Improved Veron Identification and Signature Schemes in the Rank Metric

It is notably challenging to design an efficient and
secure signature scheme based on error-correcting codes. An
approach to build such signature schemes is to derive it from
an identification protocol through the Fiat-Shamir transform.
All such protocols based on codes must be run several rounds,
since each run of the protocol allows a cheating probability of
either 2/3 or 1/2. The resulting signature size is proportional to
the number of rounds, thus making the 1/2 cheating probability
version more attractive. We present a signature scheme based
on double circulant codes in the rank metric, derived from
an identification protocol with cheating probability of 2/3. We
reduced this probability to almost 1/2 to obtain the smallest
signature among code-based signature schemes based on the
Fiat-Shamir paradigm, around 22 KBytes for 128 bit security
level. Furthermore, among all code-based signature schemes,
our proposal has the lowest value of signature plus public key
size, and the smallest secret and public key sizes. We provide
a security proof in the Random Oracle Model, implementation
performances, and a comparison with the parameters of similar
signature schemes.