UDC 621.391.15 : 519.7
1 Institute of Physics and Technology of the National Technical University “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine
 bessalov@ukr.net
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2 Institute of Physics and Technology of the National Technical University “Igor Sikorsky Kyiv Polytechnic Institute,” Kyiv, Ukraine
lusi.kovalchuk@gmail.com
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SUPERSINGULAR TWISTED EDWARDS CURVES OVER PRIME FIELDS.
I. SUPERSINGULAR TWISTED EDWARDS CURVES WITH ј -INVARIANTS 0 AND 123
Abstract. The analysis is given of the conditions of the existence of supersingular twisted Edwards curves over prime fields.
Theorems are formulated and proved about these conditions for supersingular twisted Edwards curves with ј-invariants 0 and 123, for different classes of curves.
Parameters for some supersingular curves are obtained using these results. Generalization of some previously obtained results is given, using isomorphism of curves in Weierstrass form and Edwards form.
Keywords: supersingular curve, complete Edwards curve, twisted Edwards curve, quadratic Edwards curve, twisted pair, order of point, Legendre symbol, quadratic residue, quadratic non-residue.
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