Practical and employable protocols for UC-secure circuit evaluation over ℤn

Abstract

We present a set of new, efficient, universally composable two-party protocols for evaluating reactive arithmetic circuits modulo n, where n is a safe RSA modulus of unknown factorization. Our protocols are based on a homomorphic encryption scheme with message space ℤn, zero-knowledge proofs of existence, and a novel "mixed" trapdoor commitment scheme. Our protocols are proven secure against adaptive corruptions (assuming secure erasures) under standard assumptions in the CRS model (without random oracles). Our protocols appear to be the most efficient ones that satisfy these security requirements. In contrast to prior protocols, we provide facilities that allow for the use of our protocols as building blocks of higher-level protocols. © 2013 Springer-Verlag.