Bianca Sosnovski, Queensborough Community College
2022 AWM Research Symposium
Mathematical Aspects of Cryptography

Zemor and Tillich introduced a scheme of Cayley hash functions over $SL_{2}(\mathbb{F}_{2^n})$ in 1994. Other hash functions based on the Zemor and Tillich's design have been proposed since. Cayley hash functions use non-Abelian groups, which a priori can be resistant to quantum attacks. Finding collisions for Cayley hash functions is equivalent to finding short factorizations in the underlying group. Though most instances of these hash functions have been proved insecure, it seems to not invalidate the generic scheme of which these hash functions are based on. In this talk, we present an overview of some instances of Cayley hash functions and some related open problems.

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