On the generic insecurity of the full domain hash Conference Paper

Author(s): Dodis, Yevgeniy; Oliveira, Roberto; Pietrzak, Krzysztof
Title: On the generic insecurity of the full domain hash
Title Series: LNCS
Abstract: The Full-Domain Hash (FDH) signature scheme [3] forms one the most basic usages of random oracles. It works with a family F of trapdoor permutations (TDP), where the signature of m is computed as f−1(h(m)) (here f ∈R F and h is modelled as a random oracle). It is known to be existentially unforgeable for any TDP family F [3], although a much tighter security reduction is known for a restrictive class of TDP’s [10,14] — namely, those induced by a family of claw-free permutations (CFP) pairs. The latter result was shown [11] to match the best possible “black-box” security reduction in the random oracle model, irrespective of the TDP family F (e.g., RSA) one might use. In this work we investigate the question if it is possible to instantiate the random oracle h with a “real” family of hash functions H such that the corresponding schemes can be proven secure in the standard model, under some natural assumption on the family F. Our main result rules out the existence of such instantiations for any assumption on F which (1) is satisfied by a family of random permutations; and (2) does not allow the attacker to invert f ∈R F on an a-priori unbounded number of points. Moreover, this holds even if the choice of H can arbitrarily depend on f. As an immediate corollary, we rule out instantiating FDH based on general claw-free permutations, which shows that in order to prove the security of FDH in the standard model one must utilize significantly more structure on F than what is sufficient for the best proof of security in the random oracle model.
Conference Title: CRYPTO: International Cryptology Conference
Volume: 3621
Conference Dates: August 14-18, 2005
Conference Location: Santa Barbara, CA, USA
Publisher: Springer  
Date Published: 2005-09-12
Start Page: 449
End Page: 466
Copyright Statement: ⓒ International Association for Cryptologic Research 2005
Sponsor: Supported by NSF CAREER Award CCR-0133806 and TC Grant No.CCR-0311095. Supported by the Swiss National Science Foundation, project No. 200020-103847/1
DOI: 10.1007/11535218_27
Open access: no
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