Actually, it was Kath and Sweeter from 2009 that I... I'm sorry. Can you come here? Can you hear me? Good. So I'm going to talk about computational screening. It's also the first talk this morning. But in this case, I will focus on solar energy materials. So some of the ideas behind computational screening, which you have already heard about that, but I've just put three points here. The first one is what's actually the problem that you want to solve? And so what are the properties of the green material for whatever application that you have in mind? And in order to then get any further, you need to know what we can actually compute, which is relevant for this material. And finally, since the number of possible materials is so huge, you usually have to limit somehow yourself to a part of material space. And I think these are sort of the main components that I'm also going to address. The problem that I'm going to focus on is so-called light-induced water splitting. So the idea there is to take light from the sun, make electron hole pairs and use those to split water into hydrogen and oxygen. In this case, with a tandem cell, we have two semiconductors and one taking the high energy part of the solar spectrum, the other the low energy part, and the reason that you do this is because of efficiency. It's much more efficient than having a simple material. So why do we want to do this? We want to produce hydrogen as a fuel to save the world. And in some way I'm not even kidding. This is a really serious problem with the use of fuels. So we have to do something in the not too distant future. So the devices that people work with now are really quite complicated and I'm not going to go into any details because you are not all that interested in water splitting, but the fact that we have these two semiconductors and then we probably have to protect them from the water with some protection layers and we also need some catalysts to get the chemical reactions running. And it turns out that some of these components we actually know how to do, but one real challenge is what should be the large-band gap semiconductor. Silicon will work pretty well as a low-band gap one because the optimal band gap is around 1.1 EV but the large-band gap one should be around 1.8 EV and that's the material that we would like to find. So I will discuss three different approaches to the question about the material space. One is to map out a particular class of materials and I'll look at the perovskites. The other one is to focus on known materials as we've also heard earlier today from the ICSD and the last point is to take a look at machine learning and how to use that to guide the search in material space. We've earlier done some work on oxides and oxynitrides, perovskites and they have, for many reasons, they were not optimal for this application here. One thing was that the position of the valence band maximum was too low and that's something that sulfide generally do better. So we decided in this project to concentrate on sulfide perovskites and then we have a screening funnel where we go through different properties and as a question before I think about getting TC which order should one do the different screening steps is also of course to have more demanding calculations at the end so that you do not have to do that many because you've actually discarded many of the materials. So the way that we approach this is that we take 53 different metal atoms so we have A, B as 3, A here and B there and then as an additional screening we take a small 5-apton unit cell which is allowed to distort and then see how many of these were in fact semi-conducting. So can they have a gap at all? Could I take, excuse me, a bit of water here. So after this step where we've identified these we look up in the ICSD, one of the most common structures for A, B as 3 materials and then we simply pick the 6 most common ones and then we investigate these materials in all the 6 different structures. In this way we can, these are the different structures for given material we can calculate the binding energy, the heat of formation and we can calculate the band gap which is shown here and here you can see an example where we have different structures with different energies but then we have a point here which is just as Stefano talked about, the convex hull. So this is the energy you get by combining binary components in the most efficient way. So in this way you can see that the convex hull is more stable so this material will not work, it will be unstable. And we have these error bars on that we get from using our meter-beef functions so that we have an estimate of the error bar on the prediction energies. In some cases like over here you see the convex hull is up there so it might be stable but you can see that there are several different crystal structures that we cannot really distinguish between and then it's quite important what the band gap is for these different structures because if you have a competing structure where you just get a little bit of that into your compound and it's metallic then it's terrible but if it has a fairly high band gap it might not be that important for the performance of the material but these are the kind of details you have to go into if you really want to I think find new usable materials. Then we can calculate the band gaps. Again here are the different materials and the different symbols you know the band gaps calculated for the different structures so we can focus on this green window which is relevant for water splitting around 2 EV for the band gap and then we also actually collect materials that could be relevant for photovoltaics with a band gap around 1 EV. We calculate the band gaps with GLLB which includes the derivative discontinuity and therefore gets a much better estimate of the band gap that's APB, DFT. We also try to address mobility by calculating the effective masses that's of course not in any way a complete description but it's better than nothing and then we concentrate on here you have the electron and hole masses on the materials where you can find masses which are below one electron mass. The last step which is maybe the most unusual one here is that we try to study the defect