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Open problems in hash function security

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Abstract

A cryptographic hash function compresses arbitrarily long messages to digests of a short and fixed length. Most of existing hash functions are designed to evaluate a compression function with a finite domain in a mode of operation, and the compression function itself is often designed from block ciphers or permutations. This modular design approach allows for a rigorous security analysis via means of both cryptanalysis and provable security. We present a survey on the state of the art in hash function security and modular design analysis. We focus on existing security models and definitions, as well as on the security aspects of designing secure compression functions (indirectly) from either block ciphers or permutations. In all of these directions, we identify open problems that, once solved, would allow for an increased confidence in the use of cryptographic hash functions.

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Notes

  1. Kelsey and Schneier [63] describe a second preimage attack on the Merkle-Damgård hash function that requires at most approximately \(2^{n-L}\) queries, where the first preimage is of length at most \(2^L\) blocks.

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Acknowledgments

This work was supported in part by the Research Council KU Leuven: GOA TENSE (GOA/11/007). Elena Andreeva and Bart Mennink are Postdoctoral Fellows of the Research Foundation—Flanders (FWO).

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  1. Department Electrical Engineering, ESAT/COSIC, KU Leuven, Leuven, Belgium

    Elena Andreeva, Bart Mennink & Bart Preneel

  2. iMinds, Ghent, Belgium

    Elena Andreeva, Bart Mennink & Bart Preneel

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  1. Elena Andreeva
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Correspondence to Bart Mennink.

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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Cryptography, Codes, Designs and Finite Fields: In Memory of Scott A. Vanstone”.

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Andreeva, E., Mennink, B. & Preneel, B. Open problems in hash function security. Des. Codes Cryptogr. 77, 611–631 (2015). https://doi.org/10.1007/s10623-015-0096-0

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