Welcome to the resource topic for 2022/650
Title:
Supersingular Non-Superspecial Abelian Surfaces in Cryptography
Authors: Jason T. LeGrow, Yan Bo Ti, and Lukas Zobernig
Abstract:We consider the use of supersingular abelian surfaces in cryptography. Several generalisations of well-known cryptographic schemes and constructions based on supersingular elliptic curves to the 2-dimensional setting of superspecial abelian surfaces have been proposed. The computational assumptions in the superspecial 2-dimensional case can be reduced to the corresponding 1-dimensional problems via a product decomposition by observing that every superspecial abelian surface is non-simple and separably isogenous to a product of supersingular elliptic curves. Instead, we propose to use supersingular non-superspecial isogeny graphs where such a product decomposition does not have a computable description via separable isogenies. We study the advantages and investigate security concerns of the move to supersingular non-superspecial abelian surfaces.
ePrint: https://eprint.iacr.org/2022/650
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