properties and the way we do that is by looking at the density of states if we create vacancies and what is important here is if the vacancies will introduce states in the band gap as you see here because this might be scattering centers which will destroy the properties of the material. So these materials which we call defect sensitive or they are called defect sensitive we will then remove from the screening procedure. So in the end we end up with in this case like 15 different candidates of these sulfites and then as it was also discussed before then what do we do? Luckily we have some experimental colleagues nearby that are exactly interested in water splitting and these kinds of materials and we discussed with them that they should try to look at length of the metrium sulfite as a candidate and they've done that and here is the X-ray result when they synthesize that you're not intended that you look at any particular things here except that the conclusion is that the material does actually have the predicted crystal structure also the band gap is around 2EV as measured here by spectroscopic ellipsometry and finally the photoluminescence shows a nice peak close to the band gap some indirect indication that you don't have too many problems with states in the band gap. So at the moment they're trying to actually incorporate this material in a water splitting device that's not that easy but we'll have to see what comes out of this. So there are of course many limitations in this approach we only have a particular composition we only have few structures we do not give a very accurate calculation of the band gap the mobility is only addressed by effective masses defects we only consider neutral vacancies and so on so there's room for lots of improvement but still in the end if we started out with something like 3,000 materials and we actually end up with a short list of 15 so you have a huge reduction in the number of materials that you have to worry about so a different approach than looking at a particular class of materials is to take a starting point in some of the available databases and what we have done here is to start with the ICSD as they are already calculated within the database the OQD so that has a lot of advantages one of the most difficult issues to address is the stability but these materials have actually been synthesized so that's at least not the major point for a start and also some of the properties have already been calculated within the OQD so that's a way to speed up the search to use that the first thing we address here is the abundance of the elements and the question of whether you have a monopoly market for these elements if these are meant for as energy materials that should save the world they will have to be used at very large scale and that's the reason to only focus on elements which are expected to be available at a reasonable cost so here is the screening funnel where we start by picking out these elements and then we get something like 70,000 materials then the bandgap with PBE is already calculated in the OQD so we can use that to do a pre-screening of the materials and say we'll only focus on the ones which are known to be semi-conducting and to have a bandgap less than 2EV since PBE is severely underestimating the bandgap so we expect that you wouldn't in this case miss materials which actually have say 2, 3EV of bandgap in reality so this brings down the number to around 1600 materials then we calculate the bandgap with GLLB and here you can see as expected the connection between the GLLB and the PBE bandgap is somewhat larger so we can focus on the region which is relevant for water splitting and the region relevant for photovoltaics then as before we can calculate the effective masses and here you see below this curve the ones which the fraction that actually obeys this criterion and again the same approach with the defect sensitivity and in this way we end up with 74 candidate materials so out of the whole of ICSD this is the rather small class of materials that we find and so we have a long list of the properties of these materials there are many known materials of course which was also addressed by Stefano, I mean you have to check and see does it actually behave in the way that you expect for materials which have been investigated as solar energy materials and then we can point to some particularly interesting candidates and for example this strontium sulfide is another material that is now being experimentally investigated to see how it will perform so at the end here I will say something about some of the attempts that we have in using machine learning of course there are many ways of doing machine learning different fingerprints representing new materials different doing kernel regression neural networks and so on the two questions that I am going to ask here is can we predict material properties without knowing where the atoms are the point here is that the kind of screenings that I have been talking about mostly use standard density functional theory calculations and what is really time consuming is to do the structure optimizations for all these new materials but the point is if we make a machine that can predict say the stability in the band gap for a material if we know where the atoms are it is no help because it means that we have to do the DFT calculation first in order to find the positions and then we don't need the machine another question is if we are considering very large material spaces then actually even though you might have an efficient machine it is not possible for the machine to run through all the combinations if you have 10 to the 10 or 10 to the 15 different materials this is not possible so we will need some ways of directly identifying interesting candidates instead of just trying out I put it there one example for this not related to both materials but to organic solar cells where we are interested in some what is called PCBM based blended polymer solar cells I have written down here what PCBM means because I will not be able to remember it so if you asked about it the way this works is that again you generate electron hole pairs and then crucial I am not going into any kind of details here I think