On the generic insecurity of the full domain hash

Yevgeniy Dodis, Roberto Oliveira, Krzysztof Pietrzak

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 T. Our main result rules out the existence of such instantiations for any assumption on T 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.

Original languageEnglish (US)
Title of host publicationAdvances in Cryptology - CRYPTO 2005 - 25th Annual International Cryptology Conference, Proceedings
Number of pages18
StatePublished - 2006
Event25th Annual International Cryptology Conference, CRYPTO 2005 - Santa Barbara, CA, United States
Duration: Aug 14 2005Aug 18 2005

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3621 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other25th Annual International Cryptology Conference, CRYPTO 2005
Country/TerritoryUnited States
CitySanta Barbara, CA

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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