Welcome to the resource topic for 2019/177
Title:
Genus Two Isogeny Cryptography
Authors: 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.
ePrint: https://eprint.iacr.org/2019/177
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