the main part is the fun with the machine learning and then the crucial quantities that you are after is the position of this lube level at the acceptor so that you can transfer the electron and what the band gap is for the light absorption and we are looking into a class of donor acceptor molecules where you have different possible acceptors different possible donors say backbones and then you have different side chains here indicated x and y which can have a number of different possibilities so in total this space will be something like 10 to the 14 different molecules in principle so we have done B3 lip calculation for about 4000 of these but you would not like to go into doing this to a much larger extent and you can do machine learning on this using all the atomic coordinates of the molecules using some of the standard fingerprints and it works very nicely but again how do you know the coordinates for molecules that you haven't calculated so the approach that we have taken here is to represent the molecules by strings or rather grammatical production rules so that I talked about that you had an acceptor and a donor part and you had different side groups and that's turned into a string that can be produced with some particular grammatical rules so in this case we do not have any specification of the atomic coordinates and let me say it over the end result if you do this instead of using the coordinates is that you're doing predictions of the band gap maybe 40% worse okay so it's better to have the coordinates but it's not that proof you this kind of approach has been used in a spore-goosie group also using smiles for some other molecules so this is a question of how do we represent our systems in this case without any atomic coordinates the other point was how do we make predictions without running through all the different combinations and one way of doing this is this variational autoencoder where you train a neural network so that you have an input in this case the strings and then the neural network would map this into a much lower dimensional vector space in this case in our case here it's a 32 dimensional vector space and the way that this is trained is so that you can optimally reproduce again in the output the input string so you're trying to compress the information into a vector space and then out again so that you don't lose very much information by doing this and one of the advantages is that then you can move around in this 32 dimensional vector space it's still large but because it's a vector space you can also do things like taking gradients and stuff like that to actually optimize your searches so just to show one result for this latent space is if you are doing a principle component analysis then these are the first two components of this 32 dimensional space and here you can see the data points from the training set but what you can also see is that if we now from the data set have some interesting molecules with appropriate lumo values and homo-lumo gaps they are indicated by the yellow points so the point is now that you can actually move now around you train another neural networks network to produce the numbers for the band gaps and for the lumo you train that on this space and then you can move around in the relevant part of space and then suggest new molecules without having to run through billions and billions of molecules and you can see the result here that this is the training set and this is the relevant region in this case the optical band gap and the lumo energy and here we have predicted 100 new molecules by this approach and you can see that now they lie closely in the region that we are interested in so I mean this is kind of a test this is in no way useful at the moment for these solar cells but I think it's fun to see these different approaches that can be used for finding materials so at the end some pretty naive considerations when we move to the excess scale and we can simply do much more in terms of the computer power we can stream more different materials we can do better calculations we can calculate new properties which are much more demanding than what we can do today a trivial point that I'd like to make here at the end is however when we will be able to do this we might be able to calculate not a thousand materials but a million materials or a billion but if what you are seeking for is one percent of these you will actually end up with very many candidates and you cannot go to the experimentalists with ten thousand candidates and say could you please try that out so I think a main very important challenge will be to find better and more descriptors which are relevant for the real material properties but one can really narrow down the materials that are interesting to investigate further and here are some of the people that have done this in particular Corina Kuah and Monish Pandey have done the two screening studies of the Salfa Barovskites and the ICSD Okrium Depart ok thank you


I hope you hear this Commander Terry Wilkett Terry you've had a couple days to get to me or a few days docked You had a lot of stuff you needed to move back and forth Tell me about the progress of that and tell me specifically about this huge air conditioning unit that was added to your cargo at the last minute Have you moved it yet? And was it a big hassle to get through that narrow tunnel? We have been very very busy and I think we were ahead of schedule We did take a couple days to get here. You don't get things organized and the docking went extremely well from our point of view and Frankly, Jim Riley is in charge of our transfer and he's got us ahead of schedule. I'll let him tell you about the air-conditioning unit Okay That's good. As you can see a happy-looking crew. Go ahead John everything's been going really smooth with the joint efforts between our two crews We've managed to transfer just about everything. We've got over a thousand items We've already transferred and we're just cleaning up the last ones right now Air-conditioning units fortunately fit through the hatch with just a little bit of elbow grease, but it's worked fine I have a question for you and for Michael and And for pilot Joe Edwards, you'll remember when we talked in