Cryptology ePrint Archive: Report 2009/580
A complete set of addition laws\\for incomplete Edwards curves
Daniel J. Bernstein and Tanja Lange
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.
Category / Keywords: public-key cryptography / Elliptic curves, Edwards curves, complete addition law, points at infinity.
Publication Info: to appear in J. Number Theory
Date: received 29 Nov 2009, last revised 6 Oct 2010
Contact author: tanja at hyperelliptic org
Available format(s): PDF | BibTeX Citation
Note: Fixed 2 typos.
Version: 20101006:142753 (All versions of this report)
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