 This is the abstract video for upcoming Crypto 2022 talk about quadratic multi-party randomised encodings that go beyond the OS majority privacy threshold and some of their applications. This talk is based on a joint work between Benny Epelbaum, Yuval Ishai, Arpita Patra and myself. Our work is in the field of secure multi-party computation. This is a concept introduced in the late 80s, where several parties, each one with its own private input, wish to jointly compute some functionality of their inputs. And of course, they wish to do it privately without leaking information about their private inputs. The way it's done is usually with protocols, where the parties communicate with each other over a number of rounds, and in the end receive their functionalities output. Privacy in protocols means that every coalition of up to 30s learns nothing beyond the output of the functionality. We focus on information theoretic NPC, where the adversaries are computationally unbounded, which means the simulation of the adversaries view must be either statistic, statistical or perfect. And we focus on passive adversaries, which must adhere to the protocol and not deviate. Before talking about our work, let us set a motivating example, the client-server model, which was introduced by Balcolet AL. In this model, the parties are divided into two groups, clients, which hold the inputs and receive the outputs, and servers, which hold no inputs and receive no outputs, and only assist the clients in computing their functionality. The interaction pattern resembles a distributed variant of FHD. The protocol queries over in two routes. In the first round, the clients send some message to servers. The servers then do some local computation and return the results to the clients. And then the clients can receive the functionalities output. And our first motivating question was, can we achieve a protocol in this model that is secure with an honest majority of the servers and up to T malicious clients, where we focus on T larger than half. So beyond honest majority. And this question is open even in the simplest case of three clients and three servers. Now let us move on to our model, our main model to MPRE, which was introduced by Apple Bar with our. This model is highly non-interactive and consists of a single call to some large degree to functionality. And this model is interesting because Apple Bar with our show that, for example, you can take a T private to MPRE and compile it into client server protocol that is secure with an honest majority of the servers and up to T malicious clients. Additionally, all non constructions of two MPRE are restricted to the honest majority setting so the private threshold is always less than half. And our main question was, can we construct the two MPRE with a private threshold larger than half. As it turns out, the answer is positive. In our main theorem, we have constructed the two MPRE with a privacy threshold of two thirds. In this corollary, we receive a two MPRE that is fully private in the three party settings, since two thirds of three parties gives us full privacy. This corollary immediately solves our first motivating question in the three client settings. Since we have a fully private to MPRE. Furthermore, we show an equivalence theorem between two MPRE and other models that also rely on the OT functionality. This equivalence gives us new results in those models based on our new construction of two MPRE. Also, we show a surprising connection between two MPRE and a protocol in the active security model. Let us have a quick overview of our main theorem proof. The proof is in two steps. In the first step, which we call round collapsing, we show that allowing a plain model conversation to happen before the degree to functionality of two MPRE adds no strength. So we show how to compile protocol in this plain and quadratic model to a two MPRE. And in the second step, we of course construct a protocol in this new plain and quadratic model with a desired privacy threshold. Thank you.