Collisions Are Not Incidental: A Compression Function Exploiting Discrete Geometry

  • Dimitar Jetchev
  • Onur Özen
  • Martijn Stam
Conference paper

DOI: 10.1007/978-3-642-28914-9_17

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7194)
Cite this paper as:
Jetchev D., Özen O., Stam M. (2012) Collisions Are Not Incidental: A Compression Function Exploiting Discrete Geometry. In: Cramer R. (eds) Theory of Cryptography. TCC 2012. Lecture Notes in Computer Science, vol 7194. Springer, Berlin, Heidelberg

Abstract

We present a new construction of a compression function \(\ensuremath{{\if!! {{H}} \else{{H}_{}}\fi}} \colon \ensuremath{\{0,1\}}^{3\ensuremath{n} } \rightarrow \ensuremath{\{0,1\}}^{2\ensuremath{n} }\) that uses two parallel calls to an ideal primitive (an ideal blockcipher or a public random function) from \({2\ensuremath{n} }\) to \({\ensuremath{n} }\) bits. This is similar to the well-known MDC-2 or the recently proposed MJH by Lee and Stam (CT-RSA’11). However, unlike these constructions, we show already in the compression function that an adversary limited (asymptotically in n ) to \(\mathcal{O}(2^{2\ensuremath{n} (1-\delta)/3})\) queries (for any δ > 0) has disappearing advantage to find collisions. A key component of our construction is the use of the Szemerédi–Trotter theorem over finite fields to bound the number of full compression function evaluations an adversary can make, in terms of the number of queries to the underlying primitives. Moveover, for the security proof we rely on a new abstraction that refines and strenghtens existing techniques. We believe that this framework elucidates existing proofs and we consider it of independent interest.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Dimitar Jetchev
    • 1
  • Onur Özen
    • 1
  • Martijn Stam
    • 2
  1. 1.Laboratory for Cryptologic AlgorithmsEPFLSwitzerland
  2. 2.Department of Computer ScienceUniversity of BristolUK

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