TY - JOUR
N2 - 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.
L1 - http://journals.pan.pl/Content/115226/PDF/63_2571_Dry%C5%82o_L_skl.pdf
L2 - http://journals.pan.pl/Content/115226
PY - 2020
IS - No 3
EP - 464
DO - 10.24425/ijet.2020.131899
KW - twisted Edwards curves
KW - complete set of addition formulas
KW - Gröbner bases
A1 - Dryło, Robert
A1 - Kijko, Tomasz
PB - Polish Academy of Sciences Committee of Electronics and Telecommunications
VL - vol. 66
DA - 2020.09.17
T1 - Simple Verification of Completeness of Two Addition Formulas on Twisted Edwards Curves
SP - 459
UR - http://journals.pan.pl/dlibra/publication/edition/115226
T2 - International Journal of Electronics and Telecommunications
ER -