10.1007/978-3-642-40041-4_31
Kiltz, Eike
Eike
Kiltz
Pietrzak, Krzysztof Z
Krzysztof Z
Pietrzak
Szegedy, Mario
Mario
Szegedy
Digital signatures with minimal overhead from indifferentiable random invertible functions
LNCS
Springer
2013
2018-12-11T11:56:37Z
2020-01-16T12:36:31Z
conference
https://research-explorer.app.ist.ac.at/record/2258
https://research-explorer.app.ist.ac.at/record/2258.json
493175 bytes
application/pdf
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.