Lightweight Secure Integer Comparison

We solve the millionaires problem in semi-trusted model with homomorphic encryption without using intermediate decryptions. This leads to computationally least expensive solution so far, a low bandwidth and very storage complexity. The number of modular multiplications needed is less than for one Pallier encryption. output protocol can be either publicly known, encrypted, or secret-shared. private input first player secure towards second player, even unconditionally player. also introduce an efficient client-server similar security properties.