Cryptology ePrint Archive: Report 2017/1202

Faster Cryptographic Hash Function From Supersingular Isogeny Graphs

Javad Doliskani and Geovandro C. C. F. Pereira and Paulo S. L. M. Barreto

Abstract: We propose a variant of the CGL hash, Charles et al. 2009, that is significantly faster than the original algorithm, and prove that it is preimage and collision resistant. For $n = \log p$ where $p$ is the characteristic of the finite field, the performance ratio between CGL and the new proposal is $(5.7n + 110) / (13.5\log n + 46.4)$. This gives an exponential speed up as the size of $p$ increases. Assuming the best quantum preimage attack on the hash has complexity $O(p^{\frac{1}{4}})$, we attain a concrete speed-up for a 256-bit quantum preimage security level by a factor 33.5. For a 384-bit quantum preimage security level, the speed-up is by a factor 47.8.

Category / Keywords: cryptographic protocols / Cryptographic hash functions, Supersingular elliptic curves, Isogeny graphs, Expander graphs

Date: received 13 Dec 2017, last revised 9 Apr 2019

Contact author: geovandro pereira at uwaterloo ca

Available format(s): PDF | BibTeX Citation

Version: 20190409:192547 (All versions of this report)

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