A Code-Based Undeniable Signature Scheme

Abstract : In this work we propose the first code-based undeniable signature scheme (and more generally the first post-quantum undeniable signature scheme). The verification protocols for our scheme are 3-pass zero-knowledge protocols derived from the Stern authentication protocol. There are two main ideas in our protocol, first we remark that it is possible to obtain a full-time undeniable signature from a one-time undeniable signature simply by signing the one-time public key by a standard signature. Second, we introduce a zero-knowledge variation on the Stern authentication scheme which permits to prove that one or two different syndromes are associated (or not) to the same low weight word. We give a polynomial reduction of the security of our scheme to the security of the syndrome decoding problem.