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 language | English |
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Pages (from-to) | 858-872 |
Journal | Journal of Number Theory |
Volume | 131 |
Issue number | 5 |
DOIs | |
Publication status | Published - 2011 |