### Genus Two Isogeny Cryptography

E. V. Flynn and Yan Bo Ti

##### Abstract

We study $(\ell,\ell)$-isogeny graphs of principally polarised supersingular abelian surfaces (PPSSAS). The $(\ell,\ell)$-isogeny graph has cycles of small length that can be used to break the collision resistance assumption of the genus two isogeny hash function suggested by Takashima. Algorithms for computing $(2,2)$-isogenies on the level of Jacobians and $(3,3)$-isogenies on the level of Kummers are used to develop a genus two version of the supersingular isogeny Diffie--Hellman protocol of Jao and de~Feo. The genus two isogeny Diffie--Hellman protocol achieves the same level of security as SIDH but uses a prime with a third of the bit length.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. PQCrypto 2019
Keywords
Post-quantum cryptographyIsogeny-based cryptographyCryptanalysisKey exchangeHash function
Contact author(s)
yanbo ti @ gmail com
History
Short URL
https://ia.cr/2019/177

CC BY

BibTeX

@misc{cryptoeprint:2019/177,
author = {E. V.  Flynn and Yan Bo Ti},
title = {Genus Two Isogeny Cryptography},
howpublished = {Cryptology ePrint Archive, Paper 2019/177},
year = {2019},
note = {\url{https://eprint.iacr.org/2019/177}},
url = {https://eprint.iacr.org/2019/177}
}

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