 Yeah, okay. This is better. Okay. Maybe too loud. Okay. How is everybody? Good morning How many of you are the outside registered participants? almost everybody good good to see you all and Who who is like who things are from the farthest who is from Mumbai who has come from the farthest? Tell me some state names Jammu welcome you yeah Yeah Jharkhand Anyone anything father father east may be Delhi University that's far enough good. Welcome to all of you again, and I hope everybody is excited for the day We have some fantastic speakers We have our own faculty. We have a few invited speakers from outside But mainly it's also our departments, you know sort of Expo here and you hear from a lot of our own students and so let me get started With of course a welcome to this symposium and I just want to it's like when there is a big concert There's a warm-up band, right? So I'm just the warm-up band while While people are coming in here So just to throw some stats and some some ideas at you while we wait for the main speaker So we are a pretty big department 46 faculty members now About more than thousand students lots of staff members huge buildings. You will see both these buildings as a part of the Events today, and we have been in this Institute of Eminence list of universities since 2018 and in fact this Event is possible because of the funds we get through as part of being being one of the institutes of eminence So what is generally the picture of research at CSE department IIT Bombay? We have been organizing ourselves into roughly three streams recently One is this computing systems, which is questions and problems related to you know infrastructure sort of the hardware operating systems cloud or you know networks Everything lies here also very sort of systems heavy applications lie here Then we have of course intelligent systems, which is also known as AI ML and so on so it's all about making computers closer and closer to Thinking like intelligent beings and then there is theory which is the foundation for everything every single thing it encompasses everything fundamental questions and problems of what is possible What is possible within some limited time and things are things like that? Really sort of fundamental problems, and you can see that ellipse is everywhere We actually currently have a course in the department called the theory of machine learning. So it's you know everything Yeah, this is again another list of the same things that we divide our intelligent systems streams into these three Speech and representation visual computing then networks and systems architecture compilers all of these systems And we have algorithms and complexity and then formal methods and then we have a couple of arcs that are actually encompassing all of this Digital trust which is a domain which encompasses everything and computing for development is more possibly in the first five Things there are sort of applications. Of course work here results in some algorithmic work also So this is just a picture in terms of how we are how we are sort of distributed We are fairly equal in terms of faculty in terms of in what we do PhD students, of course, you can see the trend, but they are fairly well balanced here So I had just wanted to give an overview because I'm hoping that many of you are here to find out Not only what CSE department does, but what is research about and and you know, how can you be a part of it? So a quick review here I always like to say research is about asking the questions first if you can get the habit of asking questions Then and more and more questions. You just I have to ask the sub questions and actually that kind of leads you to the answer so get into the habit of asking questions and also Whatever work you are doing get into the habit of saying what is the problem that it is solving? You're just doing something, but why? So, you know what why what how when which where can something this is what research is about and this is what Hopefully you will see and I just wanted to go through some examples very very quickly They are sort of related. They're not exactly what the talks and posters will elaborate, but these are just sort of You know, I have like 10 of 12 questions out of the probably hundred two hundred threads of Questions and problems that our faculty and students are working on Okay, I'll start with digital trust and this might be a little naive in a few 10 minutes Professor Shweta is going to talk much more deeply about The theoretical aspect of digital trust So this is just one sample problem. There are three people a margaret three They want to buy a car which is for 10 lakhs and but they don't want to tell how much money they have individually Can you do that? Can you ask? Can you figure out whether the sum is enough without knowing the individual? This is the kind of questions that You know this field asks secure multi-party communication whether you can compute a function While keeping these the inputs private So this is one of the threads that is going on and some work that has been done here I just wanted to continue the story a little bit the same question has some other theoretical underpinnings Formal methods thread of research can ask the question of can such a protocol that is developed for this purpose be formally verified Similarly, you can ask a question that you know, what's the complexity of that protocol? then moving on to computing systems the kind of work that is going on here one is about Architecture making computer computers efficient at the architecture level. So one question here is, you know, can we cleverly prefetch critical data? Which is basically critical means it can have processing stalls from low bandwidth grams in many core systems So what is the answer? Maybe related answers you'll find today for this you have to see the paper that was published Then compilers we have a question such as can we make just in time compiling more efficient by reusing compiled code from a previous run It seems a little, you know Contradictory, but maybe you can do it cleverly Then in OS and virtualization lot of things are going on one sample question is, you know How can we make container migrations use less CPU currently the very CPU heavy in networks? There's a very large project going on in the department Which is about optimizing 5g components is a part of a big project actually a lot of IITs are involved IIT Madras is involved is he's involved So can we optimize 5g components so that data throughput is almost at line rate meaning you're really meeting the physical rate that is capable for the line Then in computing for development we have some really good threads going on That is computing for climate resilience in our kid in agriculture So can we predict how vulnerable farms are? To dry spells you might ask like what is this got to do with computing it absolutely does it is basically data analysis Being able to work with you know satellite pictures. Maybe not such good pictures data. Maybe not complete data So finally it becomes a computing problem Then transport planning of course. It's a classic computing problem. Can we improve Maharashtra road services using again priori data use special data Then we have of course lots of things this is a very small representation of what's going on in the overall field of intelligence systems here There is a one thread is in in the visual computing aspect There is medical imaging can we segment objects in a medical image with less supervision like can you find what which part is the lung or maybe some Something in the lung things like that with less supervision data Then there is a speech recognition this you know, how can we recognize the code switch? Of course, which you know me abhiju karayum. Oh course, which is that right? So in English why we don't have enough data a lot of issues in intelligence systems boiled down to not having enough data in our Own languages, so that's one thread of work and then of course There is a big nice a very successful project going on in transport planning in scheduling of railways Earlier it you know it was more about special geospatial data and maybe conventional techniques here Intelligent systems based AI ML techniques are being used for scheduling What is happens with all of this work one very common outcome is publications and we are doing quite okay quite well in the publications There is a convention in publications to aim for You know sort of what I call top tier for and if you come here to do research, that's what you should aim for But other result is also Translational research products and you know, this is sort of even the earlier is is good for the nation It makes us, you know, well known in the world, but this is more directly useful For example, we have a product that was done out of this department called gelatantra, which is for Planning of the water distribution network again. It turns out to be Kind of a optimization problem and can be done with computing So this is actually being used in in lots of states and then all these other ones also that I talked in as part of the Computing for development lot of things going on here that we want people to actually use Again the outcome of some of these things is a lot of honors and awards for the faculty I don't really want to go through all of this You can check our news and our social media And we have another thing that happens when we have when you do well in a certain department You know people open like big labs and stuff like that. So that has happened recently We have a big thing called a trust lab. We will have a talk about this I think today or tomorrow I can see the schedule and also GIC. This is a geospatial hub And I think many of you might already know about e-antra. This is a Project by Ministry of Education and we do a lot of competitions and so on very very successful So this is but the point is that the engine for all of this work is really the students And the way is that the students contribute to all of this is through these three research-oriented programs Although I must say as a footnote here Our b-techs also contribute a lot to research, but this current audience. I want to talk more about the PG programs So we have MTech MS and PhD MTech you can find out more about it We'll have some info booth later, but MTech is a conventional fixed duration program It also by the way has a pretty serious almost 13 14 months thesis So doesn't mean that it is not research-oriented, but it is more fixed We have made MS a little more research-oriented in the sense that you start research right from your first semester and It is flexible so that if you're working on a slightly hard problem Let's