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Paper 2019/296

Hash functions from superspecial genus-2 curves using Richelot isogenies

Wouter Castryck and Thomas Decru and Benjamin Smith

Abstract

Last year Takashima proposed a version of Charles, Goren and Lauter’s hash function using Richelot isogenies, starting from a genus-2 curve that allows for all subsequent arithmetic to be performed over a quadratic finite field Fp^2 . In a very recent paper Flynn and Ti point out that Takashima’s hash function is insecure due to the existence of small isogeny cycles. We revisit the construction and show that it can be repaired by imposing a simple restriction, which moreover clarifies the security analysis. The runtime of the resulting hash function is dominated by the extraction of 3 square roots for every block of 3 bits of the message, as compared to one square root per bit in the elliptic curve case; however in our setting the extractions can be parallelized and are done in a finite field whose bit size is reduced by a factor 3. Along the way we argue that the full supersingular isogeny graph is the wrong context in which to study higher-dimensional analogues of Charles, Goren and Lauter’s hash function, and advocate the use of the superspecial subgraph, which is the natural framework in which to view Takashima’s Fp^2-friendly starting curve.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
isogeny-based cryptographygenus 2 hyperelliptic curveCGL hash functionRichelot isogeniessuperspecial abelian surfaces
Contact author(s)
thomas decru @ kuleuven be
History
2020-03-06: revised
2019-03-20: received
See all versions
Short URL
https://ia.cr/2019/296
License
Creative Commons Attribution
CC BY
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