  In this paper we present a new 5-pass identification scheme with asymptotic
cheating probability 1/2 based on the syndrome decoding problem. Our protocol
is related to the Stern identification scheme but has a reduced communication
cost compared to previous code-based zero-knowledge schemes, moreover our
scheme permits to obtain a very low size of public key and secret key. The
contribution of this paper is twofold, first we propose a variation on the
Stern authentication scheme which permits to decrease asymptotically the
cheating 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 challenges
from the secret key through cyclic shifts of the initial public key syndrome; a
new proof of soundness for this case is given Secondly we propose a new way to
deal 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 sent
rather than two or three. Overall our new scheme has the good features of
having a zero-knowledge security proof based on well known hard problem of
coding theory, a small size of secret and public key (a few hundred bits), a
small calculation complexity, for an overall communication cost of 19kb for
authentication (for a $2^{16}$ security) and a signature of size of 93kb
(11.5kB) (for security $2^{80}$), an improvement of 40% compared to previous
schemes based on coding theory.