say some theoretical problem or even something in systems that is just Taking time to sort of think about then you're there isn't a clock that ticks It's a clock that is a little more flexible whenever you are done anywhere from one and a half to three years You can write the thesis it gets externally reviewed and then you can go and PhD of course is the flagship program And these are the people who do most of our research for us Yeah MS also I want to all the PhD of course it's obvious But MS is a new program So I just want to say that we are having you know good publication success and also Applications and so on are being developed by these students And we have lots of awards and everything if you come here you should aim for these sort of things And one thing is that we government and industry is doing a lot Everybody recognizes that we need PhD students. We need students to do research. So very good fellowships are there Making it a compelling choice. You know, don't just join a job. Maybe come and do a PhD Yeah, we have a lot of facilities and all this we'll see Later I want to sort of wrap up for our next talk You do I do I do want to say that you know when you do research You are like of almost like a full-time research staff member and you get you know a cubicle in a nice lab You're supposed to be hanging around there the whole day and that's what we enable for for all of you Yeah, and faculty and research we have a beautiful lounge There's so many people that we couldn't take you up there But if you join here, then there is a terrace lounge that research scholars use So that's it. I don't want you know, it's more like I don't want to talk about it much You are going to listen to You know work done here and also our very eminent invited speakers So my last appeal is you know choose to stand out from the crowd be a knowledge creator Not just consumer. You know, we had too much just consumers We had to create and build things innovate disseminate and and you know find your sort of special place On the planet really by doing this stuff and join our or any I would say, you know, this thing really is our is a big Thing first appeal would be anywhere in India, but in general anywhere. Just please do research It's something that the whole world needs. So this is our admissions page. It's please watch the space There's something here, but it's it's there cling from our website also if you want to find out more. We'll be adding the Current years data soon here and that's it Hope to see you here or any other it is or I see or anywhere as master students and research students really so welcome again, and I'll give it to the emcees now to introduce our Invited speakers. Thank you Hello, everyone. Thank you, Professor Varsha. So I didn't get a chance to introduce her. She is an Amazing researcher inspiring academic great teacher and the head of the computer science and engineering department at IIT Bombay Hello, everyone. I am Ashita. I'll be your host for today's event Thank you, Varsha. Ma'am for starting this event with such an insightful Commencement address without further ado. I would just like to dive into the heart of risk Let me express my gratitude to all of you for being here in this exciting event with us It's my privilege to introduce our first keynote speaker She is professor Shweta Agriwal from the computer science and engineering department at IIT Madras in the world of cryptography Professor Shweta Agriwal is an esteemed and distinguished researcher She earned her PhD at the University of Texas at Austin and she did her post doctoral work at the University of California Her extensive research in cryptography and information security with a particular focus on post quantum cryptography Has earned her numerous accolades Including the Swarna Jayanthi Award and the ACM India Award for outstanding contributions to computing by a woman She has received best paper award at Euro Crypt Google India Faculty Award BY Award for excellence in research and teaching and she has been an invited speaker at prestigious Conferences like Asia Crypt and Women in Mathematics Ronald Rivest a famous cryptographer and computer scientist once said Cryptography is about communication in the presence of adversaries Today in her captivating talk Professor Shweta Agriwal will guide us through the intricate dance between the possible and seemingly impossible within the world of cryptography The art of negotiating with the impossible as she aptly puts it Please welcome Professor Shweta Agriwal. Can you hear can you hear me now? Okay, great. So it's great to be here Thank you all for coming. Thanks to IIT Bombay for the invitation I'm really excited to talk to all of you and thanks for the kind introduction So indeed, I'm very excited not only to be here, but you know from Varsha's introduction I see that many of you are Students who are thinking about a research career. So it's truly exciting and a privilege for me to introduce you to this beautiful field Cryptography, right? So cryptography is the art of paradox. How many of you have had a little bit of exposure to cryptography? Okay, so that's good. So a few of you Let's just sort of jump right in this talk is going to be really at a high level And I encourage you all to ask me questions as and when they come up Okay, so we have an hour, but we're not going to try to cover any ground We'll just talk and we'll stop in one hour. Okay, so that how does that sound? So please ask me questions or You know, if you have comments anytime during the talk, please do speak up. It's always more fun like that So cryptography is the science of keeping secrets and actually as we heard in the introduction You know, there was one there was one definition of cryptography about you know communicating secretly But really in the modern world cryptography has grown so much so much bigger than that Okay, so there are lots of really amazing very very surprising applications that cryptography enables The first one which is actually considered the most basic one But which staggers me even to this day after more than a decade of research in this area is this idea Of exchanging secrets within a crowd now most of us have heard the term encryption etc And you know nowadays when we talk about this exchanging secrets in the crowd people are like yeah I mean this make yeah, this is you know, just just encrypt but you know for this talk In fact, I mean for any kind of research It's good to put aside ideas of what we know and just think from very very basic first principles Okay, so this is the stage so we're here today. I'm here right with the mic Most of you are meeting me here for the very first time and now let's say that you know There's one person with whom I decide that I want to communicate in secret. Let's say the girl in the blue over there Okay, and the only channel of communication I have is this microphone Everything that I say can be heard by everybody Okay, and everything that she says can also be heard by everybody. We've never seen each other before we have no We've had no prior communication of any sort just in this moment We decided to speak and we wanted to be the case that though everybody can hear everything We say somehow only the two of us can figure out what is actually being said. There's some secret in there Do you think this is possible? How many of you think this is possible? Okay, very good So the last time that you know I gave some outreach talk and similarly people said yeah, you know this should be possible I actually abandoned my slides and spent the whole hour convincing you why this should not be possible at all Okay, but you know for the sake of the organizers I will not do this today but if you run into me again You know beware so this is super super surprising and oh, you know what I can tell you an interesting anecdote So recently I was at this Pingla interactions of computing and There we you know I was discussing this This notion of exchanging secrets within the crowd and there was a Turing Award winner there a senior gentleman And he did not actually know of this particular notion and after the entire event was over right He finally when he understood what key exchange enables his jaw dropped open Okay, so I'm just trying to tell you that this is very surprising and the fact that you think it should be possible Means that you have to think again. Okay, but I won't say anything more about this Another thing that it lets you do is it it lets you prove to somebody that you know something without telling them what you know Now let me give you an example. Okay, so now let's say that you know IIT Bombay since they're into so much fun They hand out these Sudoku puzzles to everybody. Okay, and they promise some big money to whoever solves it first So of course I want the bribe and I claim that I've solved it. Okay, so as soon as Varsha gives me this puzzle I take a look at it and I say you know I have the solution Now I want to convince everybody that I actually do have the solution Generally, how do you convince somebody of such a thing? You show the solution right So you can show the solution everybody can verify it right But here I'm not allowed to actually show you the solution So I need to convince you that I have the solution but I'm not allowed to show you the solution Is it possible for me without cheating to prove to you that I have the solution without telling you the solution? Is it possible? So maybe after all my threats in the previous bullet point now people are more afraid of saying it's possible It should not be possible but cryptography makes it possible. Okay, so again we don't have time to go into this But it's another one of these really fantastical things that cryptography allows you to do Which is why in the abstract of this talk I said you know it's really about negotiating with the impossible It's like oh you want to do this thing this does not sound like it should even be possible Cryptography says let's do it. Okay, so it's really a beautiful field In a way, assuming this is medium What if for example if you can measure the distance between speaker and receiver accurately No no no where you know just Yeah so that's what I'm saying there are some implicit assumptions about the physical medium you are making I'm talking of this room today here So this is my medium that's my assumption I came here and this is my room let's say we want to talk Suppose there is a technology by which you can measure the distances accurately Okay And hence you know the distance to the blue girl And using that property you can figure out an encryption key and then proceed with your communication Okay let's take this offline I mean what I have in mind