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Compositions of linear functions and applications to hashing

Compositions of linear functions and applications to hashing Abstract Cayley hash functions are based on a simple idea of using a pair of (semi)group elements, A and B , to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the (semi)group. In this paper, we focus on hashing with linear functions of one variable over 𝔽 p ${\mathbb{F}_{p}}$ . The corresponding hash functions are very efficient. In particular, we show that hashing a bit string of length n with our method requires, in general, at most 2 ⁢ n ${2n}$ multiplications in 𝔽 p ${\mathbb{F}_{p}}$ , but with particular pairs of linear functions that we suggest, one does not need to perform any multiplications at all. We also give explicit lower bounds on the length of collisions for hash functions corresponding to these particular pairs of linear functions over 𝔽 p ${\mathbb{F}_{p}}$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Compositions of linear functions and applications to hashing

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2016-0016
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Abstract

Abstract Cayley hash functions are based on a simple idea of using a pair of (semi)group elements, A and B , to hash the 0 and 1 bit, respectively, and then to hash an arbitrary bit string in the natural way, by using multiplication of elements in the (semi)group. In this paper, we focus on hashing with linear functions of one variable over 𝔽 p ${\mathbb{F}_{p}}$ . The corresponding hash functions are very efficient. In particular, we show that hashing a bit string of length n with our method requires, in general, at most 2 ⁢ n ${2n}$ multiplications in 𝔽 p ${\mathbb{F}_{p}}$ , but with particular pairs of linear functions that we suggest, one does not need to perform any multiplications at all. We also give explicit lower bounds on the length of collisions for hash functions corresponding to these particular pairs of linear functions over 𝔽 p ${\mathbb{F}_{p}}$ .

Journal

Groups Complexity Cryptology – de Gruyter

Published: Nov 1, 2016

References

  • Rubik s for cryptographers Notices Amer QuisquaterJ Rubik s for cryptographersNotices Amer
    Petit
  • Preimages for the Tillich Zémor hash function Selected Areas in Cryptography SAC Lecture Notes in QuisquaterJ Preimages for the Tillich Zémor hash functionSelected Areas in CryptographySAC Lecture Notes in
    Petit
  • On the undecidability of freeness of matrix semigroups Internat HarjuT KarhumäkiJ On the undecidability of freeness of matrix semigroupsInternat
    Cassaigne
  • Group - theoretic hash functions Proceedings of the First French Israeli Workshop on Algebraic Coding Lecture Notes in ZémorG Group - theoretic hash functionsProceedings of the First French Israeli Workshop on Algebraic CodingLecture Notes in
    Tillich
  • Hashing withSL mathrm Advances in cryptology Lecture Notes in ZémorG Hashing withSL mathrm Advances in cryptology CRYPTO Lecture Notes in
    Tillich
  • VSH an efficient and provable collision - resistant hash function Advances in Lecture Notes in LenstraA SteinfeldR VSH an efficient and provable collision - resistant hash functionAdvances in Cryptology EUROCRYPT Lecture Notes in
    Contini