endTime":1817.735,"body":"for more complicated instances,"},{"startTime":1817.965,"endTime":1822.274,"body":"either using ring LWE for weird"},{"startTime":1817.965,"endTime":1822.274,"body":"blind"},{"startTime":1822.405,"endTime":1826.774,"body":"or, you know, odder things than"},{"startTime":1822.405,"endTime":1826.774,"body":"say ML-KEM"},{"startTime":1826.955,"endTime":1829.415,"body":"which the gap between those"},{"startTime":1826.955,"endTime":1829.415,"body":"parameters is smaller."},{"startTime":1830.975,"endTime":1833.654,"body":"So do you think there's anything"},{"startTime":1830.975,"endTime":1833.654,"body":"like that"},{"startTime":1833.675,"endTime":1836.395,"body":"at play here if it were to hold."},{"startTime":1836.395,"endTime":1839.421,"body":"Chris - Yeah I mean all these"},{"startTime":1836.395,"endTime":1839.421,"body":"all the"},{"startTime":1839.421,"endTime":1839.735,"body":"paper"},{"startTime":1839.915,"endTime":1843.982,"body":"all these questions come down to"},{"startTime":1839.915,"endTime":1843.982,"body":"like what actual gap factor or"},{"startTime":1843.982,"endTime":1845.294,"body":"approximation factor"},{"startTime":1845.975,"endTime":1849.851,"body":"does this thing attack right and"},{"startTime":1845.975,"endTime":1849.851,"body":"I think if I remember correctly"},{"startTime":1849.851,"endTime":1851.574,"body":"with the with the chen paper"},{"startTime":1852.195,"endTime":1856.394,"body":"it was like claiming to attack a"},{"startTime":1852.195,"endTime":1856.394,"body":"factor"},{"startTime":1856.394,"endTime":1858.354,"body":"bigger than maybe what basic"},{"startTime":1858.634,"endTime":1862.733,"body":"encryption needs but sufficient"},{"startTime":1858.634,"endTime":1862.733,"body":"to break"},{"startTime":1862.733,"endTime":1865.114,"body":"needs or what like more fancy"},{"startTime":1862.733,"endTime":1865.114,"body":"crypto."},{"startTime":1865.114,"endTime":1865.955,"body":"Deirdre - Yeah, yeah."},{"startTime":1865.955,"endTime":1869.11,"body":"Chris - Needs but the specific"},{"startTime":1865.955,"endTime":1869.11,"body":"factor I think didn't really"},{"startTime":1869.11,"endTime":1871.715,"body":"matter like if that paradigm had"},{"startTime":1869.11,"endTime":1871.715,"body":"worked"},{"startTime":1871.824,"endTime":1874.974,"body":"out if that algorithm had"},{"startTime":1871.824,"endTime":1874.974,"body":"actually been correct and"},{"startTime":1874.974,"endTime":1877.495,"body":"correct analysis we're quibbling"},{"startTime":1874.974,"endTime":1877.495,"body":"over the"},{"startTime":1877.915,"endTime":1881.172,"body":"approximation factor you know is"},{"startTime":1877.915,"endTime":1881.172,"body":"it n to the one over 400 or is"},{"startTime":1881.172,"endTime":1882.854,"body":"it n to the one over 28 or is it"},{"startTime":1882.915,"endTime":1887.171,"body":"n to the you know whatever like"},{"startTime":1882.915,"endTime":1887.171,"body":"it's the same kind of story"},{"startTime":1887.171,"endTime":1889.814,"body":"broke it for n^3 and probably"},{"startTime":1887.171,"endTime":1889.814,"body":"push on"},{"startTime":1889.854,"endTime":1892.718,"body":"it a little bit you're going to"},{"startTime":1889.854,"endTime":1892.718,"body":"get it for n squared and for n"},{"startTime":1892.718,"endTime":1894.034,"body":"to the one half n to the one"},{"startTime":1894.074,"endTime":1900.304,"body":"and whatever. So yeah, like, and"},{"startTime":1894.074,"endTime":1900.304,"body":"you're talking about the sun,"},{"startTime":1900.304,"endTime":1903.675,"body":"like, do you really care what"},{"startTime":1900.304,"endTime":1903.675,"body":"the—"},{"startTime":1903.675,"endTime":1903.676,"body":"Deirdre - It's sort of like"},{"startTime":1903.675,"endTime":1903.676,"body":"asking"},{"startTime":1903.676,"endTime":1903.677,"body":"how hot is the fire when"},{"startTime":1903.676,"endTime":1903.677,"body":"everything's on fire."},{"startTime":1903.794,"endTime":1907.501,"body":"Chris - Temperature is? It's"},{"startTime":1903.794,"endTime":1907.501,"body":"freaking hot, like everything's"},{"startTime":1907.501,"endTime":1910.455,"body":"gonna burn. So it doesn't matter"},{"startTime":1907.501,"endTime":1910.455,"body":"too much. So my"},{"startTime":1910.515,"endTime":1914.209,"body":"best understanding is the"},{"startTime":1910.515,"endTime":1914.209,"body":"current paper, at least claims"},{"startTime":1914.209,"endTime":1916.695,"body":"to reach factors that would, you"},{"startTime":1914.209,"endTime":1916.695,"body":"know,"},{"startTime":1917.265,"endTime":1922.322,"body":"break all the crypto, or, you"},{"startTime":1917.265,"endTime":1922.322,"body":"know, more or less all of it."},{"startTime":1922.322,"endTime":1925.375,"body":"And, you know, so I don't really"},{"startTime":1922.322,"endTime":1925.375,"body":"get"},{"startTime":1925.954,"endTime":1929.734,"body":"too wrapped up in the exact"},{"startTime":1925.954,"endTime":1929.734,"body":"factor that's involved, because,"},{"startTime":1929.734,"endTime":1932.234,"body":"like, either it works as a new"},{"startTime":1929.734,"endTime":1932.234,"body":"paradigm,"},{"startTime":1932.335,"endTime":1936.62,"body":"or it doesn't. And if it works,"},{"startTime":1932.335,"endTime":1936.62,"body":"fundamentally, then, like, we"},{"startTime":1936.62,"endTime":1938.835,"body":"need to abandon all this stuff,"},{"startTime":1939.115,"endTime":1942.757,"body":"even though, oh, well, you're an"},{"startTime":1939.115,"endTime":1942.757,"body":"end quarter off from the factor"},{"startTime":1942.757,"endTime":1943.914,"body":"that I use that now,"},{"startTime":1944.015,"endTime":1947.986,"body":"forget about it just like go"},{"startTime":1944.015,"endTime":1947.986,"body":"away so um that's how I I see"},{"startTime":1947.986,"endTime":1948.335,"body":"this."