Paper 2021/983

A Cryptographic Hash Function from Markoff Triples

Elena Fuchs, Kristin Lauter, Matthew Litman, and Austin Tran


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.

Available format(s)
Public-key cryptography
Publication info
Preprint. MINOR revision.
Markoff triplescryptographic hash functions
Contact author(s)
efuchs @ math ucdavis edu
klauter @ fb com
mclitman @ ucdavis edu
austran @ ucdavis edu
2021-07-23: received
Short URL
Creative Commons Attribution


      author = {Elena Fuchs and Kristin Lauter and Matthew Litman and Austin Tran},
      title = {A Cryptographic Hash Function from Markoff Triples},
      howpublished = {Cryptology ePrint Archive, Paper 2021/983},
      year = {2021},
      note = {\url{}},
      url = {}
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