So you know we are very close to me abandoning this This is exactly what happened last time Everybody was like yeah and you know then at the end of the talk everyone was like no okay Let's take this offline okay but I just want to say that it's actually The assumption that you are really making is that the universe permits asymmetry in computation Okay we will be talking about this more in the rest of the talk so let's get back to it later Okay yeah great question anything else Okay so let's keep going Another thing which is sort of you know more these first two are more classic applications A much more modern one is you know you want to run machine learning algorithms But on data that is encrypted okay we'll talk more about this in the next slide And another one of my favorites is encoding a message which can be denied later So let me also get we'll also take a deeper look at this Cryptography is really a field of indisputable utility More importantly really indescribable beauty It's really like a game of chess where you always have to be one step ahead of the attacker Okay so never a dull moment So let's come to this application I told you about about computing on encrypted data And let me read from an article that appeared at Nature several years ago The dream for tomorrow's medicine is to understand the links between DNA and disease And to tailor therapies accordingly But scientists have a problem how to keep genetic data and medical records secure While still enabling the massive cloud based analysis that is needed to make meaningful associations Okay so personalized medicine is really a poster person application So I think everybody agrees that medical research is very important right And we'd like to contribute to it Now people have genetic data with them but it's also something very very private right So you don't want to just hand it over you don't really trust what people are going to do with this data So can you run some sort of algorithm which allows you to compute what you want Like let us say you know the correlation between some pattern in your DNA and some disease or something like that But while the data is still encrypted somehow so you know the data is hidden but you're still getting what you want out of it Sounds impossible right Okay here's another thing okay so activism with safety so this is what I mean So let's say that you know I'm in a regime where there's oppression and I want to organize a revolution right So of course this has happened it keeps happening it's still happening So let's say that I want to encrypt some message but it's something which is very dangerous Now let's say that I've encrypted something like that Here one thing to note is that encryption is a probabilistic algorithm so there's some randomness there And now somebody somebody comes and you know puts a gun to my head and says you published this ciphertext open it Open it right what can I do Well a hope would be that under coercion I can reveal some fake random coins are prime So remember I encrypted using some R and I got some C and under coercion what I'm doing is I'm actually giving you some fake random coin R prime Which somehow lets me explain the same ciphertext as an encryption of some very benign message Okay so this is this notion of deniable encryption Yeah we won't talk anymore about it it's just another very surprising application So in this talk right I've hopefully convinced you that cryptography allows you to cook up all these really amazing things And today what we'll do is we'll talk or kind of take a little peek at how we do this right How do we prepare all these fantastic things Okay so that's what it'll be about and as a case study we'll take sort of the most basic primitive that everybody knows about Which is just encryption okay so encryption as you already know I mean everybody has let's say a public key and a private key So my public key is known to everybody my private key is known only to me right if you want to send me a message You'll encrypt it using my public key and I'll be able to decrypt it using my private key So everyone's familiar with this notion of encryption right and there are really two properties that we want from any encryption scheme One is functionality or correctness which means what well you know if I encrypt something somebody should be able to decrypt it Otherwise it's useless right and security is that the ciphertext should leak no information So if I don't have the secret key I should be able to learn nothing about the ciphertext Okay and really cryptography is about walking this fine line right you want functionality together with security A little bit of thought will show you that these are really opposing requirements Okay anyone without the other is easy so functionality without security is definitely easy don't do you know don't encrypt Security without functionalities even easier how? Yes What should we do in that case? Like there is a 100% guarantee about secrecy because in previous slide you mentioned Okay so I think if I let me know if I understood your question correctly I think the question is that How much guarantee can you have that the secret key is indeed secret right this is the question So how it's own secret Medium Inside There's no medium okay so I'm running this setup algorithm I generate a public key and a secret key I just keep the secret key with me How we store it in where we store that key In my head let us say In that case it doesn't leak but You can write it on a paper and keep it with you We talk about machines so in that case Okay so we're going to assume that you know we generate our own secret key This is for simplicity so I should say that in practice you're right that you know secret keys can get leaked and one has to worry about that Actually this touches upon an important aspect of cryptography which is how you model security Okay so here in the modeling that I'm presenting we're really assuming that the secret keys is completely secret It is possible in the real world like there are these things called side channel attacks and so on through which you know some bits of the secret key can get leaked I mean you know people can call me and ask you know say something about my parents being in danger or something and maybe I'll just panic and give the secret key So there are lots of ways in which keys get leaked but we're not going to talk about that Okay so we're going to for the purpose of the stock and in fact for the purpose of almost most practical scenarios as well It can be assumed that the secret key is kept secret you can store it in a trusted hardware Okay or you can store it in a machine to which only you have access There are multiple ways of vaulting the secret key Okay so let's not worry does that answer your question Can we 100% say that nothing is secret? Everything should be leaked So if you very good so if we say that you know nothing is secret and everything should be leaked Then actually any sort of secrecy is impossible by definition right because if I have to protect something against somebody There has to be some asymmetry between my legitimate receiver and an eavesdropper Isn't it? I mean let us say I want to protect my information from you but I would like to send it to Preeti here So there has to be some difference in information between Preeti and you right? If both of you are looking at the same object and both of you have the same computational resources Then obviously it's not possible to get secrecy against one and not the other So this raises an important point it's worth emphasizing that you know we really need some asymmetry So in information theoretic cryptography which is another field of cryptography We can assume that you know maybe we assume that the attacker is further away The channel between me and the attacker is worse than the channel between me and the legitimate receiver That's an assumption another assumption you can make is that you know the secret key is kept secret Or even if there is leakage in the secret key you know I assume that let's say only up to 50% of the key is leaked But I have to make some assumption okay yes We are worried about problem I mean generally when we come to computing we think of computing is like 100% perfect But all these algorithms as you alluded to are probabilistic Yes So with let's say 23rd years down the line with quantum computing the game changes completely So you know sort of one of those things that the claim which is made very emphatically today May not necessarily be tomorrow with Absolutely So just wanted to put that also And in fact it's an aspect I'll touch upon even later in this talk Yes so we will in fact coincidentally be talking about this a little bit later down the line Any other questions? Okay so let's keep going Okay so functionality and security Now let's start looking a little bit more deeply at you know the cooking that I promised you will do together So functionality I want to say requires some mathematical structure Okay and security requires some hardness so let me try to go deeper into this Now I am trying to build an encryption scheme I need to build I need to use some mathematical structure So now I am thinking of my message as some sequence of bits let us say And I want to hide these So there is some mathematical structure using which you know I have to construct this scheme And I need two kind of conflicting properties one is that there should be some nice behavior in this mathematical structure We'll see examples which allows there to exist a secret key which will enable decryption Right so there has to be some structure there On the other hand there should be some computational hardness or algorithmic hardness So that if you don't have this secret then you know this problem looks hard to solve So we'll see examples of this right now like I told you we have these two conflicting requirements And we'd like to get these both together from a suitable hard problem in mathematics Okay or computer science So typically when we think of a source of hard problems we think of complexity theory right So NP complete problems NP hard problems and so on So are these you know are these going to really give us the right properties that we want Okay so the question I'd like to ask is where can I find these suitable hard problems Any idea sure So sort of maybe for now let's restrict attention to you know these computer science complexity theory classes Right so here we would hope to assume something that is widely believed something like P is not equal to NP or something like that Right and we'd like to build cryptography from it So cryptography is going to prove to us that breaking some encryption scheme is at