},{"startTime":1949.394,"endTime":1953.757,"body":"Deirdre - Okay, yeah. I think"},{"startTime":1949.394,"endTime":1953.757,"body":"it's very hard to say. It's hard"},{"startTime":1953.757,"endTime":1958.12,"body":"to just completely say, yeah,"},{"startTime":1953.757,"endTime":1958.12,"body":"no, there's a bug over here. And"},{"startTime":1958.12,"endTime":1962.268,"body":"there's a bug over there. So"},{"startTime":1958.12,"endTime":1962.268,"body":"just like chuck it in the bin,"},{"startTime":1962.268,"endTime":1965.987,"body":"as tempting as it is, just like,"},{"startTime":1962.268,"endTime":1965.987,"body":"no, no, no, it's no,"},{"startTime":1965.987,"endTime":1970.421,"body":"everything's fine. Just chuck it"},{"startTime":1965.987,"endTime":1970.421,"body":"in the bin. So I think we have"},{"startTime":1970.421,"endTime":1973.214,"body":"to say stay tuned to the"},{"startTime":1970.421,"endTime":1973.214,"body":"consensus on a—"},{"startTime":1973.214,"endTime":1977.351,"body":"Chris - Yeah, saying that the"},{"startTime":1973.214,"endTime":1977.351,"body":"proof is flawed is like an"},{"startTime":1977.351,"endTime":1979.894,"body":"insufficient conclusion to"},{"startTime":1977.351,"endTime":1979.894,"body":"things."},{"startTime":1980.154,"endTime":1980.254,"body":"Deirdre - Yeah."},{"startTime":1981.174,"endTime":1985.33,"body":"Chris - But there will be more"},{"startTime":1981.174,"endTime":1985.33,"body":"decisive conclusions in the near"},{"startTime":1985.33,"endTime":1988.214,"body":"future. I'm very confident that"},{"startTime":1985.33,"endTime":1988.214,"body":"will kind of"},{"startTime":1989.075,"endTime":1991.974,"body":"fully resolve the unknowns right"},{"startTime":1989.075,"endTime":1991.974,"body":"now."},{"startTime":1992.154,"endTime":1992.315,"body":"Deirdre - Okay."},{"startTime":1992.654,"endTime":1995.855,"body":"I hope you're right, because"},{"startTime":1992.654,"endTime":1995.855,"body":"that'll help me sleep better at"},{"startTime":1995.855,"endTime":1998.135,"body":"night with all of our"},{"startTime":1995.855,"endTime":1998.135,"body":"post-quandum options."},{"startTime":1998.855,"endTime":1999.055,"body":"Okay."},{"startTime":2000.154,"endTime":2004.599,"body":"To stop talking about lattices"},{"startTime":2000.154,"endTime":2004.599,"body":"for a second, there was another"},{"startTime":2004.599,"endTime":2006.494,"body":"paper on classic McEliece."},{"startTime":2006.654,"endTime":2010.178,"body":"I are you no we're never going"},{"startTime":2006.654,"endTime":2010.178,"body":"to stop talking about lattices"},{"startTime":2010.178,"endTime":2010.355,"body":"or—"},{"startTime":2012.095,"endTime":2012.894,"body":"Chris - How much time you got?"},{"startTime":2013.575,"endTime":2017.477,"body":"Deirdre - I mean I've been told"},{"startTime":2013.575,"endTime":2017.477,"body":"that secretly elliptic curves"},{"startTime":2017.477,"endTime":2019.754,"body":"are a lattice or something like"},{"startTime":2017.477,"endTime":2019.754,"body":"that"},{"startTime":2019.795,"endTime":2023.592,"body":"or can be represented as a"},{"startTime":2019.795,"endTime":2023.592,"body":"lattice problem um another"},{"startTime":2023.592,"endTime":2026.295,"body":"another paper uh that does not"},{"startTime":2023.592,"endTime":2026.295,"body":"seem to"},{"startTime":2026.295,"endTime":2030.342,"body":"have any AI involved but like"},{"startTime":2026.295,"endTime":2030.342,"body":"whatever"},{"startTime":2030.342,"endTime":2032.434,"body":"doesn't who cares at this point"},{"startTime":2033.315,"endTime":2038.067,"body":"A much more efficient"},{"startTime":2033.315,"endTime":2038.067,"body":"distinguisher and a not very"},{"startTime":2038.067,"endTime":2042.335,"body":"efficient decryption attack on"},{"startTime":2038.067,"endTime":2042.335,"body":"the code-based"},{"startTime":2042.494,"endTime":2048.277,"body":"cryptosystem Classic McEliece."},{"startTime":2048.717,"endTime":2053.312,"body":"but when you're telling me about"},{"startTime":2048.717,"endTime":2053.312,"body":"a public key encryption system"},{"startTime":2053.312,"endTime":2055.017,"body":"and it says, oh, we can"},{"startTime":2055.037,"endTime":2060.755,"body":"distinguish your public key from"},{"startTime":2055.037,"endTime":2060.755,"body":"a random key. And I'm just like,"},{"startTime":2060.755,"endTime":2063.257,"body":"okay, like, all right, like,"},{"startTime":2063.878,"endTime":2069.014,"body":"so? But apparently, this is like"},{"startTime":2063.878,"endTime":2069.014,"body":"a big deal in code based"},{"startTime":2069.014,"endTime":2072.317,"body":"cryptography, where code is not"},{"startTime":2069.014,"endTime":2072.317,"body":"we've"},{"startTime":2072.317,"endTime":2075.635,"body":"implemented computer code, but"},{"startTime":2072.317,"endTime":2075.635,"body":"we were using codes like the"},{"startTime":2075.635,"endTime":2077.638,"body":"Reed Solomon codes. Yeah, the"},{"startTime":2075.635,"endTime":2077.638,"body":"error."},{"startTime":2077.638,"endTime":2077.639,"body":"Chris - Error correction codes."},{"startTime":2077.797,"endTime":2081.947,"body":"Deirdre - Goppa, in this case,"},{"startTime":2077.797,"endTime":2081.947,"body":"I"},{"startTime":2081.947,"endTime":2084.397,"body":"that are underneath Classic"},{"startTime":2081.947,"endTime":2084.397,"body":"McEliece."},{"startTime":2084.418,"endTime":2088.433,"body":"Goppa codes that are underneath"},{"startTime":2084.418,"endTime":2088.433,"body":"Classic"},{"startTime":2088.433,"endTime":2090.737,"body":"us why we care about a much"},{"startTime":2088.433,"endTime":2090.737,"body":"improved"},{"startTime":2090.997,"endTime":2095.879,"body":"distinguisher attack and why we"},{"startTime":2090.997,"endTime":2095.879,"body":"worry when"},{"startTime":2095.879,"endTime":2098.898,"body":"distinguisher attack for"},{"startTime":2095.879,"endTime":2098.898,"body":"code-based"},{"startTime":2099.037,"endTime":2099.477,"body":"- Nice photography."},{"startTime":2101.138,"endTime":2103.378,"body":"Chris - Yeah, there's a bunch of"},{"startTime":2101.138,"endTime":2103.378,"body":"things to unpack here."},{"startTime":2103.557,"endTime":2107.652,"body":"So the headline paper title"},{"startTime":2103.557,"endTime":2107.652,"body":"result is like a quasi"},{"startTime":2107.652,"endTime":2112.165,"body":"polynomial time analysis of of"},{"startTime":2107.652,"endTime":2112.165,"body":"McEliece for the Classic"},{"startTime":2112.165,"endTime":2117.346,"body":"McEliece kind of parameters or"},{"startTime":2112.165,"endTime":2117.346,"body":"the asymptotic parameter Classic"},{"startTime":2117.346,"endTime":2118.517,"body":"McEliece uses."},{"startTime":2119.178,"endTime":2122.898,"body":"So quasi polynomial time means,"},{"startTime":2119.178,"endTime":2122.898,"body":"well, not quite polynomial, but"},{"startTime":2122.898,"endTime":2123.678,"body":"pretty close."},{"startTime":2124.688,"endTime":2127.536,"body":"So it's not like n to a"},{"startTime":2124.688,"endTime":2127.536,"body":"constant. It's not n cubed or n"},{"startTime":2127.536,"endTime":2129.858,"body":"to the hundred, but it's like n"},{"startTime":2127.536,"endTime":2129.858,"body":"to the log n."