## Cryptology ePrint Archive: Report 2003/034

On the (In)security of the Fiat-Shamir Paradigm

Shafi Goldwasser and Yael Tauman

Abstract: In 1986, Fiat and Shamir suggested a general method for transforming secure 3-round public-coin identification schemes into digital signature schemes. The significant contribution of this method is a means for designing efficient digital signatures, while hopefully achieving security against chosen message attacks. All other known constructions which achieve such security are substantially more inefficient and complicated in design.

In 1996, Pointcheval and Stern proved that the signature schemes obtained by the Fiat-Shamir transformation are secure in the so called Random Oracle Model'. The question is: does the proof of the security of the Fiat-Shamir transformation in the Random Oracle Model, imply that the transformation yields secure signature schemes in the real-world"?

In this paper we answer this question negatively. We show that there exist secure 3-round public-coin identification schemes for which the Fiat-Shamir methodology produces {\bf insecure} digital signature schemes for {\bf any} implementation of the Random Oracle Model' in the `real-world' by a function ensemble.

Category / Keywords: foundations / Fiat-Shamir

Date: received 18 Feb 2003, last revised 2 Feb 2004

Contact author: yael at theory lcs mit edu

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Note: Minor corrections.

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