Houston a couple weeks ago I asked you to try to put your your brain on Real intense record for the experience of going up into space for the first time So when we talked today, you could tell me about it. How was it the three of you? Right John, I remember your question, and I did my best to try to remember my thoughts on acid But I tell you what during the first few moments my thoughts were kind of overtaken by my senses as I was kind of Inundated by the vibration and the light show and the sound and those are things that I remember most But right after that the training took over and I was able to catch back up with the shuttle and pretty much Monitor the systems just like we were trained. So overall it was a pretty fantastic adventure. It looked great from the ground Joe and Jim, you want to talk to me too about this? Yeah John, it was pretty impressive from the inside. It was amazing how calm I felt all the way up to the final one or two seconds And then as soon as things started rumbling, I was kind of like Mike. It was kind of like, wow, this is it And then it was pretty impressive all the way to orbit You know just watching the light over the overhead was something that really really impressed me My first thoughts when everything was going on was thinking about my family and The light show they were getting which I thought was pretty pretty impressive inside. I imagine they thought it was pretty impressive outside too I'll tell you why you passed the micro vote our viewers were able to see the launch from a camera on top of the vehicle assembly building Which is up above where you guys were and so we watched the entire Atlantic Ocean light up As as you guys zoom past and it was loud and I mentioned it was more rambly and rattly for you How about it Joe? So that I could add a whole lot to the sensations that Mike and Jim talked about but you know the Navy fighter pilot I'm flying at an altitude of two hundred and seven miles or so and I've gone 25 times the speed of sound now So I'm a pretty happy camper How about that passed the mic down to Andy Thomas Andy for the past couple of days There has been some concern about the the space suit You'd have to wear to come home from here in an emergency didn't fit but you fixed it Have there been any other surprises like that since you got to mirror things that you just did not anticipate at all Regarding the space suit we did fix it The suit has a lot of adjustment in it and we were able to adjust it out and I was able to Put it on and take it off so to speak for me and it was a very nice fit fit like a glove the only other surprise I've had is that There's an awful lot of stuff in here. I mean it's like We've got stuff stowed in every nook and cranny on this vehicle and there's very little storage space And that's the biggest surprise that I've come across is just how restricted we are on free storage space Yeah, Andy before you pass the microphone off a senior Russian space officials said yesterday or the day before That the suit problem you pointed out was not really a problem at all and I am a I don't speak Russian as well as you do as You know, but he expressed concern about your willingness to actually complete four months on mirror At least he said that talking about the suit was sort of capricious on your part And he was concerned that this capriciousness might might last through the mission How do you feel about the mission at this point? Any chance you might not stay on me here for any reason? I'm here to stay No, the suit problem was real I mean I couldn't get it on I tried with an atoy the commander here several times to get it on it It was just impossible until we made the adjustments and then I went on fine No, I'm prepared to undertake this mission now and I'm looking forward to setting up a home in the parota module and Getting some personal things out and making it little bit and starting the adventure Well, it's gonna be quite an adventure pass the mic over to Dave Wolf if you will Dave You have given lots of advice to Andy since he came to relieve you I am sure I heard you were giving him some more Last-minute training this morning. You've said it is hard You have said that Murphy's law plays a major role in in mere operation. What other kinds of advice are you giving to Andy? Well, Andy and I are very busy working together. There's a lot of equipment here to learn how to work We've had training on the ground, but of course it's a little different in actual use But there's a lot of hints on how to live and how to be efficient and how to keep track of your items and In fact how to keep out of each other's way and then to help each other And I've learned a lot about how these cosmonauts like to live and I'm trying to pass that knowledge on to Andy Yeah, Dave, you said the other day you can feel really good in space and Another interviewer didn't really follow up on that I am fascinated by what you mean by really good in space. Tell me more about that feeling Is it can you feel better in space than you feel on earth? Or is it better on mere that it is on the shuttle? What is this good feeling describe it to me more? Well, John, it's really good. And in fact, I feel better today than when we lost talk It has to do with your mental perception of three dimensions and your ability to move around and your efficiency in motion It's if you're a scuba diver your first few dives you may not be as comfortable And you know how you can get your job done much when you get more experienced And it just keeps getting better and better and and still haven't peaked out and it's it's really good Great Dave hand the mic to your mere commander Anatoly Siloviyov if you will Commander we watched Dave Wolf on his spacewalk with you a couple of weeks ago During that walk it seemed that you were critiquing his every action telling him not to touch anything and not to move his feet What was your main concern during the spacewalk with Wolf and how did he do? I would like to say that the experiment that we performed during the EVA Basically done by performed by Dave. I helped him sometimes when he asked me to so our functions Of course were Outstanding the experiment was performed Very well, and when we were moving along the station I was