Yuval Ishai, Technion and UCLA

Abstract

A homomorphic secret sharing (HSS) scheme is a secret sharing scheme that supports a compact local evaluation of functions of the shared secret. For the purpose of applications of HSS, it is useful to make the stronger requirement that the output can be reconstructed via addition. That is, if a secret s is split into shares s_1,...,s_m, then f(s) can be written as F(s_1)+...+F(s_m) for some efficiently computable F, where addition is over a finite abelian group.

The talk will survey the state of the art on HSS and its applications, focusing mainly on: (1) computationally secure 2-out-of-2 HSS schemes for simple function classes using any one-way function, and (2) similar HSS schemes for branching programs from the DDH assumption. These can provide alternatives to fully homomorphic encryption in the context of minimizing the communication complexity and round complexity of secure computation.

Based on joint works with Elette Boyle and Niv Gilbo.

Slides    Video