Abstract. In response to the current need for fast, secure and cheap public-key cryptography, we study an interactive zero-knowledge identication scheme and a derived signature scheme that combine provable security based on the general problem of computing discrete logarithms modulo any number, short identity-based keys, very short transmission and minimal on-line computation. This leads to both e cient and secure applications well suited to the implementation on low cost smart cards. We develop complete proofs of completeness, soundness and statistical zero-knowledge property of the identi cation scheme. The security analysis of the signature scheme leads to present a novel number theoretical lemma of independent interest and an original use of the \forking lemma" technique. From a practical point of view, the possible choice of parameters is discussed and we submit performances of an actual implementation on a cheap smart card. As an example, a complete and secure authentication can be performed in less than 20 ms with low cost equipment.
Few years ago, Poupard and Stern REF provided a proof of the statistical zero-knowledge property of this scheme and the security relative to the composite discrete logarithm problem of both the identification scheme and the signature variant.
Security Analysis of a Practical "on the fly" Authentication and Signature Generation
In Eurocrypt '98, LNCS 1403
Computer Science