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Paper 2006/021

Cryptographic hash functions from expander graphs

Denis Charles, Eyal Goren, and Kristin Lauter

Abstract

We propose constructing provable collision resistant hash functions from expander graphs. As examples, we investigate two specific families of optimal expander graphs for provable hash function constructions: the families of Ramanujan graphs constructed by Lubotzky-Phillips-Sarnak and Pizer respectively. When the hash function is constructed from one of Pizer's Ramanujan graphs, (the set of supersingular elliptic curves over ${\FF}_{p^2}$ with $\ell$-isogenies, $\ell$ a prime different from $p$), then collision resistance follows from hardness of computing isogenies between supersingular elliptic curves. We estimate the cost per bit to compute these hash functions, and we implement our hash function for several members of the LPS graph family and give actual timings.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Unknown where it was published
Keywords: hash functions supersingular elliptic curves Ramanujan graphs
Contact author(s): klauter @ microsoft com
History: 2006-01-23: received
Short URL: https://ia.cr/2006/021
License: CC BY

BibTeX

@misc{cryptoeprint:2006/021,
      author = {Denis Charles and Eyal Goren and Kristin Lauter},
      title = {Cryptographic hash functions from expander graphs},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/021},
      year = {2006},
      url = {https://eprint.iacr.org/2006/021}
}