least as hard as solving some mathematical problem Okay and sorry the fonts are getting messed up but this mathematical problem we can only conjecture that this problem is hard Okay now this sounds like a problem right because it seems like I'm basing my security on a conjecture And indeed it is sort of an uneasy place to be but you know we have to conjecture something At the very least we need to conjecture that P is not equal to NP right and is this enough So is it enough for me to believe that P is not equal to NP thus this give me cryptography And it turns out that not quite so there are many words okay that possibly we might live in These were defined by Russell Limpagli also let's look at them okay so what is the first word The first word is called algorithmica so in this P is equal to NP now note that even though we believe that these are different We actually don't know right so if P is equal to NP then you know we cannot do cryptography This is heuristica which says that P is not equal to NP but finding hard problems is hard So there exist hard problems okay from which I can build cryptography but finding them is hard Then there's pestilent which says that there exist problems that are hard and I can also find them There is no asymmetry of computation okay so this is sort of formalized by saying there are no one way functions Now one way functions are the most basic primitive of cryptography what is a one way function It's a function which is easier to compute but hard to invert okay so now what would I like I would like there to be not only a problem which is hard but there should be some asymmetry Which means that it should be easy to compute in one direction and hard to compute in the other direction Okay so this is a one way function then there is another word which is defined which is called mini-grip Mini-crypt in which one way functions exist if you take a course in cryptography you will see that you know this implies the existence of symmetric key cryptography and then there is an even more brave world which is cryptomania in which we conjecture that public key encryption exists Now why am I showing you these you know different worlds because first of all you know they capture the state of our knowledge we don't know right we don't know which of these worlds we live in right So that's what we're asking here which world do we live in and the answer is that actually we have no idea Yes? Alright so for cryptomania I would like to understand if there is a more complexity Theoretic like definition or is the definition tautological that pk exists and that's cryptomania Yeah it's the latter so you know we're just saying that a world in which pk exists we call it cryptomania These are not mathematical terms so thanks for asking this these are sort of just yeah they just capture you know what we believe exists ok so if p is equal to np there is no cryptography right and then it's not enough to just assume that p is not equal to np it could be that the two are different You know but it is still hard for me to find hard problems with which to do cryptography It could be that I can find them but I don't know how to use them because there's no one way function So there are different possibilities and we're just loosely defining these as these ok So we don't know ok but we have to we want to hide our information So we're going to conjecture that we live in cryptomania ok so we will build cryptography Assuming that certain problems you know are hard in a way that allows us to build crypto Are there any questions? Yes? They are stronger yeah so you know they are stronger and stronger assumptions Any other questions? Yes? Ma'am what does it mean that finding hard problem is finding hard means exponentially For example yeah you could think of an exponentially hard problem like you know let's take an example Like you know maybe I think you know so let's take an np hard problem ok Like let's say the travelling salesperson problem or something like that Now is it easy for me to find an instance of a graph where this problem is hard we know It is hard in the worst case but can I find an instance efficiently where I know this Problem is hard this is what I mean ok so we are going to make conjectures about You know problems that we can actually sample from like we can find problems that We believe that this problem is hard I mean this instance of the problem is hard Ok does that answer your question? So we know that the problem is hard but the given instance is hard or not is the question Yes Very good question So yeah if we know that one way functions exist We don't know I mean so if we assume Yeah so do we know that we can invert the function The assumption is that it is hard to invert But I mean a solution exists that is not a problem Yeah a solution exists ok so back to encryption ok so now you know I want us in this lecture To actually build an encryption scheme ok so let's do that So you know we this is where we were we want to have some problem which you know allows me to Get both correctness and security and here is a candidate which we actually use ok so this is called The closest vector problem on lattices this is what a lattice looks like ok so this is a simple Two dimensional lattice just think of it as a periodic arrangement of points And the question that we are asking here is that if I give you some arbitrary point in space Ok so some point t can I find which is the closest lattice point to this point This is the question ok is it clear so this this lattice is our mathematical structure That I was you know talking about so now we are getting you know more warmed up So more concrete examples so this is my mathematical structure so it's a periodic Arrangement of points and I represent it using some basis vectors so most of us are Used to these basis vectors right so I have these basis vectors here just two and I take Integer linear combinations of them ok so this is a discrete space and all these Integer linear combinations like if I take b1 plus b2 b1 plus 2 b2 and so on I get points right and these will be arranged in this nice way and the question I am asking is that you know if I give you some arbitrary point in space some t Which is my closest lattice point ok so this is the question ok so you see like this Little circle here yeah so here is my point t and I am trying to find within this circle Is there like a lattice point this is my problem and a little bit you know More formally a lattice as I already told you so it's a set of points with a periodic Arrangement the simplest lattice you can think of is you know just the integer lattice And in this in these slides we are only looking at two dimensional lattices But when we work with them we will actually look at multi-dimensional ok So hundreds of dimensions ok so this this is a simple lattice and you know I Can apply a linear transformation via some you know matrix b let us say And I can get another lattice ok and this b is going to be like my basis matrix So it's the basis vectors of my lattice I will take integer linear combinations Of them and get the whole lattice so yeah it's a discrete subgroup of Rn This is actually a nice mathematical definition and this is my closest vector Problem I already told you what this problem is like this is a little bit more Formally so mu is some parameter I give you ok so I want you to find me a point A lattice point within some distance mu ok this is this is the question Now this problem is you know a very hard problem and when I say hard actually The the efficient the efficiency of solving this problem is exponential In the dimension of the lattice so this is why I need high dimensions And I also want to say that the decision version of this problem is also hard So what I showed you is a search version that I give you t and I am asking you to Find some close lattice point a decision version will will be you know I give you a point and I ask you is this close to the lattice or far from the lattice Ok so there can again there can be like some measure of that Like if I am within this distance mu let us say then you know I am close to the lattice Otherwise I am far ok so this is this is the problem that we will we will use So now you know I gave you a problem which I told you is hard ok Now how do we know it's hard you know so actually the version of it that we Will use in cryptography is an approximate version And really speaking we only conjecture that this is hard because you know we've Studied it for decades we don't know lattices actually have been studied for Hundreds of years in computer science they've been studied for decades And we don't know of better algorithms so cryptography is also like a sort of You know trying to make the best of what we have like in Algorithms we want to solve problems right we want to do it efficiently Most of the times we cannot right and you know when we cannot we can hope to at least Do some something useful with it like cryptography ok So this this is our hard problem so remember we were saying there should be Functionality and security right and for security we need some problem to be Hard but I also need functionality right so I need some mathematical structure Which enables me to get functionality ok so where am I going to get this Structure or you know where am I going to get my correctness from So here we'll introduce this really cool notion of trapdoor functions Ok so what's a trapdoor function so let's generate some function f and a trapdoor T what are these these objects so this function is you know some function Going from some domain D to some range R ok and this is a one-way function So what does that mean I have this domain range right I have some point X in the domain I apply this function I get to some point in the range And as I already told you I mean if I give you X I can compute f of X which is Y I can do this efficiently If I give you Y I don't know how to go back to X Ok this is one-wayness and what a trapdoor function lets you do is it lets you Invert given this trapdoor is the concept making sense Ok so in general I don't know how to invert this function But I want to give you some secret information that lets you invert it Now maybe you're thinking you know we're just reducing the problem to Another problem which is sort of true but I'll show you how to build these trapdoors Are there any questions ok so fine so I showed you a lattice right I showed you A hard problem on a lattice and I told you that we're going to use trapdoors In order to get you know the correctness of our encryption scheme We're building it now ok so let me first show you what these Trapdoors can look like and this is just going to be like a construction