Rong Wan
Abstract
This paper studies the nonsupersingular elliptic curve whose background field is the big prime field and presents an algorithm of constructing elliptic curves, and the time-requirement analysis of the algorithm is given.
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This paper studies the nonsupersingular elliptic curve whose background field is the big prime field and presents an algorithm of constructing elliptic curves, and the time-requirement analysis of the algorithm is given.
Key concepts: Schoof's algorithm, Hessian form of an elliptic curve, Elliptic curve point multiplication, Elliptic curve, Tripling-oriented Doche–Icart–Kohel curve, Supersingular elliptic curve, Prime (order theory), Modular elliptic curve