giving Dave some hints because this is very naturally his first time in open space and we have a lot of Equipment particularly in the area that we are for example, there are Star trackers and other equipment So I was explaining to him the best way of avoiding The equipment and I recall the first time I went out into space first EVA. I did I was given the same advice Thanks commander. We like the new haircut by the way for Bonnie Dunbar. You've been conducting environmental experiments Back in the space have all week. What should we know about these projects so far and One final question for you. You've been to mere before and said before launch You didn't expect to see much different. Is it much different than your trip a couple of years ago? Answer your last question It's nice to be back. It's a lot more familiar than it was in 1995 and of course that and it totally Was my commander at Star City. We trained together for a year. So it was nice to come back and see him again The experiments that I'm working back on in a safe have are basically technology experiments for Life support for future space stations and vehicles one of them the VRA Was designed to help purify water the other one of the OAs for detecting different compounds in the air and like all technologies that you have to test them sometime in their real environment These devices were designed on the ground to operate in a microgravity environment. And as you know, we don't have any waitlist rooms on the earth So you have to bring them to space to test them and right now we're testing them I think DRA Unfortunately experience a shutdown of one of its regulators, but we're working on VLA and we hope to bring it back up today And we'll gain a lot of valuable information on it that'll feed into the future All right, we're all out of time for those of you. We didn't get to talk to I'm sorry about that But we'll look forward to seeing many of you back on earth soon and Andy Thomas will talk to you in space again Hopefully in the next few weeks to see how you're settling in. It's good to see all of you. You look great This is mission control Houston and this view once again of the double space have module in endeavors payload Bay in the aft section of the space have module is mission specialist Bonnie Dunbar and in the foreground mission specialist Jim Riley and with his back to the Camera Dave Wolf who has just completed his 119 day stay as a member of a mere crew The astronauts have just completed stowing away one of the experiments that was conducted during wolf's tenure on the mere space station for its Return trip back to earth and have been conversing over the past several minutes with the scientific community here in Houston to ensure that the stowage was accomplished properly and Provide the status of that stowage down to the payload community here in Houston


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So one three four five three eight Okay Now we random names and box numbers same amount of times and put them side by side to see who's got what They say ten five and five Names first ten times One two three four five six seven eight nine and ten Shane see down to Paul B and ten times on the box numbers here One two three four five six seven eight nine and ten One down to four All right Shane see with one Eric s5 Brandon K6 Matthew G3 Francis D8 Tim Z7 Jason R2 Paul B with box four We get the results posted Get your link and chat call it whose boxes who's as we go along here That's the block Twitch here is for you to let's do this Superfracture time I say super fractured time at least like a red we pulled some black autos and ten We need some other like red or super or something box one Box one is for Shane see good luck Shane We can start off the case hot here Manga madness. 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It's Han and Chewbacca with a Obi-Wan Kenobi refractor Bail Organa refractor Tim Z bottle three. So we're sold out. Nice. Thank you, Tim. Good luck, buddy Got one more after this everybody. That's it more breaks tomorrow with Sam Kira refractor monikers Obi-Wan fractors Sierra Junda Aqua Dio to 199 Like Aqua Digio almost manga madness Soto hit a giant bomb slam the bat down against the Yankees. Oh man. Oh So good reef cargo refractor Mando monikers Jabba the huts refractor auto Dave Barclay's Jabba the huts Princess Leia, Organa refractor That is a first appearance is fin gold to 50 12 of 50 gold thin nice card refractor Owen Lars Fractor crosshair manga madness off there Dark Lord of the Sith monikers is Darth Vader Babu Frick refractor a what the Frick Fractor that's too. There's a Darth Vader The anniversary set there monikers fin and ray. Okay, just do it here monikers fin and ray All right, that'll do it. Thanks again everybody for joining the break just one more case coming up next


In the key exchange session, the first octopond has a password to indicate the key exchange that can be found in your home, in your answer, on the phone, to add any phrases you can not go up, so the key has to ring to this number. Hi everyone, I'm Sophia, and I'm going to talk about what the octopond can be exchanged. And since this is true of work with a pair on the phone, Julia has said that you push the call and made a phrase out of it, and Julia is in the audience. So, I want to start with a motivation, which could be a very familiar one. So imagine that we have as involved, and all we want to do is talk to one another securely, but all we have is an instant share on the same channel. We do also have a shared password, but as passwords tend to be, their passwords very low and should be, so they change to directly as of directly. The password also has a second problem, which is that it's kind of noisy, meaning it differs in a few places. So here, where L has a zero, Bob has an outside. So despite these two difficulties, the two have found Bob's left hand to the shared password to a read on the high-end stream of the draft key. So if they had an X and A in the middle, that in the middle of the game was about, I bear this to you, just like they draw up all of their messages. Alice and Bob want to make sure that no matter what this X and A does, he should learn anything at all about their