Operations of Points on Elliptic Curve in Affine Coordinates

Futa, Yuichi; Okazaki, Hiroyuki; Shidama, Yasunari

doi:10.2478/forma-2019-0026

Abstract

In this article, we formalize in Mizar [1], [2] a binary operation of points on an elliptic curve over GF(p) in affine coordinates. We show that the operation is unital, complementable and commutative. Elliptic curve cryptography [3], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.

References

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Operations of Points on Elliptic Curve in Affine Coordinates

Abstract

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