by picture So this is my two-dimensional lattice ok this is one basis of this lattice this is another one There can be many different bases depending on the bases I have You know just by eyeballing it you can see that I can you know divide the space Into these parallelopipers right so I can just kind of chop up space around the Lattice points you know parallel to the bases vectors and I get these parallelopipers And different bases will give me different parallelopipers ok so far so good Now I'm going to introduce this notion of a good basis So what do all this can be made mathematically rigorous But just for the sake of intuition ok what is a good basis It's a basis which is you know quite short hand waving here But quite short and almost orthogonal ok we'll see why we like these bases So if I have a basis which you know is is fairly short and quite and you know fairly orthogonal This can be mathematically you would want like the Gram-Schmidt norm of the bases to be bounded in some way But this this is the right intuition then I'm going to call it good And you know if I have this good basis and I ask this question about the closest vector Right so I give you an arbitrary point in space and I'm asking you what's my closest lattice point Right then it turns out that I can actually solve this problem So you know the way that we do this given any bases ok What I can do is that I can always output the center of the parallelopipers that contains T Ok so I have my basis right I have these parallelopipers And I'm giving you an arbitrary point somewhere and I'm asking you which is my closest lattice point Now for any basis it is possible for me to find the center of the parallelopipers In which this point T lives this is true not only for a good basis but for any basis I can always do this but if my basis is good right then this answer will be pretty good Ok whereas if my basis is bad like this right then I'm going to output So this is my parallelopiped right this is the center of the parallelopiped that contains this point T And I'm going to output this as my closest lattice point But you can see just again just by eyeballing that this point is closer this point is also closer than this point Ok so again this can be made rigorous But when I have a bad basis and I output the center of the parallelopiped that contains my desired point Then this turns out to be off by a large margin whereas if I have a good basis then I can solve this you know fairly well Ok so this is an asymmetry that we have ok so Sorry It seems like the intuition is about a flow function which will capture it It's I think you may have the right intuition more than flow it's like a rounding So it could be yeah so what you can do is I mean I have some point right And I can just try to express it in the basis and round off the difference this will sort of give me the center Ok so if it's a good basis then it's Exactly yeah exactly So now the closest vector problem that we saw as well as other problems they are hard If I give you an arbitrary basis ok but if I give you a good quality basis then actually I can solve these problems And this is the asymmetry that we will use in building our encryption scheme Ok so we are going to use our short basis as a cryptographic trapdoor Ok and now I claim that we have everything we need to build our first public key encryption scheme So we have a lattice right this is our mathematical structure It has some nice structure it's this additive structure we saw a trapdoor on this Ok so what did we see just to recap we saw that if I give you an arbitrary or you know some bad basis for this lattice Then solving this closest vector problem is hard If I give you a good basis then solving this is easy right And recovering the good basis from the bad basis is hard Ok and in the absence of the good basis I don't I don't know how to solve this problem So that is our hardness Now I'd like us to design a public key encryption scheme using this Yes so like I said we can make it rigorous so you know there will be some property that it satisfies So in a public key encryption scheme we have a setup algorithm which will generate the public and the secret key Now who can guess what should be the public key and what should be the secret key here What should be our public key what The lattice parameters could be the public key and the basis could be the private key So there are which basis I mean the good basis should Good so good so you know that's right on trap I mean if something is you know letting me do cool thing solving hard problems It should be kept secret so our good basis will be our secret key Our public key can be a bad basis Ok not just lattice parameters but actually a bad basis because I also need to do stuff publicly So my you know my key generation or setup will give me a good and a bad basis let us say And I'll keep the good basis secret I'll publish the bad basis Now you have to encrypt something Now for simplicity let's try to just encrypt a single bit a 0 or a 1 I want to encrypt either a 0 or a 1 And I need to do this using my bad basis How should I do it the intuition is that the attacker in the absence of the good basis Should not be able to tell if it is a 0 or a 1 the 2 should look the same So the encryption of 0 should look similar to the encryption of 1 So this is where the hardness of our problem the hardness of CVP should come in right So can you guess how would I encrypt what is hard what did we say is hard Finding the closest lattice vector is hard even distinguishing Whether I am close or far to the lattice is hard Can we think of how could we use this to encrypt a bit any thoughts Ok so let me re-interpret what you said I think what you are trying to say is that 0 should be somehow close and 1 should be somehow far That's exactly the right intuition and why do we get that intuition Because it's hard to distinguish close from far right And I want it to be hard to distinguish 0 from 1 So let me encode 0 by you know close and 1 by far for instance Right and now how will I decrypt anyone else a secret basis Right as the secret key and what can this do It can figure out right is my point close or far So that's it that's our first public encryption scheme So we will make the bad basis public we will make the good basis secret Ok to encrypt we will use the bad basis For 0 we will output a point which is close to the lattice So using a bad basis also we can do this how Take the bad basis you know just take some linear combination Get a lattice point and just shift it a little bit Ok it's easy even using a bad basis to output some lattice point right BX For any integer X is a lattice point and now I'll just shift it a little bit I'll just add a little bit of noise to it perturb it a little bit This gives me a point which is close What gives me a point which is far But turbid by much more for example So this is the way in which Can we reinterpret as like X axis Y axis as 0s and 1s And more and more bits more and more computation is there Then if we go into multi dimensional version of the vector space Then the point can be easily found out So it also shows that the cryptography is 100% possible No At that point when we go multi dimensional Actually no so I don't think that's the right intuition So the axis really don't have anything to do with 0 or 1 0 or 1 is being encoded We compare it with hardware like we compare that algorithm Because we are mapping our algorithm into cryptography by hard And something like hard problem and not hard problem So if we map that problem as some hardware system computation Then we can say that can we say like that In my judgment no we cannot But we can talk more offline to make sure that I understand what you are saying I don't think such a mapping is really possible Any other questions? So yeah as I already said in order to decrypt We use t to figure out whether it's close or far And the security comes from the hardness of the closest vector problem And the correctness comes from the properties of the good basis that we saw Are there any questions? Yes Go from one basis to another Because we don't know how to do it So it's not easy or it's just not something we can do So how do we generate the basic? There is no in cryptography in fact in computer science I mean we cannot disambiguate hard and don't know how to do it We don't know how to do it therefore we conjecture it is hard So this closest vector problem has been studied very very thoroughly It's one of the problems which actually solving it exactly is even NP hard But as I said earlier you know NP hardness we don't know how to use it We need something which is average case hard Which means that if I sample a random lattice CVP should be hard on that lattice which I sampled Otherwise if there exists a lattice which is which you know has CVP hard I don't know how to use that Right so because we built this encryption scheme For this I need the B I need the T right I need to construct them So we need average case hardness and we are going to actually use like an approximate version of the closest vector problem which is not NP hard So actually getting cryptography from NP hardness is one of the outstanding open questions in the field of cryptography We don't know how to do it So we will use a version of the problem which is not NP hard But which we don't know how to solve and when we say we don't know I mean this is a very educated we don't know It's not just looking at it for two minutes and saying we don't know It's been studied over decades and we don't know the community The global scientific community does not know after several decades of rigorous study So we believe that let us say that fine let us say that our conjecture is even false We at least don't expect the attacker to figure this out in time to break it You see so that's why I said it's like a chess game We don't actually know You know we guess we believe we conjecture that this problem is hard And we prove that in order to break this encryption scheme you will need to solve the closest vector problem And we expect that the attacker cannot solve this problem Does that answer your question? If you have a lattice finding a good basis and a bad basis is that is doable So sampling a lattice together with a good basis is doable But given a particular lattice finding and this is intuitive I mean I can sample short vectors which are nearly orthogonal Take integer linear combinations of those and that define that to be my lattice So this is actually where you know when we saw the many worlds So this is a way of sort of sampling a problem with a solution You see so I can find I mean I first pick the solution and then I build the problem So