passwords, in case they want to read those passwords later, or the key they read on, and they manage to read on the key. So whose natural application is something like this, would be this type of password. So imagine that Alice and Bob are trying to also keep using natural passwords, but one of them that could read the key word. So it has been shown that tolerating some errors in password entry would have been able to user experience a lot of applications. So another scenario that would be useful is that Alice and Bob are trying to keep by an access time. So here, imagine that Bob has some resource that Alice wants to use, and Bob stores it database. Iris scans the longing to all of his authorized users, and when Alice wants to access the resource, she takes a fresh scan of her iris and tries to use that to authenticate. So her fresh scan is going to be similar to, but not an exact match for, the iris scan that Bob has stored. So they're going to need to do something tricky. Another application is authentication based on physical proximity. So here, the passwords would be something like noisy and low entropy environmental readings. And this would be probably useful in the very new future when self-driving cars are everywhere, and they want to help one another navigate their surroundings by sharing information about what they see. So in a situation like this, it would be pretty important for these cars to prove to one another that they're actually nearby to prevent some remote attacker from feeding them all false information. So authentication based on shared imperfect secrets or passwords is a very active area of research, and we can sort of categorize this work based on what password problems it deals with. So first, does it deal with passwords that are low entropy? And when I say that a password has low entropy, I mean that it's possible to hit on the correct password realistically by brute force enumeration. So maybe a 30-bit string, I would consider to have low entropy. The second question is, does this work deal with passwords that don't match exactly and might have some noise? So we can see the related work as partially filling in this table. The nicest cell in this table is the high entropy exact match cell. And in that cell we have privacy amplification. So we still need something because even though the passwords are high entropy and exact, they might not be uniformly distributed. So these privacy amplification protocols are very efficient, but they pay for this efficiency by having some leakage about the password used. And in the high entropy situation, that's totally fine because there's so many bits of entropy that throwing out a few is totally totally okay. But because we have some leakage, we can't directly apply these techniques to the low entropy setting. So in the low entropy scenario, we have a different set of protocols called Password Authenticated Key Exchange or PINK. And in these protocols, it's very important that there be no leakage at all about the passwords. So in particular, they even prevent offline dictionary attacks by an active participant or a man in the middle. So anyone who doesn't know the password that sees a transcript of an execution that they either participated in or just observed, they shouldn't be able to then use that transcript to test their password guesses. So moving to the fuzzy match setting, in the high entropy scenario, we have information reconciliation and robust fuzzy extractors. But these also have some leakage just like their exact match counterparts and for the same reason they don't translate into the low entropy world. And in fact, the only thing we have in the literature for the low entropy fuzzy match setting is just generic two-party computation in the unauthenticated channels model. So this is something we can use really anywhere in this table and it tends to be pretty inefficient because it's so generic. So in our paper, we focus on this cell in the table for the first time. We introduce a new primitive which we call fuzzy password authenticated p-exchange or fuzzypake. And we define a fuzzypake and we give two efficient constructions of this thing. So next I want to talk a little bit more about our security definition of fuzzypake. So like I told you before, if Alice and Bob share two passwords that are actually close, they want to be able to talk to one another and as a result of this conversation, they want to both hold the same high entropy session key k. And any active or passive man in the middle should learn nothing at all about the passwords or the key as long as that man in the middle doesn't already know some password that's close enough. If the two of them don't have passwords that are similar, so maybe Alice's password is curiouser and Bob's is, can we fix it? In this situation, they shouldn't end up agreeing on a secret key and neither of them should learn anything at all about the other's password. And this should be the case even if one of them is malicious and doesn't follow the protocol. So there are a few complications in defining a fuzzypake. And the first of these is that, well for any key agreement protocol, it's very important that the protocol be composable. Key agreements is never the ultimate goal. Whenever you want to agree on a key, you probably want to then use that key in a different protocol. So you want to make sure that the protocols remain secure even if other things are also being executed. The second difficulty is that just like pake, we really need to be secure against offline dictionary attacks. We're dealing with low entropy passwords, so we want to make sure that malicious participants and men in the middle, even if they've saved a transcript, they can't then use that to test their guesses. So the approach we take is we generalize the universally composable functionality for pake given by Kaneti Halevi, Katz, Lindell, and Mackenzie. And I'm not going to tell you anything more about this definition. It's the full definitions in the paper. So next I want to tell you about our two constructions. So the first of these uses regular non-fuzzypake together with something called robust secret sharing. And the second uses Yao's garbled circuits. And some of you might find this pretty