Threshold Decryption and Zero-Knowledge Proofs for Lattice-Based Cryptosystems

We present a variant of Regev’s cryptosystem first presented in [Reg05], but with a new choice of parameters. By a recent classical reduction by Peikert we prove the scheme semantically secure based on the worst-case lattice problem GapSVP. From this we construct a threshold cryptosystem which has a very efficient and non-interactive decryption protocol. We prove the threshold cryptosystem secure against passive adversaries corrupting all but one of the players, and againts active adversaries corrupting less than one third of the players. We also describe how one can build a distributed key generation protocol. In the final part of the paper, we show how one can, in zero-knowledge - prove knowledge of the plaintext contained in a given ciphertext from Regev’s original cryptosystem or our variant. The proof is of size only a constant times the size of a ciphertext. 

• Type: Conference
• Year: 2010
• Where: TCC
• Authors: Rikke Bendlin, Ivan Damgård
• Keywords: Cryptography, Original Cryptosystem, Regev’s Cryptosystem, TCC 2010, Threshold Cryptosystem Secure