Isogeny-based Cryptography using Isomorphisms of Superspecial Abelian Surfaces

ePrint Report: Isogeny-based Cryptography using Isomorphisms of Superspecial Abelian Surfaces
Pierrick Gaudry, Julien Soumier, Pierre-Jean Spaenlehauer

We investigate the algorithmic problem of computing isomorphisms between products of supersingular elliptic curves, given their endomorphism rings. This computational problem seems to be difficult when the domain and codomain are fixed, whereas we provide efficient algorithms to compute isomorphisms when part of the codomain is built during the construction. We propose an authentication protocol whose security relies on this asymmetry. Its most prominent feature is that the endomorphism rings of the elliptic curves are not hidden. Furthermore, it does not require a trusted setup.

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