Kiltz, Eike and Pietrzak, Krzysztof and Szegedy, Mario
(2013)
*Digital signatures with minimal overhead from indifferentiable random invertible functions.*
In: CRYPTO: International Cryptology Conference, August 18-22, 2013, Santa Barbara, CA, USA.

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## Abstract

In a digital signature scheme with message recovery, rather than transmitting the message m and its signature σ, a single enhanced signature τ is transmitted. The verifier is able to recover m from τ and at the same time verify its authenticity. The two most important parameters of such a scheme are its security and overhead |τ| − |m|. A simple argument shows that for any scheme with “n bits security” |τ| − |m| ≥ n, i.e., the overhead is lower bounded by the security parameter n. Currently, the best known constructions in the random oracle model are far from this lower bound requiring an overhead of n + logq h , where q h is the number of queries to the random oracle. In this paper we give a construction which basically matches the n bit lower bound. We propose a simple digital signature scheme with n + o(logq h ) bits overhead, where q h denotes the number of random oracle queries. Our construction works in two steps. First, we propose a signature scheme with message recovery having optimal overhead in a new ideal model, the random invertible function model. Second, we show that a four-round Feistel network with random oracles as round functions is tightly “public-indifferentiable” from a random invertible function. At the core of our indifferentiability proof is an almost tight upper bound for the expected number of edges of the densest “small” subgraph of a random Cayley graph, which may be of independent interest.

Item Type: | Conference or Workshop Item (Paper) |
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Subjects: | 000 Computer science, knowledge & general works > 000 Computer science, knowledge & systems 000 Computer science, knowledge & general works > 000 Computer science, knowledge & systems > 004 Data processing & computer science |

Research Group: | Pietrzak Group |

SWORD Depositor: | Sword Import User |

Depositing User: | Sword Import User |

Date Deposited: | 02 Dec 2016 08:42 |

Last Modified: | 05 Sep 2017 14:26 |

URI: | https://repository.ist.ac.at/id/eprint/685 |

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