A code-based blind signature

Abstract

In this paper we give the first blind signature protocol for code-based cryptography. Our approach is different from the classical original RSA based blind signature scheme, it is done in the spirit of the Fischlin approach [9] which is based on proofs of knowledge. To achieve our goal we consider a new tool for zero-knowledge (ZK) proofs, the Concatenated Stern ZK protocol, which permits to obtain an authentication protocol for concatenated matrices. A signature is then obtained from the usual Fiat-Shamir heuristic. We describe our blind signature protocol for cryptography based on Hamming metric and show how it can be extended to rank based cryptography. The security of our blind protocol is based on the security of a trapdoor function for the syndrome decoding problem: the CFS signature scheme for Hamming distance and on the more recent RankSign protocol for rank metric. We give proofs in the random oracle model (ROM) for our blind signature scheme, which rely on the Syndrome Decoding problem. The parameters we obtain for our protocol are practical for rank metric (200kBytes) for the signature length and 15kBytes for public key size) and a little less practical for Hamming distance.