this is not this is doable this is not hard But if I fix the lattice and I ask you to find this short basis Then I am basically reduced to trying all possible combinations of short vectors And this will take me exponential time Is this clear to everybody? Yeah Bad basis Like when we discussed bad basis we said that it is possible that the answers that it would give would not be accurate So if we are No we said that it is not possible The word possible is not the one that we used We said it is highly unlikely that the answer to the closest vector problem that the bad basis gives you is a good answer Right But note that in encryption we are actually not solving any hard problem at all We are creating an instance for somebody to solve do you see that So like my question was just that is it possible that if we use a very arbitrary basis Could it be so bad that we actually end up outputting the opposite like we end up encrypting 0 as a No this is what I am trying to say that let's I will finish whenever how much time do I have Yeah Yeah Yeah yeah yeah Yeah so Varsha I will finish in within 5 minutes So actually this is only part 1 of the talk I will just skip the second part So this was the warm up and then I was going to show some advanced crypto like something we worked on We will just skip that all together So what I wanted to say is that let's be very careful about where these bases are being used So previously what we said was that using the bad basis it is hard for me to solve this CVP What does that mean using the bad basis it's hard for me to decrypt which is what I want Using the public key it's hard for me to decrypt this is perfectly what I want Using the bad basis it is very easy for me to encrypt Note the difference right this is the fundamental asymmetry that we are playing with Why is it easy so I told you that you know just integer linear combinations of the basis vectors Whether good whether bad if you go back to you know the slides right like any of these slides So these are these basis vectors right if I just add them with each other right I get points in the lattice so does everyone agree with me that I can generate points in the lattice Irrespective of the quality of my basis just take integer combinations right you will get some point Now I can push it away from the lattice how just perturb it add some noise to it just push it away This is easy right so pushing it a bit away or quite a bit away this is easy so encryption always works Okay and the so it is not that because the bad basis is bad it is also bad for encryption The beauty is that it is good for what it needs to be good for and it is bad for what it needs to be bad for Because of the asymmetry between encryption and decryption Encryption is about creating a bad problem everyone knows to do that in life know Solving hard problems is hard creating problems everyone can do right So I will just conclude here okay so I just wanted to say that you know so all of cryptography Is you know this sort of jugalbandi between correctness and security algorithms and complexity structure and randomness Okay and it has lots and lots of open problems it is at the very heart of the science of computing As I already told you we do not know how to use NP complete problems for cryptography We do not really know how hard are the problems that we do not know how to use And this is something that my advisor told me when I was a PhD student cryptographers rarely sleep well And really this is true okay I do not know I am supposed to be selling this field to you But really I mean you know you do not know anything okay so you do not sleep well but you know it Okay and if this one bad enough so again some more reverse advertisement here okay so quantum enters the picture These are you know computers that use quantum rather than classical physics and they break all number theoretic cryptography Okay so I am going to skip all this and I will just say that in summary okay so cryptography is powerful Cryptography is surprising I did not want to skip these slides right so But most importantly cryptography is beautiful okay and I hope you will join us in this wonderful adventure Thank you very much Thank you thank you Professor Agriwal for such an interesting talk I hope it's inspired you all to explore the amazing yet paradoxical world of cryptography We would now like to express our gratitude to Professor Shweta Agriwal With the token of appreciation I'd like to request Professor Sharad to do the honors Thank you ma'am thank you so much In the words of Grace Hopper a famous computer scientist The most damaging phrase in the English languages it's always been done that way Risk is our way to show our commitment to challenge the status quo and push beyond the limits of convention With these words we will transition to our next speaker I am pleased to introduce an esteemed member of our faculty Professor Swapriva Nath Professor Nath is an assistant professor at the department of CSE here at IIT Bombay His research lies at the intersection of economics and computation With applications spanning social and industrial paradigms His work has been published in top AI and multi-agent systems conferences His accolades include Fulbright Nehru Post-Doctoral Grant TCS PhD Fellowship and the Honorable Mention Award of Yahoo Key Scientific Challenges Program So today he will be talking about multi-agent AI from a game theoretic viewpoint And show how robust AI systems can be built with such agent So let's welcome Professor Swapriva Nath on the stage Okay so thanks for the great introduction and welcome you all So this talk is going to be about artificial intelligence Which I think everybody is really very excited about But with a small caveat that there is this multi-agent thing And I'll give you examples and try to motivate why this multi-agent part is important So I am Swapriva, I am a faculty here So the moment you think about artificial intelligence what comes to your mind Some random guesses? Chat GPT Chat GPT, great Large language models, auto correction when you type in Grammatical corrections, then detection of faces and all those things Now if you have already known that area well Then you must have known that behind every artificial intelligence technique There is an optimization problem that is running behind So beta, deep learning, training your deep learning is an optimization problem And several other things which are all optimization problems I will try to call that as a single agent problem, why? Because you are trying, you are given a bunch of data And you are trying to learn something from it And in some sense you are solving the optimal solution for yourself Or maybe the person who is trying to learn How is multi-agent systems different from them So let me start with an example and it's a very toy example Don't take it too much to your heart, but this is how to introduce it So imagine two, one kingdom, here is the king and the queen So the kingdom And both of them are model kings and queens So they have artificial intelligence at their hand And they can design systems, so they can use AI for two different purposes To develop better agricultural techniques So maybe something to do, how to do a hybrid type of a crop or something else Or they can use AI for more not so nice things like warfare Developing guns or weaponry, aircrafts So that you can actually attack the other nation And essentially try to capture that nation Now in this diagram, so you can see And let's imagine when AI is definitely expensive and also time consuming So you cannot really invest your resources and effort on both of them Both agriculture and war So for simplicity, let us assume You can only spend on either agriculture completely or on warfare completely No mixing is possible Now the numbers, so I'll place some numbers in these boxes And that is, you can imagine that how much amount of happiness, satisfaction Or let's say profit that they are going to get If these two individuals choose that pair of actions So remember there is a slight difference from the other type of AI problems That we discussed about Here the outcome depends on the pair of choices Or the combination of the choices that all the players So in this case two players, the pair of choices that they make That gives out an outcome So imagine if both of them had chosen agriculture or used AI for agriculture Both of them could have developed They could have solved their food security issues And then they get some amount of happiness Which I'm just quantifying by this number 5 The actual units or the numbers are immaterial All that matters is how they compare with the other numbers Now if both of them go for warfare Of course you can imagine that they will engage in conflict So I have deliberately chosen the numbers smaller Because now there will be a lot of destruction and other things So your happiness or your profit will not be as high as If both of them have chosen agriculture A vastly interesting thing happens A very curious thing happens When one of them chooses agriculture The other chooses war So for instance in this case I mean these are symmetric cases Why these numbers? Because if let's say the king chooses agriculture And the queen chooses war Then the warfare So because king has spent no energy or effort in warfare They won't be able to defend their own country So with warfare the kingdom will actually rule over And essentially take care of all the agricultural produce That they have made In addition they will have additional land And maybe prisoners etc So they will have more happiness So of course on top of 5 that they have produced They will also have something more And the kingdom loses everything They have lost their own maybe life and some land And all agricultural produce everything And the symmetric opposite thing happens Now imagine you are the queen And which of this agriculture or war choices would you have made? Just give a second, give a minute of thought And think about what should have happened You should have done if you are in the position of the queen Assuming that you have no communication And no communication with the other country And even if you communicate then also there is a chance That the other country will not actually listen to you Or certain contracts will not be feasible to satisfy here So what should you have done? How many are in favor of agriculture? So if you are a very highly optimistic person How many are in favor of war? Very good, so I don't need to take this lecture So the reason here is the following So this is the problem and the decisions have to be simultaneous Because this is happening for a long period of time So investing in agriculture or