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In this paper we present a new 5-pass identification scheme with asymptoticcheating probability 1/2 based on the syndrome decoding problem. Our protocolis related to the Stern identification scheme but has a reduced communicationcost compared to previous code-based zero-knowledge schemes, moreover ourscheme permits to obtain a very low size of public key and secret key. Thecontribution of this paper is twofold, first we propose a variation on theStern authentication scheme which permits to decrease asymptotically thecheating probability to 1/2 rather than 2/3 (and very close to 1/2 in practice)but with less communication. Our solution is based on deriving new challengesfrom the secret key through cyclic shifts of the initial public key syndrome; anew proof of soundness for this case is given Secondly we propose a new way todeal with hashed commitments in zero-knowledge schemes based on Stern's scheme,so that in terms of communication, on the average, only one hash value is sentrather than two or three. Overall our new scheme has the good features ofhaving a zero-knowledge security proof based on well known hard problem ofcoding theory, a small size of secret and public key (a few hundred bits), asmall calculation complexity, for an overall communication cost of 19kb forauthentication (for a $2^{16}$ security) and a signature of size of 93kb(11.5kB) (for security $2^{80}$), an improvement of 40% compared to previousschemes based on coding theory.

A new zero-knowledge code based identification scheme with reduced communication