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Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves

Dryło Robert, Kijko Tomasz

International Journal of Electronics and Telecommunications

2020

Vol. 66, No. 3

459--464

Daniel Bernstein and Tanja Lange [9] proved that two given addition formulas on twisted Edwards elliptic curves ax² + y² = 1 + dxy are complete (i.e. the sum of any two points on a curve can be computed using one of these formulas). In this paper we give simple verification of completeness of these formulas using a program written in Magma, which is based on the fact that completeness means that some systems of polynomial equations have no solutions. This method may also be useful to verify completeness of additions formulas on other models of elliptic curves.