### 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 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 language | English (US) |
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Title of host publication | Advances in Cryptology - CRYPTO 2005 - 25th Annual International Cryptology Conference, Proceedings |

Pages | 449-466 |

Number of pages | 18 |

Volume | 3621 LNCS |

State | Published - 2006 |

Event | 25th Annual International Cryptology Conference, CRYPTO 2005 - Santa Barbara, CA, United States Duration: Aug 14 2005 → Aug 18 2005 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 3621 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 25th Annual International Cryptology Conference, CRYPTO 2005 |
---|---|

Country | United States |

City | Santa Barbara, CA |

Period | 8/14/05 → 8/18/05 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Advances in Cryptology - CRYPTO 2005 - 25th Annual International Cryptology Conference, Proceedings*(Vol. 3621 LNCS, pp. 449-466). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3621 LNCS).

**On the generic insecurity of the full domain hash.** / Dodis, Yevgeniy; Oliveira, Roberto; Pietrzak, Krzysztof.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Cryptology - CRYPTO 2005 - 25th Annual International Cryptology Conference, Proceedings.*vol. 3621 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3621 LNCS, pp. 449-466, 25th Annual International Cryptology Conference, CRYPTO 2005, Santa Barbara, CA, United States, 8/14/05.

}

TY - GEN

T1 - On the generic insecurity of the full domain hash

AU - Dodis, Yevgeniy

AU - Oliveira, Roberto

AU - Pietrzak, Krzysztof

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33745155794&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33745155794&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:33745155794

SN - 3540281142

SN - 9783540281146

VL - 3621 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 449

EP - 466

BT - Advances in Cryptology - CRYPTO 2005 - 25th Annual International Cryptology Conference, Proceedings

ER -