New Zémor-Tillich Type Hash Functions Over GL2 (𝔽pn)

Abstract

Abstract We present a large class of new Zémor-Tillich type hash functions whose target space is the finite group GL2(𝔽pn) for any prime p and power n. To do so, we use a novel group-theoretic approach that uses Tits’ “Ping-Pong Lemma” to outline conditions under which a set of matrices in PGL2(𝔽p((x))) generates a free group. The hash functions we form are secure against known attacks, and simultaneously preserve many of the desired features of the Zémor-Tillich hash function. In particular, our hash functions retain the mall modifications property.