[Resource Topic] 2009/580: A complete set of addition laws\\for incomplete Edwards curves

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A complete set of addition laws\for incomplete Edwards curves

Authors: Daniel J. Bernstein, Tanja Lange


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.

ePrint: https://eprint.iacr.org/2009/580

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