},{"startTime":2130.207,"endTime":2131.858,"body":"Right. That's that's what"},{"startTime":2130.207,"endTime":2131.858,"body":"they're going after."},{"startTime":2132.338,"endTime":2135.158,"body":"And there's a specific reason"},{"startTime":2132.338,"endTime":2135.158,"body":"why the log n is there,"},{"startTime":2135.338,"endTime":2137.057,"body":"but we won't get into it."},{"startTime":2139.237,"endTime":2142.297,"body":"So this is like asymptotically"},{"startTime":2139.237,"endTime":2142.297,"body":"good"},{"startTime":2142.537,"endTime":2145.037,"body":"because the previous thing we"},{"startTime":2142.537,"endTime":2145.037,"body":"had"},{"startTime":2145.198,"endTime":2148.497,"body":"was a paper from Eurocrypt 25."},{"startTime":2150.717,"endTime":2151.858,"body":"I think it was 25, yes."},{"startTime":2153.318,"endTime":2156.757,"body":"That was a slightly sub"},{"startTime":2153.318,"endTime":2156.757,"body":"exponential,"},{"startTime":2157.098,"endTime":2160.557,"body":"like n to, sorry, two to the"},{"startTime":2157.098,"endTime":2160.557,"body":"like n,"},{"startTime":2161.537,"endTime":2164.638,"body":"and then some logs that happen"},{"startTime":2161.537,"endTime":2164.638,"body":"to log factors"},{"startTime":2164.838,"endTime":2166.037,"body":"that end up being less than one."},{"startTime":2166.458,"endTime":2167.158,"body":"Okay, something like that."},{"startTime":2167.178,"endTime":2169.517,"body":"So just barely slightly better"},{"startTime":2167.178,"endTime":2169.517,"body":"than two to the n"},{"startTime":2169.898,"endTime":2172.577,"body":"and not like actually practical,"},{"startTime":2172.858,"endTime":2174.497,"body":"like this only kicked in for"},{"startTime":2172.858,"endTime":2174.497,"body":"very large n's."},{"startTime":2175.398,"endTime":2179.358,"body":"So that was sort of the first"},{"startTime":2175.398,"endTime":2179.358,"body":"bang"},{"startTime":2179.517,"endTime":2181.277,"body":"or the first shot heard around"},{"startTime":2179.517,"endTime":2181.277,"body":"the world."},{"startTime":2181.517,"endTime":2182.537,"body":"And then this result is like,"},{"startTime":2182.557,"endTime":2184.438,"body":"oh no, it's not two to the"},{"startTime":2182.557,"endTime":2184.438,"body":"nearly n,"},{"startTime":2184.557,"endTime":2186.057,"body":"it's like n to the log n."},{"startTime":2186.398,"endTime":2189.638,"body":"So vastly, vastly better in"},{"startTime":2186.398,"endTime":2189.638,"body":"terms of complexity."},{"startTime":2190.237,"endTime":2194.077,"body":"And they actually gave concrete"},{"startTime":2190.237,"endTime":2194.077,"body":"estimates"},{"startTime":2194.418,"endTime":2196.317,"body":"for the specific McEliece"},{"startTime":2194.418,"endTime":2196.317,"body":"parameters,"},{"startTime":2197.418,"endTime":2202.118,"body":"showing that the runtimes are"},{"startTime":2197.418,"endTime":2202.118,"body":"something like 2¹¹⁵,"},{"startTime":2202.807,"endTime":2204.618,"body":"or is it 2¹¹⁴, 2¹,"},{"startTime":2205.017,"endTime":2208.138,"body":"something like in the 2 to the"},{"startTime":2205.017,"endTime":2208.138,"body":"low 100s, right?"},{"startTime":2209.717,"endTime":2210.878,"body":"That was for distinguishing."},{"startTime":2211.148,"endTime":2212.858,"body":"Okay, so distinguishing is like,"},{"startTime":2213.498,"endTime":2217.377,"body":"oh, you give me a key that is"},{"startTime":2213.498,"endTime":2217.377,"body":"McEliece key,"},{"startTime":2218.038,"endTime":2219.337,"body":"or it's just totally random"},{"startTime":2218.038,"endTime":2219.337,"body":"junk."},{"startTime":2220.258,"endTime":2222.718,"body":"And they can tell which is"},{"startTime":2220.258,"endTime":2222.718,"body":"which, right?"},{"startTime":2222.718,"endTime":2223.738,"body":"They can tell which one it is."},{"startTime":2224.458,"endTime":2225.738,"body":"That's what the algorithm does."},{"startTime":2227.178,"endTime":2228.758,"body":"And they have a proof, like a"},{"startTime":2227.178,"endTime":2228.758,"body":"rigorous proof"},{"startTime":2228.917,"endTime":2230.577,"body":"that it works within this"},{"startTime":2228.917,"endTime":2230.577,"body":"running time."},{"startTime":2231.057,"endTime":2233.058,"body":"Okay, so like, why do we care?"},{"startTime":2233.078,"endTime":2235.098,"body":"Who cares about distinguishing"},{"startTime":2233.078,"endTime":2235.098,"body":"the key?"},{"startTime":2235.838,"endTime":2237.598,"body":"It's because of the techniques"},{"startTime":2238.618,"endTime":2240.318,"body":"that actually allow you to do"},{"startTime":2238.618,"endTime":2240.318,"body":"it."},{"startTime":2240.457,"endTime":2242.818,"body":"It's like the ideas, the"},{"startTime":2240.457,"endTime":2242.818,"body":"algebra,"},{"startTime":2242.998,"endTime":2245.857,"body":"the new approach that they"},{"startTime":2242.998,"endTime":2245.857,"body":"brought to this problem"},{"startTime":2245.877,"endTime":2247.737,"body":"That's very unlike anything"},{"startTime":2245.877,"endTime":2247.737,"body":"else."},{"startTime":2248.707,"endTime":2250.618,"body":"And they were able to extend the"},{"startTime":2248.707,"endTime":2250.618,"body":"technique,"},{"startTime":2251.707,"endTime":2254.797,"body":"also do decoding, basically,"},{"startTime":2255.047,"endTime":2257.617,"body":"or like recover the message from"},{"startTime":2255.047,"endTime":2257.617,"body":"a ciphertext, right?"},{"startTime":2257.797,"endTime":2259.218,"body":"Given the ciphertext, recover"},{"startTime":2257.797,"endTime":2259.218,"body":"the message."},{"startTime":2260.117,"endTime":2262.46,"body":"And the way it works is like"},{"startTime":2260.117,"endTime":2262.46,"body":"very similar to the"},{"startTime":2262.46,"endTime":2263.158,"body":"distinguisher."},{"startTime":2263.248,"endTime":2266.438,"body":"They basically glue the"},{"startTime":2263.248,"endTime":2266.438,"body":"ciphertext onto the public key,"},{"startTime":2267.337,"endTime":2269.837,"body":"like as if it was just a slight"},{"startTime":2267.337,"endTime":2269.837,"body":"key,"},{"startTime":2270.777,"endTime":2271.958,"body":"and they do some fiddling with"},{"startTime":2270.777,"endTime":2271.958,"body":"it,"},{"startTime":2272.057,"endTime":2273.017,"body":"and they run the distinguisher."