A complete set of addition laws for incomplete Edwards curves

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Abstract

Edwards curves were the first curves shown to have a complete addition law. However, the completeness of the addition law depends on the curve parameters and even a complete Edwards curve becomes incomplete over a quadratic field extension. This paper covers arbitrary Edwards curves and gives a set of two addition laws that for any pair of input points P1, P2 produce the sum P1+P2.
Original languageEnglish
Pages (from-to)858-872
JournalJournal of Number Theory
Volume131
Issue number5
DOIs
Publication statusPublished - 2011

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