From Identification to Signatures Via the Fiat–Shamir Transform: Necessary and Sufficient Conditions for Security and Forward-Security
Michel Abdalla⋆, Jee Hea An, Mihir Bellare, Chanathip Namprempre · IEEE Transactions on Information Theory · 2008
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. In this paper, minimal (meaning necessary and sufficient) conditions on the identification scheme to ensure security of the signature scheme in the random oracle model are determined, both in the usual and in the forward-secure cases. Specifically, it is shown that the signature scheme is secure (respectively, forward-secure) against chosen-message attacks in the random oracle modelifandonlyifthe underlying identification scheme is secure (respectively, forward-secure) against impersonation underpassive(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.