Abstract:Consider the following scenario with N +2 parties, A, B, X1, X2, ???, XN. Party A has a secret a, party B has a secret b, and party Xi has a secret xi, for i = 1, ???,N. They want to know if a = b without revealing any information about their secrets. We propose a distributed protocol for this problem based on the Paillier threshold homomorphic encryption scheme with a public broadcast channel. This protocol is suitable for voting which requires public verifiability. This protocol is secure and robust in an honest majority environment. We proved the security in a formal framework for secure multi-party computation.