Cryptophia’s Short Combiner for Collision-Resistant Hash Functions

  • Arno Mittelbach
Conference paper

DOI: 10.1007/978-3-642-38980-1_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7954)
Cite this paper as:
Mittelbach A. (2013) Cryptophia’s Short Combiner for Collision-Resistant Hash Functions. In: Jacobson M., Locasto M., Mohassel P., Safavi-Naini R. (eds) Applied Cryptography and Network Security. ACNS 2013. Lecture Notes in Computer Science, vol 7954. Springer, Berlin, Heidelberg


A combiner for collision-resistant hash functions takes two functions as input and implements a hash function with the guarantee that it is collision-resistant if one of the functions is. It has been shown that such a combiner cannot have short output (Pietrzak, Crypto 2008); that is, its output length is lower bounded by roughly 2n if the ingoing functions output n-bit hash values. In this paper, we present two novel definitions for hash function combiners that allow to bypass the lower bound: the first is an extended semi-black-box definition. The second is a new game-based, fully black-box definition which allows to better analyze combiners in idealized settings such as the random-oracle model or indifferentiability framework (Maurer, Renner, and Holenstein, TCC 2004). We then present a new combiner which is robust for pseudorandom functions (in the traditional sense), which does not increase the output length of its underlying functions and which is collision-resistant in the indifferentiability setting. Our combiner is particularly relevant in practical scenarios, where security proofs are often given in idealized models, and our combiner, in the same idealized model, yields strong security guarantees while remaining short.


hash functions combiners collision resistance multi-property combiner 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Arno Mittelbach
    • 1
  1. 1.Darmstadt University of TechnologyGermany

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