 Hi everyone. In my talk, I'll be telling you about how we built short leakage resilient and non-magical secret sharing schemes. This is trying to work with Nishant Chandra and Bhavna Kanagruti and Sai Lakshmi Bhavna over to. What are secret sharing schemes? They are these really cool primitives introduced by Shamir and Blakely in 1979 and your Bob consists of some secret S, which he doesn't want to store entirely at the same location. So instead, he splits it into n parts S1 through SN which are called shares and the property that we seek from such a scheme is firstly of correctness, which tells you that if you have at least T of these shares, that should help Bob recover the secret S. T particularly is some value less than equal to n, which we call threshold and the second property sort is that of privacy, which tells you that if you although have less than T shares, that should not give any information about Bob's secret. So in other words, this is captured by saying that regardless of which secret you pick, S or S prime, two distinct secrets, the set of less than T shares of S looks close to the corresponding set of shares for S prime. And particularly in the stock, we'll be in the information theoretic setup, so the closeness is in the sense of statistical distance. About two decades later, the kosher in 1996 introduced something called leakage attacks and naturally the question is what if in addition to T minus 1 shares, the adversary gets some arbitrary bounded bits of leakage from the remaining shares as well. Well, turns out such an information could be lethal. And in fact, Guruswamy and Wooter show in 2016 that the Shamir secret sharing scheme, which is one of the widely used secret sharing schemes in all the protocols, that breaks even if you give one bit of leakage from all the remaining shares besides the full shares. So naturally, this led to the advent of leakage resiliency secret sharing schemes introduced by Zimbosky and Petrizak in 2007 under the same setup with a similar correctness guarantee. Now we seek something stronger than just a privacy and what we seek is called leakage resilience. So instead of saying just that T minus 1 shares look close, I now consider some targeted function family F and let's say I pick some function from this family. So we'll come to what kind of function families have been considered. But if I pick some function, instead of saying that T minus 1 shares are close, I want that F applied on all these shares, all N shares, that gives no information about S. So just like how we captured privacy, this is captured by saying that for any two distinct secrets SS prime, F applied on shares of S looks close enough to the F applied on shares of S prime. So this is the leakage resilience property sort. What is a particular family that gives you an example? Well, this was one of the most studied families since the introduction called local leakage family and it is one of the weaker leakage families introduced. So particularly the function family F that we consider is this local leakage family which is a non-adaptive and independent leakage class by which I mean that the adversary would send this function F which consists of N separate functions F1 through Fn in one shot non-adaptively. And the response that he gets is essentially Fi applied on each of the share Si. So this is basically an independent leakage on every share and of these N leakage responses, T minus 1 are full shares and the remaining would be some arbitrary function outputting mu bits from the shell. So this would be the family of interest for our talk. However, there have been several other stronger families introduced in literature. But common to all families or generally to leakage resilience sharing is this question that stands from the fact that we have known about Shamir secret sharing scheme which gives optimal share size for regular secret sharing schemes. So naturally the question is can we get any leakage resilience secret sharing scheme that achieves this optimal share size which with the leakage would be message length plus mu where mu is the number of bits of leakage that you give per share. And we answer in this work this question with an affirmative yes, particularly our result is that for we get the first information theoretic leakage resilience secret sharing scheme for the threshold access structure against the local leakage family which allows mu bits of leakage from from the remaining shares besides the T minus one full shares and we managed to get a share size of message length plus mu. To know more about the result come attend the talk on Monday August 15th at 9.20 am roughly at the beautiful UC Santa Barbara campus. Looking forward to see you in person. Thank you.