A digital signature scheme based on linear error-correcting block codes

Abstract

A true trapdoor digital signature scheme is presented. The scheme uses linear error-correcting block codes in a manner similar to that of the McEliece public-key cryptosystem, the Rao-Nam private-key cryptosystem, and the three digital signature schemes proposed by Xinmei, Harn and Wang, and the authors. All these digital signature schemes have been shown to be susceptible to a number of attacks. The signature scheme described in this paper derives its security from the complexity of three problems: the decoding of general linear error-correcting block codes, the factoring of large matrices, and the derivation of a matrix from its right inverse. It is shown that the proposed scheme is resistant to the attacks that proved successful when used against the aforementioned digital signature schemes as well as other attacks. The required public key storage is about 3n ² bits. The complexity of the signature generation and validation algorithms are O(n ²) and O(nk) bit operations respectively, thus making the scheme amenable to use in high data rate applications.