 Hello everyone, welcome to this video abstract presentation on Efficient Adaptively Secured Byzantine Agreement for Long Messages. My name is Chenda and I'm at Entity Research and this is joint work with Amai from UC Riverside, Julian from CISPA and Kartik from Duke University. So what is Byzantine Agreement? So Byzantine Agreement is a distributed protocol among a bunch of parties which are connected via some communication network and basically the setting is each party has their own input so PI has XI as input and they need to compute an output that satisfies two security guarantees. The first guarantee is called consistency meaning that all the honest parties output the same value and the second guarantee is validity meaning that if all honest parties have the same value as input X then this should be the value that they output and of course the thing is that these two security guarantees must hold even when a subset of the parties is corrupted or becomes corrupted during the protocol execution. So when we talk about Byzantine Agreement protocols, a main efficiency metric is what we call the communication complexity. The communication complexity is basically the number of bits that honest parties have to communicate during the protocol execution and ideally it's not hard to think that the best case scenario is if the communication complexity of the Byzantine Agreement is something like N times L where L is the number of, is the input size in bits and N is the number of parties. So if we take the best, the most communication efficient protocols that exist nowadays these are sub-credit communication protocols starting from the works of Algorand and some follow-ups afterwards. These protocols achieve a communication complexity that looks more like O of poly of kappa N times L where kappa is some sort of security parameter. So there is an overhead of poly of kappa with respect to the ideal communication complexity that we would like to achieve. So these solutions don't quite give us what we want. But there is another line of works which is actually like a very traditional line of works starting from the 80s by Turbin and Cohen which are called extension protocols. And these are protocols that assume like a broadcast or a Byzantine Agreement protocol for a short message and it kind of expands it to a protocol for Byzantine Agreement for a long message with L bits. And there is a long line of works in this direction and the most efficient protocol or the previous most efficient was recently published at disk by Nayak, Ren, Xi, Badia and Xian disk 2020 and their protocol achieves a communication of N times L plus N squared times kappa. This basically means that if the input size is long enough, in particular if the input size is at least of size kappa times N linear in the number of parties, then the protocol achieves optimal communication N times L. So in this work we ask whether we can further improve the communication complexity of the protocols that we have nowadays and we answer in the affirmative. So our protocol achieves communication N times L plus N times poly of kappa. What does this mean? This means that our protocol is optimal for an input range that is of size poly of kappa. In particular we can think about the input range as being sub-linear in the number of parties. A little bit more formally, what is our main contribution? Our paper basically says that there are Byzantine Agreement protocols that achieve adaptive security. This means that the parties can become corrupted during the protocol execution and the communication complexity is NL plus N times poly of kappa as I said for L bit inputs, meaning the optimal communication is achieved for very sub-linear sized inputs and we give two protocols in two flavors. The first protocol is a synchronous protocol that tolerates up to N over two corruptions and the second is an asynchronous protocol that tolerates up to any fraction up to N over three corruptions. So for more details I refer you to the e-print version of the paper or the long talk that will happen at the confidence. Thank you very much.