},{"startTime":2273.738,"endTime":2277.159,"body":"And if their distinguisher says"},{"startTime":2273.738,"endTime":2277.159,"body":"looks good, that means you have"},{"startTime":2277.159,"endTime":2279.478,"body":"a zero in this position of your"},{"startTime":2277.159,"endTime":2279.478,"body":"ciphertext."},{"startTime":2279.478,"endTime":2280.057,"body":"Deirdre - Oh, no."},{"startTime":2280.057,"endTime":2282.599,"body":"Chris - And if it says looks"},{"startTime":2280.057,"endTime":2282.599,"body":"random to me, that means you"},{"startTime":2282.599,"endTime":2284.658,"body":"have a one as the error in that"},{"startTime":2282.599,"endTime":2284.658,"body":"position."},{"startTime":2284.658,"endTime":2285.378,"body":"Deirdre - Oh, no."},{"startTime":2285.378,"endTime":2288.245,"body":"Chris - So you can very easily"},{"startTime":2285.378,"endTime":2288.245,"body":"recover all the bits of the"},{"startTime":2288.245,"endTime":2291.612,"body":"error vector in the ciphertext"},{"startTime":2288.245,"endTime":2291.612,"body":"by just kind of running the"},{"startTime":2291.612,"endTime":2295.277,"body":"distinguisher a bunch of times"},{"startTime":2291.612,"endTime":2295.277,"body":"with slightly bigger parameters."},{"startTime":2295.277,"endTime":2295.278,"body":"Deirdre - Oh."},{"startTime":2296.337,"endTime":2299.498,"body":"Chris - So that's the natural"},{"startTime":2296.337,"endTime":2299.498,"body":"thing."},{"startTime":2299.817,"endTime":2304.724,"body":"And I should say, the fact that"},{"startTime":2299.817,"endTime":2304.724,"body":"you can use a distinguisher to"},{"startTime":2304.724,"endTime":2309.872,"body":"follow the error and actually do"},{"startTime":2304.724,"endTime":2309.872,"body":"the decoding is not a big shock,"},{"startTime":2309.872,"endTime":2310.678,"body":"let's say."},{"startTime":2310.688,"endTime":2312.577,"body":"I mean, it's very clever. It's a"},{"startTime":2310.688,"endTime":2312.577,"body":"cool idea."},{"startTime":2312.908,"endTime":2316.392,"body":"But in codes and lattices and"},{"startTime":2312.908,"endTime":2316.392,"body":"everything, we have all these"},{"startTime":2316.392,"endTime":2319.576,"body":"kinds of different search"},{"startTime":2316.392,"endTime":2319.576,"body":"decision reductions that are"},{"startTime":2319.576,"endTime":2319.998,"body":"called."},{"startTime":2320.198,"endTime":2323.2,"body":"It just says, like, oh, if you"},{"startTime":2320.198,"endTime":2323.2,"body":"have a distinguisher, you can"},{"startTime":2323.2,"endTime":2326.355,"body":"kind of leverage it to solve and"},{"startTime":2323.2,"endTime":2326.355,"body":"follow the error and solve LWE"},{"startTime":2326.355,"endTime":2327.017,"body":"and whatever."},{"startTime":2327.837,"endTime":2332.367,"body":"So search to decision reductions"},{"startTime":2327.837,"endTime":2332.367,"body":"are like very common in this"},{"startTime":2332.367,"endTime":2336.218,"body":"general milieu and this version"},{"startTime":2332.367,"endTime":2336.218,"body":"of such a reduction."},{"startTime":2337.357,"endTime":2343.943,"body":"So they have a way to decrypt a"},{"startTime":2337.357,"endTime":2343.943,"body":"ciphertext in like a comparable"},{"startTime":2343.943,"endTime":2345.537,"body":"amount of time."},{"startTime":2345.558,"endTime":2348.558,"body":"I'm not saying exactly. There's"},{"startTime":2345.558,"endTime":2348.558,"body":"overhead to it for sure."},{"startTime":2349.297,"endTime":2353.309,"body":"But in quasi polynomial time and"},{"startTime":2349.297,"endTime":2353.309,"body":"there are some heuristics that"},{"startTime":2353.309,"endTime":2353.957,"body":"they need."},{"startTime":2354.078,"endTime":2357.059,"body":"They can't prove it completely"},{"startTime":2354.078,"endTime":2357.059,"body":"that it works, but in all their"},{"startTime":2357.059,"endTime":2359.893,"body":"evidence, you know, suggests"},{"startTime":2357.059,"endTime":2359.893,"body":"that, yeah, this actually does"},{"startTime":2359.893,"endTime":2360.138,"body":"work."},{"startTime":2362.197,"endTime":2365.407,"body":"And then the natural thing that"},{"startTime":2362.197,"endTime":2365.407,"body":"they say in the paper is like,"},{"startTime":2365.407,"endTime":2367.618,"body":"oh, by the way, we have this"},{"startTime":2365.407,"endTime":2367.618,"body":"distinguisher."},{"startTime":2368.098,"endTime":2371.572,"body":"Obviously, a really important"},{"startTime":2368.098,"endTime":2371.572,"body":"thing would be can you recover"},{"startTime":2371.572,"endTime":2373.457,"body":"the secret key from a public"},{"startTime":2371.572,"endTime":2373.457,"body":"key?"},{"startTime":2374.098,"endTime":2377.977,"body":"Right. And they say, like,"},{"startTime":2374.098,"endTime":2377.977,"body":"conceptually, our ideas ought to"},{"startTime":2377.977,"endTime":2380.318,"body":"be applicable to that question,"},{"startTime":2377.977,"endTime":2380.318,"body":"too."},{"startTime":2380.578,"endTime":2383.851,"body":"like let's get the secret key"},{"startTime":2380.578,"endTime":2383.851,"body":"from the public key, but we'll"},{"startTime":2383.851,"endTime":2385.017,"body":"leave that for later."},{"startTime":2385.697,"endTime":2387.517,"body":"Okay, so stay tuned."},{"startTime":2388.537,"endTime":2389.997,"body":"It's basically what they're"},{"startTime":2388.537,"endTime":2389.997,"body":"telling us."},{"startTime":2391.078,"endTime":2394.498,"body":"David - Um and they weren't like"},{"startTime":2391.078,"endTime":2394.498,"body":"they were trying to do pir"},{"startTime":2394.498,"endTime":2396.917,"body":"they're like private information"},{"startTime":2394.498,"endTime":2396.917,"body":"retrieval"},{"startTime":2396.977,"endTime":2400.424,"body":"right like this was not a group"},{"startTime":2396.977,"endTime":2400.424,"body":"of people that this didn't just"},{"startTime":2400.424,"endTime":2402.037,"body":"come out of the like uh crypt"},{"startTime":2402.197,"endTime":2405.022,"body":"analysis community this came out"},{"startTime":2402.197,"endTime":2405.022,"body":"of like privacy and they were"},{"startTime":2405.022,"endTime":2406.598,"body":"trying to build something on"},{"startTime":2405.022,"endTime":2406.598,"body":"there."},{"startTime":2406.598,"endTime":2406.599,"body":"Chris - Yeah."