Sufficient conditions for sound tree hashing modes

Authors Guido Bertoni, Joan Daemen, Michaël Peeters, Gilles Van Assche



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Guido Bertoni
Joan Daemen
Michaël Peeters
Gilles Van Assche

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Guido Bertoni, Joan Daemen, Michaël Peeters, and Gilles Van Assche. Sufficient conditions for sound tree hashing modes. In Symmetric Cryptography. Dagstuhl Seminar Proceedings, Volume 9031, p. 1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/DagSemProc.09031.15

Abstract

We consider the general case of tree hashing modes that make use of an underlying compression function. We consider such a tree hashing mode sound if differentiating it from a random oracle, assuming the underlying compression function is a random oracle can be proven to be hard. We demonstrate two properties that such a tree hashing mode must have for such a proof to exist. For each of the two properties we show that several solutions exist to realize them. For some given solutions we demonstrate that a simple proof of indifferentiability exists and obtain an upper bound on the differentiability probability of $q^2/2^n$ with $q$ the number of queries to the underlying compression function and $n$ its output length. Finally we give two examples of hashing modes for which this proof applies: KeccakTree and Prefix-free Merkle-Damgard.
Keywords
  • Tree Hashing
  • Indifferentiability

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