Better two-round adaptive multi-party computation

Abstract

The only known two-round multi-party computation protocol that withstands adaptive corruption of all parties is the ingenious protocol of Garg and Polychroniadou [TCC 15]. We present protocols that improve on the GP protocol in a number of ways. First, concentrating on the semi-honest case and taking a different approach than GP, we show a two-round, adaptively secure protocol where: - Only a global (i.e., non-programmable) reference string is needed. In contrast, in GP the reference string is programmable, even in the semi-honest case. - Only polynomially-secure indistinguishability obfuscation for circuits and injective one way functions are assumed. In GP, subexponentially secure IO is assumed. Second, we show how to make the GP protocol have only RAM complexity, even for Byzantine corruptions. For this we construct the first statistically-sound non-interactive Zero-Knowledge scheme with RAM complexity.