},{"startTime":2406.818,"endTime":2409.38,"body":"David - Like oh well our scheme"},{"startTime":2406.818,"endTime":2409.38,"body":"doesn't work because of this"},{"startTime":2409.38,"endTime":2411.118,"body":"result oh wait doesn't that"},{"startTime":2409.38,"endTime":2411.118,"body":"apply to this"},{"startTime":2411.257,"endTime":2417.498,"body":"other thing like is that um uh"},{"startTime":2411.257,"endTime":2417.498,"body":"like that seems bad for what"},{"startTime":2417.498,"endTime":2421.158,"body":"like mcgleese generally like do"},{"startTime":2417.498,"endTime":2421.158,"body":"you"},{"startTime":2421.178,"endTime":2423.602,"body":"think there's something about"},{"startTime":2421.178,"endTime":2423.602,"body":"mcgleese that it was like"},{"startTime":2423.602,"endTime":2425.578,"body":"perhaps understudied relative to"},{"startTime":2423.602,"endTime":2425.578,"body":"other things"},{"startTime":2425.857,"endTime":2431.242,"body":"Or like, why do you think that"},{"startTime":2425.857,"endTime":2431.242,"body":"this kind of popped out of a"},{"startTime":2431.242,"endTime":2436.627,"body":"somewhat unrelated field rather"},{"startTime":2431.242,"endTime":2436.627,"body":"than from the cryptanalysis"},{"startTime":2436.627,"endTime":2437.278,"body":"itself?"},{"startTime":2437.518,"endTime":2441.613,"body":"Is there any takeaway from that,"},{"startTime":2437.518,"endTime":2441.613,"body":"or is it just the way the world"},{"startTime":2441.613,"endTime":2441.938,"body":"goes?"},{"startTime":2441.938,"endTime":2441.939,"body":"Chris - I mean, I can spec."},{"startTime":2442.018,"endTime":2443.597,"body":"Yeah, I can speculate."},{"startTime":2443.738,"endTime":2448.654,"body":"I mean, I think a lot of things"},{"startTime":2443.738,"endTime":2448.654,"body":"we're learning from these AI"},{"startTime":2448.654,"endTime":2451.238,"body":"papers is that like big results"},{"startTime":2451.418,"endTime":2455.295,"body":"can come from using very"},{"startTime":2451.418,"endTime":2455.295,"body":"different kinds of math than an"},{"startTime":2455.295,"endTime":2455.718,"body":"error."},{"startTime":2457.617,"endTime":2462.876,"body":"Right, the CVP result, it was"},{"startTime":2457.617,"endTime":2462.876,"body":"just pulled"},{"startTime":2462.876,"endTime":2465.037,"body":"error correcting codes."},{"startTime":2466.268,"endTime":2469.528,"body":"Certain ideas from error"},{"startTime":2466.268,"endTime":2469.528,"body":"correcting codes, of course,"},{"startTime":2469.528,"endTime":2471.597,"body":"were used in complex lab"},{"startTime":2469.528,"endTime":2471.597,"body":"problems,"},{"startTime":2471.807,"endTime":2476.839,"body":"like I don't know, but the"},{"startTime":2471.807,"endTime":2476.839,"body":"specific sophisticated tools"},{"startTime":2476.839,"endTime":2477.678,"body":"that the."},{"startTime":2478.957,"endTime":2483.058,"body":"Not the ones that, you know,"},{"startTime":2478.957,"endTime":2483.058,"body":"you're difficult to use."},{"startTime":2483.148,"endTime":2487.428,"body":"So the AI's were able to bring"},{"startTime":2483.148,"endTime":2487.428,"body":"like very different math to"},{"startTime":2487.428,"endTime":2490.358,"body":"these problems than most of the"},{"startTime":2487.428,"endTime":2490.358,"body":"experts,"},{"startTime":2490.608,"endTime":2491.717,"body":"you know, working on work."},{"startTime":2495.298,"endTime":2496.438,"body":"for the CVP result."},{"startTime":2497.157,"endTime":2499.518,"body":"They brought all this function"},{"startTime":2497.157,"endTime":2499.518,"body":"field math"},{"startTime":2500.218,"endTime":2501.917,"body":"and error correcting codes and"},{"startTime":2500.218,"endTime":2501.917,"body":"things like that."},{"startTime":2502.417,"endTime":2505.198,"body":"And, you know, this, we did"},{"startTime":2502.417,"endTime":2505.198,"body":"simple error"},{"startTime":2506.038,"endTime":2507.397,"body":"in the problem before,"},{"startTime":2507.637,"endTime":2510.457,"body":"but nothing like the tools that"},{"startTime":2507.637,"endTime":2510.457,"body":"were"},{"startTime":2511.058,"endTime":2512.278,"body":"by Astra to this problem."},{"startTime":2513.217,"endTime":2515.357,"body":"And so maybe what happened here"},{"startTime":2515.498,"endTime":2517.557,"body":"was something similar where, you"},{"startTime":2515.498,"endTime":2517.557,"body":"know,"},{"startTime":2517.557,"endTime":2520.098,"body":"the cryptanalysis had been a"},{"startTime":2517.557,"endTime":2520.098,"body":"pretty narrow"},{"startTime":2521.098,"endTime":2522.397,"body":"for a long time, right?"},{"startTime":2522.518,"endTime":2525.59,"body":"like it had basically come down"},{"startTime":2522.518,"endTime":2525.59,"body":"to information set decoding"},{"startTime":2525.59,"endTime":2527.657,"body":"problem and people were just"},{"startTime":2525.59,"endTime":2527.657,"body":"saying like"},{"startTime":2527.977,"endTime":2534.288,"body":"how quickly can I decode uh and"},{"startTime":2527.977,"endTime":2534.288,"body":"follow errors and decrypt it um"},{"startTime":2534.288,"endTime":2537.037,"body":"and so pushing on that same"},{"startTime":2537.897,"endTime":2540.852,"body":"direction for many years you"},{"startTime":2537.897,"endTime":2540.852,"body":"know didn't yield anything"},{"startTime":2540.852,"endTime":2542.877,"body":"really substantially new but"},{"startTime":2540.852,"endTime":2542.877,"body":"then when"},{"startTime":2542.938,"endTime":2546.921,"body":"people were able to bring very"},{"startTime":2542.938,"endTime":2546.921,"body":"different kinds of mathematical"},{"startTime":2546.921,"endTime":2548.097,"body":"algebraic geometry"},{"startTime":2550.837,"endTime":2555.305,"body":"from 2005 uh you know all of a"},{"startTime":2550.837,"endTime":2555.305,"body":"sudden new things become"},{"startTime":2555.305,"endTime":2558.698,"body":"possible when you start doing"},{"startTime":2555.305,"endTime":2558.698,"body":"these clever"},{"startTime":2558.798,"endTime":2563.645,"body":"algebraic high degrees varieties"},{"startTime":2558.798,"endTime":2563.645,"body":"and all kinds of stuff like that"},{"startTime":2563.645,"endTime":2565.918,"body":"so very new tools open up some"},{"startTime":2566.438,"endTime":2571.245,"body":"some right and new exciting"},{"startTime":2566.438,"endTime":2571.245,"body":"results this group was trying to"},{"startTime":2571.245,"endTime":2574.098,"body":"build what's called doubly"},{"startTime":2571.245,"endTime":2574.098,"body":"efficient"},{"startTime":2574.418,"endTime":2577.91,"body":"peer so very specific kind of"},{"startTime":2574.418,"endTime":2577.91,"body":"pir that um we basically have"},{"startTime":2577.91,"endTime":2579.898,"body":"only one construction of it's"},{"startTime":2577.91,"endTime":2579.898,"body":"from"},{"startTime":2580.678,"endTime":2582.418,"body":"LWE or Ring LWE actually."