An identity-based identification scheme based on discrete logarithms modulo a composite number

Abstract

We first describe a modification of Schnorr’s identification scheme, in which the modulus is composite (instead of primé). This modification has some similarity with Brickell-McCurley’s one, presented at the same conference. Then, by establishing a new set-up, we derive the first identity-based identification scheme based on discrete logarithms. More precisely, it is based on discrete logarithm modulo a composite number, a problem known to be harder than factorization problem. This scheme has interesting and somewhat paradoxical features. In particular, any user can choose his own secret, and, provided the parameters have convenient sizes, even the trusted center is unable to retrieve it from the public key (contrary to any identity-based scheme known until now).