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 bit-string 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 constantround 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 en-