},{"startTime":2582.418,"endTime":2582.419,"body":"Deirdre - Yeah."},{"startTime":2583.037,"endTime":2584.277,"body":"Chris - Years ago, I think."},{"startTime":2585.037,"endTime":2586.717,"body":"And naturally"},{"startTime":2586.898,"endTime":2588.138,"body":"people have been trying to build"},{"startTime":2588.938,"endTime":2589.898,"body":"doubly efficient beer from"},{"startTime":2590.678,"endTime":2591.537,"body":"many other assumptions."},{"startTime":2592.317,"endTime":2594.477,"body":"So far, I don't think anything"},{"startTime":2592.317,"endTime":2594.477,"body":"has really come up."},{"startTime":2594.967,"endTime":2596.187,"body":"They ran into this barrier"},{"startTime":2597.927,"endTime":2599.927,"body":"to follow their narrative in the"},{"startTime":2597.927,"endTime":2599.927,"body":"paper."},{"startTime":2599.927,"endTime":2601.187,"body":"They ran into this barrier and"},{"startTime":2599.927,"endTime":2601.187,"body":"realized,"},{"startTime":2601.457,"endTime":2603.667,"body":"oh, we can't get it from this"},{"startTime":2601.457,"endTime":2603.667,"body":"technique"},{"startTime":2604.806,"endTime":2606.526,"body":"because mumble, mumble, mumble."},{"startTime":2606.907,"endTime":2612.427,"body":"and then, oh, wait, that break"},{"startTime":2606.907,"endTime":2612.427,"body":"Classic McEliece in quasi-poly"},{"startTime":2612.427,"endTime":2612.887,"body":"time."},{"startTime":2613.246,"endTime":2618.591,"body":"So it's super cool how different"},{"startTime":2613.246,"endTime":2618.591,"body":"ideas can just cross-pollinate"},{"startTime":2618.591,"endTime":2619.367,"body":"like this"},{"startTime":2619.367,"endTime":2620.387,"body":"and have on a—"},{"startTime":2620.461,"endTime":2625.027,"body":"One thing that I saw repeatedly"},{"startTime":2620.461,"endTime":2625.027,"body":"remarked"},{"startTime":2625.027,"endTime":2629.919,"body":"started getting attention was"},{"startTime":2625.027,"endTime":2629.919,"body":"that I heard from more than one"},{"startTime":2629.919,"endTime":2634.566,"body":"person, yeah, but we were always"},{"startTime":2629.919,"endTime":2634.566,"body":"a little suspicious about"},{"startTime":2634.566,"endTime":2635.954,"body":"Classic McEliece."},{"startTime":2637.194,"endTime":2641.594,"body":"And like, I am younger than"},{"startTime":2637.194,"endTime":2641.594,"body":"Classic McEliece by at least a"},{"startTime":2641.594,"endTime":2642.135,"body":"decade."},{"startTime":2643.075,"endTime":2645.234,"body":"So I don't have any of that"},{"startTime":2643.075,"endTime":2645.234,"body":"context."},{"startTime":2645.474,"endTime":2647.375,"body":"I've just heard that it is a"},{"startTime":2645.474,"endTime":2647.375,"body":"thing that exists."},{"startTime":2647.675,"endTime":2650.677,"body":"is like one of a handful of"},{"startTime":2647.675,"endTime":2650.677,"body":"instances of code-based, you"},{"startTime":2650.677,"endTime":2652.315,"body":"know, public key cryptography."},{"startTime":2653.514,"endTime":2657.939,"body":"And I've heard that it's like"},{"startTime":2653.514,"endTime":2657.939,"body":"old and trusted and it's still"},{"startTime":2657.939,"endTime":2658.615,"body":"standing."},{"startTime":2658.954,"endTime":2662.855,"body":"So like, it sounds fine to me."},{"startTime":2663.274,"endTime":2666.37,"body":"Like, you know, I, now that you"},{"startTime":2663.274,"endTime":2666.37,"body":"look at like a, you can do"},{"startTime":2666.37,"endTime":2668.055,"body":"distinguisher attacks like this"},{"startTime":2668.254,"endTime":2669.974,"body":"on it and, you know, it smells a"},{"startTime":2668.254,"endTime":2669.974,"body":"little something."},{"startTime":2670.835,"endTime":2675.074,"body":"Why do we believe these codes"},{"startTime":2670.835,"endTime":2675.074,"body":"are strong or like, you know,"},{"startTime":2675.074,"endTime":2677.194,"body":"strong one way and, you know,"},{"startTime":2677.274,"endTime":2679.559,"body":"have a trap door the other day,"},{"startTime":2677.274,"endTime":2679.559,"body":"other way, you know, all that"},{"startTime":2679.559,"endTime":2680.474,"body":"sort of stuff. And like,"},{"startTime":2681.014,"endTime":2684.73,"body":"I just don't look at the deep"},{"startTime":2681.014,"endTime":2684.73,"body":"literature there to convince"},{"startTime":2684.73,"endTime":2687.274,"body":"myself, because I've never"},{"startTime":2684.73,"endTime":2687.274,"body":"really needed"},{"startTime":2687.415,"endTime":2692.087,"body":"to. But like, why? Like, do you"},{"startTime":2687.415,"endTime":2692.087,"body":"have a sense of like, why"},{"startTime":2692.087,"endTime":2695.175,"body":"there's sort of a vibe in the"},{"startTime":2692.087,"endTime":2695.175,"body":"field of"},{"startTime":2695.274,"endTime":2698.977,"body":"just sort of like, yeah, but we"},{"startTime":2695.274,"endTime":2698.977,"body":"were always like a little bit"},{"startTime":2698.977,"endTime":2701.014,"body":"suspect. I was a little suspect"},{"startTime":2698.977,"endTime":2701.014,"body":"of"},{"startTime":2701.034,"endTime":2701.555,"body":"Mikalese."},{"startTime":2701.954,"endTime":2706.084,"body":"Yeah. Oh, I think Matt Green"},{"startTime":2701.954,"endTime":2706.084,"body":"publicly said it, right? It was"},{"startTime":2706.084,"endTime":2710.074,"body":"always sketchy. But probably a"},{"startTime":2706.084,"endTime":2710.074,"body":"lot of people think that as"},{"startTime":2710.074,"endTime":2713.784,"body":"well. And unfortunately, I'm not"},{"startTime":2710.074,"endTime":2713.784,"body":"younger than McEliece"},{"startTime":2713.784,"endTime":2714.695,"body":"cryptosystem."},{"startTime":2715.614,"endTime":2719.6,"body":"I mean, I can tell you the"},{"startTime":2715.614,"endTime":2719.6,"body":"things that I have heard and the"},{"startTime":2719.6,"endTime":2721.594,"body":"things that I believe myself."},{"startTime":2722.715,"endTime":2726.132,"body":"One is that a lot of"},{"startTime":2722.715,"endTime":2726.132,"body":"variants"},{"startTime":2726.132,"endTime":2729.891,"body":"proposed over the over the years"},{"startTime":2726.132,"endTime":2729.891,"body":"to try and make it more"},{"startTime":2729.891,"endTime":2730.575,"body":"efficient."