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

In 1986, Fiat and Shamir proposed a general method for transforming secure 3-round public-coin identification schemes into digital signature schemes. The idea of the transformation was to replace the random message of the veri.er in the identification scheme, with the value of some deterministic"hash" function evaluated on various quantities in the protocol and on the message to be signed.The Fiat-Shamir methodology for producing digital signature schemes quickly gained popularity as it yields efficient and easy to implement digital signature schemes. The most important question however remained open: are the digital signatures produced by the Fiat-Shamir methodology secure__ __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 transformation yields insecure digital signature schemes for any "hash" function used by the transformation. This is in contrast to the work of Pointcheval and Stern which proved that the Fiat-Shamir methodology always produces digital signatures secure against chosen message attack in the "Random Oracle Model" when the hash function is modelled by a random oracle.Among other things, we make new usage of Barak's technique for taking advantage of non black-box access to a program, this time in the context of digital signatures.