A homomorphic LWE based E-voting scheme
Résumé
In this paper we present a new post-quantum electronic voting protocol. Our construction is based on LWE fully homomorphic encryption and the protocol is inspired by existing e-voting schemes, in particular Helios. The strengths of our scheme are its simplicity and transparency, since it relies on public homomorphic operations. Further-more, the use of lattice-based primitives greatly simplifies the proofs of correctness, privacy and verifiability, as no zero-knowledge proof are needed to prove the validity of individual ballots or the correctness of the final election result. The security of our scheme is based on classical SIS/LWE assumptions, which are asymptotically as hard as worst case lattice problems and relies on the random oracle heuristic. We also propose a new procedure to distribute the decryption task, where each trustee provides an independent proof of correct decryption in the form of a publicly verifiable cipher-text trapdoor. In particular, our protocol requires only two trustees, unlike classical proposals using threshold decryption via Shamir’s secret sharing.