Ideal-to-isogeny algorithm using 2-dimensional isogenies and its application to SQIsign

ePrint Report: Ideal-to-isogeny algorithm using 2-dimensional isogenies and its application to SQIsign

Hiroshi Onuki, Kohei Nakagawa

The Deuring correspondence is a correspondence between supersingular elliptic curves and quaternion orders. Under this correspondence, an isogeny between elliptic curves corresponds to a quaternion ideal. This correspondence plays an important role in isogeny-based cryptography and several algorithms to compute an isogeny corresponding to a quaternion ideal (ideal-to-isogeny algorithms) have been proposed. In particular, SQIsign is a signature scheme based on the Deuring correspondence …

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