},{"startTime":2730.936,"endTime":2734.441,"body":"Let's make the key smaller."},{"startTime":2730.936,"endTime":2734.441,"body":"Let's use some different codes."},{"startTime":2734.441,"endTime":2736.376,"body":"Let's not use binary GAPA codes."},{"startTime":2736.576,"endTime":2737.856,"body":"Let's use some other family of"},{"startTime":2736.576,"endTime":2737.856,"body":"codes."},{"startTime":2739.816,"endTime":2742.856,"body":"Virtually all of these got"},{"startTime":2739.816,"endTime":2742.856,"body":"broken."},{"startTime":2744.275,"endTime":2747.515,"body":"And for some reason, the"},{"startTime":2744.275,"endTime":2747.515,"body":"original, you know,"},{"startTime":2747.715,"endTime":2750.076,"body":"McEliece didn't."},{"startTime":2751.133,"endTime":2754.373,"body":"I don't have a sense that the"},{"startTime":2751.133,"endTime":2754.373,"body":"community ever really understood"},{"startTime":2755.393,"endTime":2756.613,"body":"at some deep level why"},{"startTime":2757.604,"endTime":2762.584,"body":"All these like proposed and they"},{"startTime":2757.604,"endTime":2762.584,"body":"just self-destruct, right?"},{"startTime":2762.685,"endTime":2767.643,"body":"everything else around it is, is"},{"startTime":2762.685,"endTime":2767.643,"body":"just a"},{"startTime":2767.643,"endTime":2772.05,"body":"of uncomfortable. Everything"},{"startTime":2767.643,"endTime":2772.05,"body":"else around it is, is just a"},{"startTime":2772.05,"endTime":2776.693,"body":"disaster. So that's kind of"},{"startTime":2772.05,"endTime":2776.693,"body":"uncomfortable. And then I think,"},{"startTime":2776.693,"endTime":2780.942,"body":"I mean, another aspect of it is"},{"startTime":2776.693,"endTime":2780.942,"body":"like, people just don't"},{"startTime":2780.942,"endTime":2785.585,"body":"understand what it is that makes"},{"startTime":2780.942,"endTime":2785.585,"body":"it, you know, kind of okay,"},{"startTime":2785.585,"endTime":2788.105,"body":"where all these variants aren't."},{"startTime":2788.145,"endTime":2788.444,"body":"Deirdre - Mm-hmm."},{"startTime":2789.105,"endTime":2792.946,"body":"Chris - And the level of"},{"startTime":2789.105,"endTime":2792.946,"body":"diversity of breadth of ideas"},{"startTime":2792.946,"endTime":2796.425,"body":"that had brought to attack it"},{"startTime":2792.946,"endTime":2796.425,"body":"were not that wide."},{"startTime":2797.704,"endTime":2801.424,"body":"They kind of all came down to"},{"startTime":2797.704,"endTime":2801.424,"body":"this variations of information"},{"startTime":2801.424,"endTime":2802.244,"body":"set decoding."},{"startTime":2802.964,"endTime":2806.361,"body":"Let's just treat the public code"},{"startTime":2802.964,"endTime":2806.361,"body":"and then try to decode the"},{"startTime":2806.361,"endTime":2807.064,"body":"random code."},{"startTime":2807.145,"endTime":2807.425,"body":"Deirdre - Mm-hmm."},{"startTime":2808.504,"endTime":2810.484,"body":"Chris - We'll attack on the"},{"startTime":2808.504,"endTime":2810.484,"body":"public keys themselves."},{"startTime":2810.734,"endTime":2815.685,"body":"But obviously, it was just like"},{"startTime":2810.734,"endTime":2815.685,"body":"a permutation and a linear"},{"startTime":2815.685,"endTime":2817.683,"body":"transform of this code."},{"startTime":2818.565,"endTime":2824.043,"body":"so it just has this it just has"},{"startTime":2818.565,"endTime":2824.043,"body":"this kind of feeling why if this"},{"startTime":2824.043,"endTime":2826.565,"body":"is okay exactly makes it okay"},{"startTime":2827.785,"endTime":2833.735,"body":"when all these other things okay"},{"startTime":2827.785,"endTime":2833.735,"body":"I at least never found a you"},{"startTime":2833.735,"endTime":2837.305,"body":"know a good solution for these"},{"startTime":2833.735,"endTime":2837.305,"body":"things"},{"startTime":2838.104,"endTime":2841.851,"body":"so that's you know probably why"},{"startTime":2838.104,"endTime":2841.851,"body":"you know when I was in school I"},{"startTime":2841.851,"endTime":2843.785,"body":"would talk to you know I"},{"startTime":2841.851,"endTime":2843.785,"body":"remember"},{"startTime":2843.805,"endTime":2846.115,"body":"talking to some professors about"},{"startTime":2843.805,"endTime":2846.115,"body":"it and they're like yeah we"},{"startTime":2846.115,"endTime":2847.565,"body":"don't know what the hell is this"},{"startTime":2846.115,"endTime":2847.565,"body":"thing"},{"startTime":2847.785,"endTime":2850.75,"body":"like we just don't know what to"},{"startTime":2847.785,"endTime":2850.75,"body":"think of it right and like"},{"startTime":2850.75,"endTime":2852.624,"body":"scientifically you want to"},{"startTime":2850.75,"endTime":2852.624,"body":"understand"},{"startTime":2853.305,"endTime":2857.129,"body":"you know you want to have a"},{"startTime":2853.305,"endTime":2857.129,"body":"reasonable explanation for why"},{"startTime":2857.129,"endTime":2859.344,"body":"this thing is plausibly secure"},{"startTime":2857.129,"endTime":2859.344,"body":"and"},{"startTime":2860.665,"endTime":2863.805,"body":"I never heard one at least you"},{"startTime":2860.665,"endTime":2863.805,"body":"know um yeah."},{"startTime":2863.805,"endTime":2866.203,"body":"Deirdre - Hmm. This"},{"startTime":2863.805,"endTime":2866.203,"body":"unfortunately is reminding me of"},{"startTime":2866.203,"endTime":2871.387,"body":"the oil and vinegar and variants"},{"startTime":2866.203,"endTime":2871.387,"body":"that are being tried out,"},{"startTime":2871.387,"endTime":2874.844,"body":"especially for post-quantum"},{"startTime":2871.387,"endTime":2874.844,"body":"signatures."},{"startTime":2875.745,"endTime":2880.873,"body":"And there have been, I think"},{"startTime":2875.745,"endTime":2880.873,"body":"it's wedge attacks against a lot"},{"startTime":2880.873,"endTime":2885.574,"body":"of these more complicated,"},{"startTime":2880.873,"endTime":2885.574,"body":"smaller, faster versions that"},{"startTime":2885.574,"endTime":2890.531,"body":"oil and vinegar is a specific"},{"startTime":2885.574,"endTime":2890.531,"body":"flavor of multivariate public"},{"startTime":2890.531,"endTime":2891.985,"body":"key cryptography."},{"startTime":2892.705,"endTime":2897.763,"body":"And it just seems like all of"},{"startTime":2892.705,"endTime":2897.763,"body":"these other ones, except OG oil"},{"startTime":2897.763,"endTime":2902.989,"body":"and vinegar, and I think mayo,"},{"startTime":2897.763,"endTime":2902.989,"body":"which has like a slight tweak on"},{"startTime":2902.989,"endTime":2907.205,"body":"oil and vinegar, just keep, they"},{"startTime":2902.989,"endTime":2907.205,"body":"keep falling down."