A new protocol for conditional disclosure of secrets and its applications

Abstract

Many protocols that are based on homomorphic encryption are private only if a client submits inputs from a limited range S. Conditional disclosure of secrets (CDS) helps to overcome this restriction. In a CDS protocol for a set S, the client obtains server's secret if and only if the client's inputs belong to S and thus the server can guard itself against malformed queries. We extend the existing CDS protocols to work over additively homomorphic cryptoSystems for every set from NP/poly. The new construction is modular and easy to apply. As an example, we derive a new oblivious transfer protocol with log-squared communication and a millionaire's protocol with logarithmic communication. We also implement private, universally verifiable and robust multi-candidate electronic voting so that all voters only transmit an encryption of their vote. The only hardness assumption in all these protocols is that the underlying public-key cryptosystem is IND-CPA secure and the plaintext order does not have small factors. © Springer-Verlag Berlin Heidelberg 2007.