Abstract. The Fiat-Shamir paradigm for transforming identification schemes into signature schemes has been popular since its introduction because it yields efficient signature schemes, and has been receiving renewed interest of late as the main tool in deriving forward-secure signature schemes. We find minimal (meaning necessary and sufficient) conditions on the identification scheme to ensure security of the signature scheme in the random oracle model, in both the usual and the forwardsecure cases. Specifically we show that the signature scheme is secure (resp. forward-secure) against chosen-message attacks in the random oracle model if and only if the underlying identification scheme is secure (resp. forward-secure) against impersonation under passive (i.e.. eavesdropping only) attacks, and has its commitments drawn at random from a large space. An extension is proven incorporating a random seed into the Fiat-Shamir transform so that the commitment space assumption may be removed.
This is not a contradiction, since the security of the signature scheme in the random oracle model relies on relatively weak security properties of the ID scheme, namely the security of the latter against impersonation under passive attack REF .
From identification to signatures via the Fiat-Shamir transform: Minimizing assumptions for security and forward-security
Proceedings of Eurocrypt 2002, volume 2332 of LNCS
Computer Science