### Abstract

RSA Full Domain Hash (RSA-FDH) is a digital signature scheme, secure again chosen message attacks in the random oracle model. The best known security reduction from the RSA assumption is nontight, i.e., it loses a factor of q _{s} , where q _{s} is the number of signature queries made by the adversary. It was furthermore proved by Coron (EUROCRYPT 2002) that a security loss of q _{s} is optimal and cannot possibly be improved. In this work we uncover a subtle flaw in Coron's impossibility result. Concretely, we show that it only holds if the underlying trapdoor permutation is certified. Since it is well known that the RSA trapdoor permutation is (for all practical parameters) not certified, this renders Coron's impossibility result moot for RSA-FDH. Motivated by this, we revisit the question whether there is a tight security proof for RSA-FDH. Concretely, we give a new tight security reduction from a stronger assumption, the Phi-Hiding assumption introduced by Cachin et al (EUROCRYPT 1999). This justifies the choice of smaller parameters in RSA-FDH, as it is commonly used in practice. All of our results (positive and negative) extend to the probabilistic signature scheme PSS.

Original language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 537-553 |

Number of pages | 17 |

Volume | 7237 LNCS |

DOIs | |

Publication status | Published - 2012 |

Event | 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2012 - Cambridge, United Kingdom Duration: 15 Apr 2012 → 19 Apr 2012 |

### 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 | 7237 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Conference

Conference | 31st Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2012 |
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Country | United Kingdom |

City | Cambridge |

Period | 15/04/12 → 19/04/12 |

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## Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 7237 LNCS, pp. 537-553). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7237 LNCS). https://doi.org/10.1007/978-3-642-29011-4_32