warfare takes a little bit of time And you cannot suddenly switch between one from the other So if you have already invested you have to stay with that Let's say for a year or so So imagine the situation of the queen If the king chooses agriculture What are the options that the queen has? Between agriculture and warfare you can see So I did not explain what these numbers mean So this tuple you can see that each of these numbers The first number corresponds to the happiness of the queen The second one is the happiness of the king So everywhere that's the meaning of the number So if you look at the happiness So the first entry in that tuple is the happiness of the queen So therefore if you look at the situation where the king has chosen agriculture The optimistic people who are sitting there So if they are choosing agriculture The queen should actually choose war Because that's giving him more happiness more utility And here we are assuming Yes the table is known This is publicly known The numbers are publicly known Doing is not known They are trying to take this decision simultaneously So here we are assuming that everybody is self-interested They only care about their kingdom or kingdom Does not care anything about the other one So that brings us to the warfare Now if you do the same thing You apply the same logic on warfare It's better to defend your country Rather than getting ruled over by somebody else So again war turns out to be the outcome So those majority of you who are actually warmongers They were actually right And like it or not That's the prediction that we can give In a situation where people are completely competitive Amongst each other This the war comma war So we call this the strategy or the action war As a dominant strategy The reason for saying that is that No matter what the other person is doing It's still better to pick that strategy Over the other one The equilibrium would have changed Equilibrium would have changed So these numbers I have chosen carefully If the numbers were different Then yes you can see that the equilibrium The conclusion that I am making Would have been different So here I am just trying to motivate One special situation where What is collectively optimistic Is not the equilibrium outcome So we call this war comma war This strategy profile of war comma war As the dominant strategy equilibrium The first time that we are using This word equilibrium And this is where the multi agent part comes in In multi agent systems We do not really talk about Optimal solutions Because there is no optimal solution here If you say that agriculture comma agriculture Is an optimal solution Yes they are collectively optimal But they are not an equilibrium So equilibrium is this war comma war And therefore in a multi agent scenario We will shift our notion From being that of an optimal solution To an equilibrium solution That is the first diversion That happens here And one can see that the Collectively based outcome Is actually the optimistic solution Both being agriculture And that essentially changes When you look at the self interested agents Now so taking an inverse view of this That how we actually design systems If we want this agriculture comma agriculture To be an outcome The equilibrium outcome That is exactly what we are heading towards So let me give you one Few more examples Essentially to actually motivate This whole question Adding resources blindly Does not improve the society So this example fits very well With the IIT Bombay campus So let's say A is the location Where all the hostile blocks are And B is the location of all the lecture halls And each morning the students Need to reach to their destination Their lecture halls for their lectures And there are two possible paths One via B, one via C And these paths have certain things So let's say for simplification Hundred students Each of them have a bicycle And they can bicycle through this path In two different ways And there are characteristics Special characteristics of each of these roads So this path, this road A to C And B to D are wide highways Maybe the larger ones Where it does not really matter How many bicycles are moving there It always takes 600 seconds Just to go from A to C Similarly from B to D A to B and C to D are congested lanes And if the number of vehicles increase Then it actually increases your travel time So one vehicle going there Takes five seconds Two vehicles ten seconds and so on So N2 is the number of vehicles That is traveling on these roads Now let's ask this question So if you are the vehicle One of those students Who are riding a bicycle Which path should you have taken Given that there are other people Everybody is trying to minimize the time To reach to their destination Flipper coin So the first individual Just flip a coin and go one of them Now suppose the moment You have started taking your bicycle You have seen that someone is taking This other path, let's say ABD path What should you do to minimize You take the other path So you don't conflict The third one again flip a coin Fourth one takes the path Which the previous person did not take So in some sense you are splitting This thing and you can See that why this is an equilibrium The way we have defined it before So when we have this original circuit Original path So you can imagine the 50 vehicles Will go on each of these paths So what will be the total time The time taken by each of these vehicles 600 plus 50 vehicles going here 850 850 Seconds For each of these vehicles So now the IITB administration Has decided we will have A tele-transporter device So the moment you are in B you are in C So this is a one way traffic So suppose I have A kind of a shortcut route Which takes negligible time Corresponding to all these other times Now can you tell me the same answer What would be your Your choices now The first one will take Which path A to B and then CD So that will take just 5 plus 5 The second one Second one will also take the same path Why So the second one If takes this ABCD path So now there are two individuals So 10 plus 10 which is Much smaller than 600 plus anything So this is a one way path You cannot go the other way So Is everyone convinced that the second person Will also take the ABCD path So anyone Is the number of vehicles Which are traveling in that path So that's what we are trying to find out So let's say I'm Starting with the first vehicle Who is taking that path So then it's just 5 seconds at that point The second one is thinking about So at this point everybody is thinking about Whether to take that path So N2 is the number of vehicles on this path So what will happen So yeah, go ahead Does the person at A Know how many vehicles are between CD While he is at A Not at this point But given that You can Right, I mean even if You do not know that The path between A to B Right Still you should be choosing AB, right So imagine the situation Where 99 people are going Through this path AB And you know this You have just seen all the 99 people Have gone before you Would you ever take AC Because 99 times 5 Will still be smaller than 600 So you will never take this AC path No matter what happens after B Right So Is that example clear to everyone So what will be the final Equilibrium outcome in this case Everybody will take this ABCD path Now calculate the time for that Now 1000 Okay So actually It's a bad design So adding resources Blindly does not improve your society So this is one example When you have multiple Self-interested individuals All of which are trying to minimize their time To reach the destination You should choose this design Of this tele-transporting device In some place where you actually Help the people and not reduce Their time of traveling So B, D and AC are not used at all Those resources are not used And these are not toy examples There are real world examples Newly built bridge just to take care Of the congestion Okay, so design is important That's what I want to drive home Now the question is how do we design A better society and that is exactly The other part of this talk Which is to design So far we have given predictive guarantees Now we are going to give prescriptive Guarantees And here for simplicity I am assuming that there is a cake That we need to divide and you can imagine Of a cake you can think of resources Spectrum resources or any kind Of divisible resources And you want to do a fair allocation Or fair division of this What is assumed for this resource Is that they are heterogeneous Which means that the equal amount So if I cut a piece here And cut the same sized piece Somewhere else because maybe This piece has some cherries on top Of it or it has more chocolate And you like chocolate And it has a different value Different happiness for you Than something which does not have them So it may always happen So you cut the same sized piece But you like one piece over the other So that is heterogeneity in the resource It is perfectly divisible You can cut it in whatever way You want And the preferences are differing That is the same cut piece Of chocolate I might not like chocolate that much Than chocolate So that piece is highly valuable for you And very less valuable for you So this is differing preferences Across different individuals Now for simplicity What we typically do is imagine this cake As a real line interval To make things simple Line between 0 and 1 And your valuation is like a distribution Over this 0 and 1 Different people may have different valuations The size of the piece that you get You just integrate over your valuation Of that piece and that is your total value For that piece And what is now, and we are also going To use the normalization, that the total value For the entire cake, if you get the entire cake That is valued 1, that is the normalization Now We have not defined what is a fair division Here. So one can say That a fair division is where You get your piece which is at least More than the average So you have, you are satisfied Because at least you got An average share, more than the average share There is Another notion of Fairness which is called the Envy-freeness. So imagine Somebody envy, so suppose There are two kids And the mother tries to cut this cake On the birthday And one person gets a piece And complains that the other person The other kid got a larger piece Or I like his or her piece more Than my own piece. Then there is a situation Of envy. And I want To ensure that that never happens That is everybody is At least as much happy as He would have, he or she would have got The other piece. So the value For, so here the little bit Of notation, the value that you get For your own allocation that is Ai is at least as much