Lattice signature scheme without trapdoor based on learning with errors

Abstract

We provide an alternative scheme for lattice-based digital signature without using hash-and-sign paradigm of C. Gentry, C. Peikert, and V. Vaikuntanathan (STOC 2008). Our signature scheme basically follows the methodology of ``rejection sampling" of V. Lyubashevsky and "Fiat-Shamir transformation". Not only the sizes of public key, secret key, and signature are quite remarkable but also the signing step is relatively simple while the hash-and-sign paradigm requires a very large trapdoor matrix. We then provide the security analysis of our scheme based on Learning With Errors and analyze the appropriate parameters.