},{"startTime":2907.354,"endTime":2911.427,"body":"And a lot of this sounds very"},{"startTime":2907.354,"endTime":2911.427,"body":"similar to the story you told of"},{"startTime":2911.427,"endTime":2913.565,"body":"codes that are code-based"},{"startTime":2911.427,"endTime":2913.565,"body":"crypto."},{"startTime":2915.065,"endTime":2917.915,"body":"Chris - Yeah, there are a lot of"},{"startTime":2915.065,"endTime":2917.915,"body":"similarities, like you say, like"},{"startTime":2917.915,"endTime":2919.163,"body":"people propose things to try"},{"startTime":2919.174,"endTime":2925.704,"body":"to improve the efficiency, you"},{"startTime":2919.174,"endTime":2925.704,"body":"know, just"},{"startTime":2925.944,"endTime":2936.47,"body":"So understand is, you know, good"},{"startTime":2925.944,"endTime":2936.47,"body":"in"},{"startTime":2936.47,"endTime":2940.785,"body":"them to work or not work."},{"startTime":2943.925,"endTime":2946.165,"body":"Deirdre - Thank you very much"},{"startTime":2943.925,"endTime":2946.165,"body":"for taking on a tour"},{"startTime":2946.344,"endTime":2948.764,"body":"on various sections of"},{"startTime":2946.344,"endTime":2948.764,"body":"post-quantum"},{"startTime":2948.884,"endTime":2951.484,"body":"David - One last important"},{"startTime":2948.884,"endTime":2951.484,"body":"question, though."},{"startTime":2951.484,"endTime":2951.485,"body":"Chris - David?"},{"startTime":2952.064,"endTime":2952.225,"body":"Yes."},{"startTime":2952.225,"endTime":2954.056,"body":"David - How are you feeling"},{"startTime":2952.225,"endTime":2954.056,"body":"about Michigan football this"},{"startTime":2954.056,"endTime":2954.304,"body":"season?"},{"startTime":2955.884,"endTime":2959.243,"body":"Chris - This season. Well, can"},{"startTime":2955.884,"endTime":2959.243,"body":"we talk about like what's"},{"startTime":2959.243,"endTime":2961.504,"body":"happened since the last time I"},{"startTime":2959.243,"endTime":2961.504,"body":"was on?"},{"startTime":2962.185,"endTime":2962.685,"body":"David - Oh, yeah."},{"startTime":2962.685,"endTime":2965.442,"body":"Chris - We got a national"},{"startTime":2962.685,"endTime":2965.442,"body":"championship in football. We got"},{"startTime":2965.442,"endTime":2967.544,"body":"a national championship in"},{"startTime":2965.442,"endTime":2967.544,"body":"basketball."},{"startTime":2967.544,"endTime":2967.545,"body":"David - I mean, champions."},{"startTime":2967.545,"endTime":2967.546,"body":"Oh, yeah."},{"startTime":2967.994,"endTime":2969.304,"body":"Chris - Who's got it better than"},{"startTime":2967.994,"endTime":2969.304,"body":"us, man?"},{"startTime":2969.304,"endTime":2969.305,"body":"David - Mm-hmm."},{"startTime":2970.584,"endTime":2971.645,"body":"Nobody, although."},{"startTime":2974.425,"endTime":2976.244,"body":"we don't need to talk about what"},{"startTime":2974.425,"endTime":2976.244,"body":"happened."},{"startTime":2976.244,"endTime":2976.245,"body":"Chris - So."},{"startTime":2976.405,"endTime":2978.105,"body":"David - Kind of in between some"},{"startTime":2976.405,"endTime":2978.105,"body":"of those things"},{"startTime":2978.645,"endTime":2980.044,"body":"but like right now"},{"startTime":2980.215,"endTime":2981.925,"body":"you know we asked grandma"},{"startTime":2982.415,"endTime":2983.584,"body":"for Kenny Dillingham"},{"startTime":2984.014,"endTime":2986.024,"body":"and she said what Kyle"},{"startTime":2984.014,"endTime":2986.024,"body":"Whittingham"},{"startTime":2986.645,"endTime":2988.084,"body":"and there we are"},{"startTime":2988.685,"endTime":2989.504,"body":"that's gonna be great."},{"startTime":2990.269,"endTime":2992.353,"body":"Yeah, and I'm excited to see you"},{"startTime":2990.269,"endTime":2992.353,"body":"at the Rose Bowl in a few"},{"startTime":2992.353,"endTime":2992.609,"body":"months."},{"startTime":2994.125,"endTime":2995.326,"body":"Congrats, Michigan football."},{"startTime":2995.625,"endTime":2995.925,"body":"Go blue."},{"startTime":3000.766,"endTime":3001.026,"body":"Cool."},{"startTime":3001.385,"endTime":3001.546,"body":"All right."},{"startTime":3001.665,"endTime":3002.185,"body":"Where's my thing?"},{"startTime":3002.726,"endTime":3003.466,"body":"Oh, gosh."},{"startTime":3003.466,"endTime":3004.286,"body":"I do this every time."},{"startTime":3005.726,"endTime":3008.006,"body":"I have a spiel that I have to"},{"startTime":3005.726,"endTime":3008.006,"body":"give."},{"startTime":3008.046,"endTime":3008.605,"body":"Chris - Sponsor read."},{"startTime":3008.885,"endTime":3009.046,"body":"Deirdre - Yes."},{"startTime":3009.466,"endTime":3009.685,"body":"Well,"},{"startTime":3010.185,"endTime":3012.165,"body":"David - No, we did our one"},{"startTime":3010.185,"endTime":3012.165,"body":"sponsor read of the year."},{"startTime":3012.165,"endTime":3013.306,"body":"Deirdre - We do one a year."},{"startTime":3013.306,"endTime":3013.766,"body":"David - And we thank them very"},{"startTime":3013.306,"endTime":3013.766,"body":"much."},{"startTime":3013.766,"endTime":3013.767,"body":"Chris - Hmm."},{"startTime":3014.326,"endTime":3015.055,"body":"David - But we did the one."},{"startTime":3015.055,"endTime":3017.005,"body":"Deirdre - Um where is it okay"},{"startTime":3015.055,"endTime":3017.005,"body":"Security Cryptography Whatever"},{"startTime":3017.005,"endTime":3018.294,"body":"is a side project from Deirdre"},{"startTime":3017.005,"endTime":3018.294,"body":"Connolly,"},{"startTime":3018.413,"endTime":3021.782,"body":"Thomas Ptacek, and David Adrian."},{"startTime":3018.413,"endTime":3021.782,"body":"You can find the podcast online"},{"startTime":3021.782,"endTime":3023.334,"body":"@scwpod, and the hosts online"},{"startTime":3023.433,"endTime":3027.138,"body":"@durumcrustulum, @tqbf and"},{"startTime":3023.433,"endTime":3027.138,"body":"@davidadrian. You can buy merch"},{"startTime":3027.138,"endTime":3028.893,"body":"online at security at merch"},{"startTime":3029.304,"endTime":3032.671,"body":"that Security Cryptography"},{"startTime":3029.304,"endTime":3032.671,"body":"Whatever.com and if you like the"},{"startTime":3032.671,"endTime":3034.413,"body":"pod give us a five-star review"},{"startTime":3034.653,"endTime":3037.754,"body":"Go blue!"}]}