Abstract
We discuss the security of group-theoretic hash functions for cryptographic purposes. Those functions display several attractive features: they can be computed quickly, and it can be shown that local modifications of the plaintext necessarily change the hashed values. We show why the first such proposal given in [Zém91] is not secure, by giving a probabilistic algorithm for finding collisions. However, our attack is based on the special form of the matrices which were originally chosen. We propose alternative schemes which seem to be immune to such attacks.
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Tillich, JP., Zémor, G. (1994). Group-theoretic hash functions. In: Cohen, G., Litsyn, S., Lobstein, A., Zémor, G. (eds) Algebraic Coding. Algebraic Coding 1993. Lecture Notes in Computer Science, vol 781. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57843-9_12
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DOI: https://doi.org/10.1007/3-540-57843-9_12
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