alarming because I said earlier that I really wanted to avoid using generative party computation because it's inefficient. And here I'm saying that I'm going to use like one of the most famous generic two party computation schemes. But we actually don't use it in the straightforward way. We do something special specifically for fuzzypake that is actually pretty fast. So these two constructions, even though both of them realize fuzzypake, differ in a few ways. The first of these is what notions of similarity between passwords they support. So until now I've just been saying similar for some notion of similarity. And the Yao's garbled circuit construction actually supports any efficiently computable notion of similarity. But the pake and robust secret sharing construction is limited to hamming distance. The Yao's garbled circuit construction pays for its generality with lower efficiency. So both in terms of number of rounds and computation. It's more expensive. So I want to start by talking about the less general but more efficient construction. And because we're talking about hamming this distance, I'm going to assume that our two passwords are of the same length. So this construction follows a very natural template. Our two parties, Alice and Bob, they do share a secret. It's a problematic secret, but a secret nonetheless. So we're going to have one of them, without loss of generality, let's say Alice, pick the key she wants to agree on with Bob and encrypt it to Bob using their shared secret as the encryption key. So using the password as an encryption key. And this is going to have to be some very special form of encryption because this encryption is going to have to tolerate error in the encryption and decryption keys. It's going to have to work even if the encryption key and the decryption key are a little bit different. But even assuming that we have this magical encryption, we have the problem that the encryption key, the password, is low entropy. And any eavesdropper who sees this cipher text is going to be able to really narrow down the options for this session key just by trying, just by going through the password space and trying to decrypt. So we address this by turning every single character of the password into a high entropy key. We're going to expand the entropy of every password character. And Alice and Bob are going to do this using PIC. So PIC is a tool that takes in low entropy objects that match or don't match and gives the parties high entropy objects that also match or don't match based on whether the low entropy objects did. Alice and Bob are going to run PIC for every single character in their password. And whenever the password characters match, they're going to get back the same key and whenever they don't, they're going to get back different keys. And at the end, they're going to have this list of what we're going to call character keys, high entropy character keys that match or don't match depending on whether the corresponding characters did. So one crucial observation here is that it's very important for neither Alice or Bob to learn whether they agree on any given character. So imagine that Alice's password is what I have here, but Bob's password is we can fix it. So if Alice learns whether she agrees with Bob on any given character, despite the fact that she doesn't know a password close to Bob's, she's going to learn that, you know, his first character isn't P. And for low entropy passwords, this is a lot of leakage. This is not acceptable. So we introduce a UC definition for a new flavor of PIC, which we call implicit only. And this new flavor of PIC specifically has this property that neither party learns whether they succeeded in agreeing on a key, so they don't have key confirmation. And one of the famous PIC protocols, EKE2, actually has this property, this implicit only property. And that's the PIC protocol that we use. All right, so now when Alice does this magic encryption step, instead of using her password as the encryption key, she's going to use her list of character keys. And Bob is going to use his list of character keys to decrypt. So this magical encryption really quickly, it works through a combination of robust secret sharing of the message of the secret key K, together with a one-time pad encryption of the secret sharing using the character keys as a pad. And this is very similar to the code offset construction of Jules and Blottenberg. So I'm not going to give you any more details about this. I'm going to leave it at that. And next I want to talk about our Yau's Garbled Circuit construction. So like I said earlier, this one is more general, but less efficient. So one of the tracks yesterday heard a lot about Yau's Garbled Circuits already. So I'm not going to spend too long introducing them. I'm going to be minimalistic here. So Yau's Garbled Circuits are a two-party computation scheme where the two parties play different roles. One of them is going to be a garbler and one of them is going to be the evaluator. So the garbler takes the function that they want to compute and garbles it. And she then sends this garbled function or garbled circuit to the evaluator. And the evaluator is able to evaluate this garbled circuit and learn the function output. And there are a lot of steps here I'm skipping. Really high level. This is how it is. So the way we can use something like this for Fuzzy Pink is just have one of our parties garble a closeness circuit. So the circuit is going to take in the two passwords as input, compare them, and if they're similar enough it's going to output Alice's chosen session key. And if the two passwords are too different it's maybe not going to output anything. And then Bob is going to evaluate this. The problem with doing something like this is that Yau's garbled circuits offer asymmetric security guarantees. So they're secure no matter what the evaluator does. The evaluator can be malicious and still won't be able to learn anything at all about Alice's input apart from the actual computation output. But Alice the garbler has to be semi-honest. If she chooses to instead be malicious there is a lot she can do to screw things up. She could for instance just garble a totally different circuit. She could