Twisted Edwards Curves

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Abstract

This paper introduces “twisted Edwards curves,” a generalization of the recently introduced Edwards curves; shows that twisted Edwards curves include more curves over finite fields, and in particular every elliptic curve in Montgomery form; shows how to cover even more curves via isogenies; presents fast explicit formulas for twisted Edwards curves in projective and inverted coordinates; and shows that twisted Edwards curves save time for many curves that were already expressible as Edwards curves.

Permanent ID of this document: c798703ae3ecfdc375112f19dd0787e4. Date of this document: 2008.03.12. This work has been supported in part by the European Commission through the IST Programme under Contract IST–2002–507932 ECRYPT, and in part by the National Science Foundation under grant ITR–0716498. Part of this work was carried out during a visit to INRIA Lorraine (LORIA).