Efficient Ring Signature and Group Signature Schemes Based on q -ary Identification Protocols

While designing ring signature and group signature is a relatively mature area, few published schemes are both efficient and quantum attack-resilience. In this paper, we present two new signature schemes based on coding theory. First, we present two new zero-knowledge (ZK) identification protocols based on the construction of (Cayrel, P.L., Véron, P. and Alaoui, S.M.E.Y. (2010) A Zero-Knowledge Identification Scheme Based on the q-ary Syndrome Decoding Problem. Proceedings of SAC 2010, Waterloo, Ontario, Canada, August 12-13, pp. 171-186. Springer, Berlin) in order to improve efficiency of code-based digital signature schemes. We then transform the newly proposed ZK protocols into a ring signature scheme and a group signature scheme. Our schemes enjoy a significant improvement in efficiency since reducing the cheating probability decreases the interaction rounds. Specially, with the security level of 2 y public key and signature are 14.5 KB and 52 KB in our ring signature scheme, while the corresponding sizes are 400 KB and 2384 KB in the scheme of (Cayrel, P. L., Alaoui, S. M. E. Y., Hoffmann, G. and Véron, P. (2012) An improved threshold ring signature scheme based on error correcting codes. Proceedings of WAIFI 2012, Bochum, Germany, July 16-19, pp. 45-63. Springer, Berlin). At the security level of 2 -80, the sizes of public key and signature are 32 KB and 113.8 KB in our group signature scheme, as compared with 2.5 MB and 20 MB in the scheme of (Alamélou, Q., Blazy, O., Cauchie, S. and Gaborit, P. (2017) A codebased group signature scheme. Des. Codes Cryptogr., 82, 469-493) and 642 KB and 114 KB in the scheme of (Ezerman, M.F., Lee, H.T., Ling, S., Nguyen, K. and Wang, H. (2015) A provably secure group signature scheme from code-based assumptions. Proc. ASIACRYPT 2015, Auckland, New Zealand, November 29-December 3, pp. 260-285. Springer, Berlin).