as Your own valuation for the other piece Some other j. And this If you can ensure for every agent Then you can say That this is an envy-free allocation So for the simple example Of one cake and two kids Can you come up with, I'm sure That how many of you have siblings So you have encountered this problem At home, at some point of your life So how did you solve this Or how your mother or father Solved this problem, exactly So, so yeah So I'm just going to call So essentially the answer That was given is essentially A solution for the For the For the two agent problem, I call it I cut you choose algorithm So the mother says that one of you Cut this piece, the cake And the other person gets to choose first And why does this algorithm work So let's see why this So my first question Is this proportional? How many says things no? Why? The person who will cut will try to do it Such that no matter which one he gets He'll be happier But the person who choose will definitely Will try to go to the envy-free Direction where he will try to Choose the one which he values more So the first individual Who is cutting is cutting exactly In half according to his view Right? Yeah So that is Proportional That is proportional for him And the other person gets If there is a larger piece He gets at least half Half of the entire cake So the argument that you gave Is actually proportional So this is the same argument For proportional So imagine the situation that someone So here you know that When you are cutting the cake You are not going to pick the first piece So if you cut it unequally There is a chance that the larger piece So you will cut it exactly In half according to your view So if you like the cherry Maybe you will also cut the cherry in half So So you are equally happy with any piece So that satisfies This proportionality constraint For player one The first player And the second player gets to choose So if she feels that There is a larger piece Then according to her view She will pick that And she will be at least half happy So is it envy free So use the same logic You are cutting it exactly in half So you are indifferent between these two pieces No matter whether your sibling Gets the other piece Or you get this piece Doesn't matter, you are indifferent You do not envy this part Any of these pieces So player one is indifferent between these two The other player does not envy So the piece That she picks Is at least as much as the other piece That's why she has picked it So this actually satisfies Both these conditions Both this proportional fairness So this is an animation of showing how So it might not be The physical half Because these are valued half So maybe this part is half Because you like chocolate And the whole chocolate portion is on this part And something else which is Which is not very valuable for you So it is proportional And it is also envy free I don't really have time to explain So this is For cases where Actually you have a divisible resource But You can actually extend these ideas For indivisible objects as well And let me just skip that So That's where we are In these examples I hope that I am able to communicate to you That a game The way we define game in game theory Is an interaction between two agents Multiple agents All of which are trying to maximize their own happiness In this terminology We'll be using the term utility And the game theory part That is the first part where we are trying to predict What will happen in that game Is predicting the outcome of the game And therefore it's a predictive approach And in the later parts where we are trying to design Let's say how to cut this cake In a fair way That is falling under this Paradigm of mechanism design Where we are trying to give a prescription How you should design this algorithm Such that certain good things happen Fairness happens Many other things happen And the application So these are toy examples but the applications are many So In the mechanism design The moment you search for something You get certain types of ads Maybe you have received You have purchased a ticket For A destination The very next time You see different ads on different pages Is About the destination of booking hotels In your destination place How did they know it? Because you have While booking you have That email has come So they are processing it And gathering the information That you have actually purchased a ticket Let's say to Goa and they start Showing you ads Hotels in Goa What tours and travels in Goa and so on So those online advertising So what happens behind the hood Is there are certain advertisers The hotel owners or the travel owners They pay Google The moment you click on one of those ads And they want to show They are essentially trying to buy your eyeballs And that is exactly how this online advertising Works The other Brilliant application is stable matching So the matching of the students To universities Hospitals to doctors All these things are situations Where every individual has Some self-interest So the hospital wants to get the best doctors The university wants to get The best students and the students also Want to get into the best university So you need to have some sort of Stability in the matching that you are doing It should not happen that the university And the student would like to break away So after this The declaration of the results are made The assignments are made they will break away And go to a new assignment That should not happen that is The idea of stable matching The idea of stable matching is also used In human organ exchanges And this is a very exciting area So kidney exchanges You know that kidney The typical human being Can survive with only one of the kidneys And depending on Various things like Maybe You want to donate one kidney to one of your Relatives who have lost both the kidneys But you do not match medically So there are lots of things that Blood group and tissue type And so on You do not match but you are a willing donor There might be somebody else Who is also looking for a kidney And their relative also does not match So this donor And the patient Pair you can consider as one Individual who are actually looking For a donor So if you have a situation Where your relative can actually Donate to that patient And that patient's donor is also Able to medically able to donate you Then you are actually saved Both these lives will be saved And that is exactly what this kidney exchange Algorithms do Maybe you have a cycle where you can Donate all these things and then Finally you have all these persons Lives saved So how do you do this There is a huge amount of literature And there are in certain countries There are algorithms run By the nation which actually Runs these kidney exchanges Things Federated learning, so this is a new paradigm So in federated learning So the Google keyboard that you use You can see that the moment you start With your Google keyboard It's actually not giving you Suggestions or auto corrections That well, particularly if you are Using some Indian languages But over time it is learnings Getting smarter and smarter So how does it do Maybe there are different other Users who are also using the same Language and In a certain way they are collecting All this information, the learning at a Central place and that Language model is then Pushed into each of these devices So this is the whole idea of federated Learning. Now the question is Again why should people contribute So maybe this is a very simple example But think of a medical Situation where everybody has Some medical data and you want to Write a model for disease prediction Or disease recovery But that might Require a lot of data Some hospitals which has a lot of medical Data will only contribute To that federated learning process If they get some payoff out of it And If you just use Federated learning as it is There might be a possibility, small hospitals Which do not have sufficient data They might just freeride The data of the others. So this Is also an exciting area Of incentivizing federated learning That's Happening for the past few years. Peer grading Let me talk about that offline If you are interested, airline Scheduling. So many examples where You can actually have this kind Of a strategic behavior. At the same Time you have certain components of Learning or artificial intelligence But you also need to take care of The fact that people are self-interested And all that you can get is an Equilibrium outcome and not An optimal outcome. Yeah, go ahead. So game theory is about multiple Players. So We are trying to give an equilibrium That is only for two participants That's why it is The examples that we have just given Is only to illustrate because I can only show two players here Otherwise it will get confusing. Yeah, so any number of players You can include Any other questions? Okay, so Yeah, I will not get into Any further details. Just want to Show that there are certain So in our group There are certain interesting Areas of research In all of these areas but in particular These auctions which We have recently worked with two Of our students. So If you are a student who are interested I urge you to Take a look at our Our group's website Talk to some of the students. I can see Drashti there Can you just, yeah, so you can feel free To talk to them during the I will definitely be around But also talk to them Vidit is also there I can't see anybody else Ram, no Yeah, so please feel free And also attend all the The student poster sessions to Student talks So there will be much more interesting things And I welcome you all To take a look at Those group websites and Talk to all of us Thanks very much for your attention Thank you, Professor Soprava For such an insightful talk Very interesting examples We would like to express our gratitude To Professor Soprava with a token of Appreciation. I would like to request Professor Bhaskaran to do the honors Can we have a round of applause? Thank you, sir I hope you all have been Enjoying the event so far. It's time To break for tea. I have a few Announcements here So the first announcement is For the participants, those Who have not registered yet They can register in the break Important announcement for Outstation participants Need to collect the travel allowance form And submit it with all The signed bills tomorrow There is one more announcement Those who are interested in knowing About the admission procedures of MTECH, MS and PhD Professor Ajit will be there At the admissions desk You can contact Right outside So grab a cup of tea Stretch your legs I encourage you to engage in some conversations Of that fact. I will see you after 20 minutes at 11 o'clock Thank you