garble a circuit that always returns the same key that's fooling Bob into agreeing with her like no matter what his password was. So like I just said Yau's garbled circuits don't guarantee correctness against a malicious garbler and they actually also don't guarantee privacy against a malicious garbler because if Alice garbled something along the lines of a circuit that just returns maybe a few bits of Bob's password once she learns the function output she's going to learn information about Bob's input that she shouldn't have learned. The upside is that Yau's garbled circuits are actually really fast as two-party computation goes. There are a lot of transformations out there that guarantee correctness and privacy in Yau's garbled circuits against either party being malicious. But the downside of all of these is that if you consider pre-processing a part of the computation the overhead is going to be pretty high. There's like a lot of cool works here that I didn't list over the recent years. There is one more transformation which is called dual execution which has a very small overhead so it's only twice as expensive as regular Yau's garbled circuits. But the downside of dual execution is that it gives one bit of leakage to the adversary. And especially in our setting when we're dealing with passwords that have very low entropy, one bit of leakage can be crucial. We don't want that. So we modify dual execution to eliminate this leakage when it matters specifically for Fuzzy Pink. So all right let's have Alice garble this close in a circuit like we did before. And instead of outputting yes the passwords are close or no they're not close this circuit is going to output a yes or no key. So it's going to output the yes key if the two passwords are close and the no key if they aren't. So she sends the circuit over to Bob. Bob is going to evaluate it and learn one of the two keys. And because this isn't secure against a malicious garbler, against a malicious Alice, we're going to do this whole thing again in the other direction also. So now Bob gets to play the role of the garbler. Alice has to play the role of evaluator and as the evaluator she can't cheat. So what Alice is going to do once we do both of these steps is she's going to take her own yes key. She's going to take the one key that she learned from Bob's circuit. She's going to XOR them and the result is going to be her session key. And Bob is going to do the exact same thing on his side. So if both parties were honest and if both circuits decided that, you know, yes the passwords are close, they are close in this picture, then clearly these two are going to actually agree on a key. They're going to be XORing the same key. So the same pairs of keys. If the passwords are actually far, then Alice is going to be using her own yes key but Bob's no key and Bob is going to be using his own yes key but Alice's no key. So they're going to be XORing two totally different independent pairs of keys and they're going to end up with different session keys. Now let's say Alice is trying to fool Bob into agreeing with her. Well as the garbler, she can cheat. She can make Bob, you know, get the get her yes key out of her circuit even if his password is far away from hers. But since she can't cheat as the evaluator, there's really nothing she can do to learn anything about Bob's yes key, this blue key over here. So there's nothing a malicious Alice can do to agree with Bob when their passwords are actually far. So we can view what we just did as a variation of dual execution in the general case. So dual execution has very symmetric guarantees. No matter what the correct computation output is, dual execution guarantees that, you know, both parties will either get the correct answer or know that cheating took place and it lets an adversary get one bit of leakage. We make a trade. We say that, okay well when the computation output is yes, when the correct output is yes, we're going to let the adversary still have their one bit of leakage and we're also going to, you know, give up on correctness. We're not going to have any correctness guarantees. But in exchange we want better things in the case that the correct computation output is no. So not only do we want a correctness guarantee, we also want to eliminate the one bit of leakage. So this actually turns out to be the perfect trade-off for fuzzy-pick. Because in fuzzy-pick, intuitively, we only care about security against an adversary that doesn't already know the password. And if the adversary doesn't already know the password, then we're in the no case. So in the no case, we're guaranteeing that the adversary can't learn anything about the password and can't fool our parties into agreeing on a key. But in the yes case, when the adversary already knows a password that's close enough, the adversary can fool the other party into not agreeing with them, which they can really do anyway just by using a random thing as their password. And they get to learn one additional bit of leakage, which is also arguably okay, because they already have all the information they need in order to agree on a key. All right, so in conclusion, there's been a lot of work on key exchange based on imperfect secrets. We're the first to look at the low entropy fuzzy match setting, and we give you security definitions for this new primitive called fuzzy-pick, and two different constructions, which are on different points on the sort of efficiency generality curve, so are probably useful in slightly different scenarios. All right, thanks everyone for listening. Right, so a malicious man in the middle gets to execute fuzzy-pick with each of our Alice and Bob, if they want to, and each online execution gives them one password guess. So he learns an end of two proximity queries. So he gets to basically try to guess, so he gets both answers, not just an end. Okay, thanks. But that's really as good as we can do for something like PIC. Can you say something about the model and assumptions? I assume the first construction is any PIC, the second you use CRS, your random oracle, what do you need? We do use CRS and something very close to the random, and actually the random oracle in both of them, I think. Yeah. Okay, thanks again.