Verifiable Decryption for BGV

Abstract

In this work we present a direct construction for verifiable decryption for the BGV encryption scheme by combining existing zero-knowledge proofs for linear relations and bounded values. This is one of the first constructions of verifiable decryption protocols for lattice-based cryptography, and we give a protocol that is simpler and at least as efficient as the state of the art when amortizing over many ciphertexts.

To prove its practicality we provide concrete parameters, resulting in proof size of less than KB for ciphertexts with message space 2048 bits. Furthermore, we provide an open source implementation showing that the amortized cost of the verifiable decryption protocol is only 76 ms per message when batching over ciphertexts.