Deuring for the People: Supersingular Elliptic Curves with Prescribed Endomorphism Ring in General Characteristic

ePrint Report: Deuring for the People: Supersingular Elliptic Curves with Prescribed Endomorphism Ring in General Characteristic

Jonathan Komada Eriksen, Lorenz Panny, Jana Sotáková, Mattia Veroni

Constructing a supersingular elliptic curve whose endomorphism ring is isomorphic to a given quaternion maximal order (one direction of the Deuring correspondence) is known to be polynomial-time assuming the generalized Riemann hypothesis [KLPT14; Wes21], but notoriously daunting in practice when not working over carefully selected base fields.
In this work, we speed up the computation …

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