Efficient multiparty computation for arithmetic circuits against a covert majority

Abstract

We design a secure multiparty protocol for arithmetic circuits against covert adversaries in the dishonest majority setting. Our protocol achieves a deterrence factor of with O(Mn 2 t 2 s) communication complexity and O(Mn 3 t 2) exponentiations where s is the security parameter, n is the number of parties and M is the number of multiplication gates. Our protocol builds on the techniques introduced in (Mohassel and Weinreb, CRYPTO'08), extending them to work in the multiparty case, working with higher deterrence factors, and providing simulation-based security proofs. Our main underlying primitive is a lossy additive homomorphic public key encryption scheme where the lossiness is critical for the simulation-based proof of security to go through. Our concrete efficiency measurements show that our protocol performs better than previous solutions for a range of deterrence factors, for functions such as AES and matrix multiplication. © 2013 Springer-Verlag Berlin Heidelberg.