Cryptology ePrint Archive: Report 2021/983

A Cryptographic Hash Function from Markoff Triples

Elena Fuchs and Kristin Lauter and Matthew Litman and Austin Tran

Abstract: Cryptographic hash functions from expander graphs were proposed by Charles, Goren, and Lauter in [CGL] based on the hardness of finding paths in the graph. In this paper, we propose a new candidate for a hash function based on the hardness of finding paths in the graph of Markoff triples modulo p. These graphs have been studied extensively in number theory and various other fields, and yet finding paths in the graphs remains difficult. We discuss the hardness of finding paths between points, based on the structure of the Markoff graphs. We investigate several possible avenues for attack and estimate their running time to be greater than O(p). In particular, we analyze a recent groundbreaking proof in [BGS1] that such graphs are connected and discuss how this proof gives an algorithm for finding paths.

Category / Keywords: public-key cryptography / Markoff triples, cryptographic hash functions

Date: received 22 Jul 2021

Contact author: efuchs at math ucdavis edu, klauter at fb com, mclitman at ucdavis edu, austran at ucdavis edu

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Version: 20210723:091152 (All versions of this report)

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