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In 1986 Fiat and Shamir exhibited zero-knowledge based identification and digital signature schemes which require only 10 to 30 modular multiplications per party. In this paper we describe an improvement of this scheme which reduces the verifier's complexity to less than 2 modular multiplications and leaves the prover's complexity unchanged.The new variant is particularly useful when a central computer has to verify in real time signed messages from thousands of remote terminals, or when the same signature has to be repeatedly verified.

An Improvement of the Fiat-Shamir Identification and Signature Scheme