Digital Signatures with Minimal Overhead from Indifferentiable Random Invertible Functions

  • Eike Kiltz
  • Krzysztof Pietrzak
  • Mario Szegedy
Conference paper

DOI: 10.1007/978-3-642-40041-4_31

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8042)
Cite this paper as:
Kiltz E., Pietrzak K., Szegedy M. (2013) Digital Signatures with Minimal Overhead from Indifferentiable Random Invertible Functions. In: Canetti R., Garay J.A. (eds) Advances in Cryptology – CRYPTO 2013. Lecture Notes in Computer Science, vol 8042. Springer, Berlin, Heidelberg

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 + logqh, where qh 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(logqh) bits overhead, where qh 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.

Keywords

digital signatures indifferentiability Feistel Additive combinatorics Cayley graph 

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Copyright information

© International Association for Cryptologic Research 2013

Authors and Affiliations

  • Eike Kiltz
    • 1
  • Krzysztof Pietrzak
    • 2
  • Mario Szegedy
    • 3
  1. 1.Horst-Görtz Institute for IT SecurityRuhr-Universität BochumGermany
  2. 2.Institute of Science and TechnologyAustria
  3. 3.Rutgers UniversityUSA

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