Abstract

We propose two improvements to the Fiat Shamir authentication and signature scheme. We reduce the communication of the Fiat Shamir authentication scheme to a single round while preserving the efficiency of the scheme. This also reduces the length of Fiat Shamir signatures. Using secret keys consisting of small integers we reduce the time for signature generation by a factor 3 to 4. We propose a variation of our scheme using class groups that may be secure even if factoring large integers becomes easy. 1 Introduction and Summary The Fiat--Shamir signature scheme (1986) and the GQ--scheme by Guillou and Quisquater (1988) are designed to reduce the number of modular multiplications that are necessary for generating signatures in the RSA--scheme. Using multicomponent private and public keys Fiat and Shamir generate signatures much faster than with the RSA--scheme. The drawback is that signatures are rather long. They are about t--times longer than RSA--signatures, where t is the round nu...

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