An Efficient Pseudo-Random Generator with Applications to Public-Key Encryption and Constant-Round Multiparty Computation

We present a pseudo-random bit generator expanding a uniformly random bitstring r of length k/2, where k is the security parameter, into a pseudo-random bit-string of length 2k − log(k) using one modular exponentiation. In contrast to all previous high expansion-rate pseudo-random bit generators, no hashing is necessary. The security of the generator is proved relative to Paillier’s composite degree residuosity assumption. As a first application of our pseudo-random bit generator we exploit its efficiency to optimise Paillier’s crypto-system by a factor of (at least) 2 in both running time and usage of random bits. We then exploit the algebraic properties of the generator to construct an efficient protocol for secure constant-round multiparty function evaluation in the cryptographic setting. This construction gives an improvement in communication complexity over previous protocols in the order of nk, where n is the number of participants and k is the security parameter, resulting in a communication complexity of O(nk|C|) bits, where C is a Boolean circuit computing the function in question. keywords: constant-round cryptographic protocols, multi-party computation, pseudo-random generator, public-key encryption.