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Bellini, Emanuele, Caullery, Florian, Gaborit, Philippe, Manzano, Marc, Mateu, Victor.  2019.  Improved Veron Identification and Signature Schemes in the Rank Metric. 2019 IEEE International Symposium on Information Theory (ISIT). :1872—1876.

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.

Gorbenko, Y., Svatovskiy, I., Shevtsov, O..  2016.  Post-quantum message authentication cryptography based on error-correcting codes. 2016 Third International Scientific-Practical Conference Problems of Infocommunications Science and Technology (PIC S T). :51–54.

In this paper we analyse possibilities of application of post-quantum code based signature schemes for message authentication purposes. An error-correcting code based digital signature algorithm is presented. There also shown results of computer simulation for this algorithm in case of Reed-Solomon codes and the estimated efficiency of its software implementation. We consider perspectives of error-correcting codes for message authentication and outline further research directions.