Author(s)

Kazuyuki Fujii¹, Hiroshi Oike²

¹International College of Arts and Sciences, Yokohama City University, Yokohama, Japan.
²Takado, Yamagata, Japan.

In this paper we revisit the addition of elliptic curves and give an algebraic proof to the associative law by use of MATHEMATICA. The existing proofs of the associative law are rather complicated and hard to understand for beginners. An ‘‘elementary” proof to it based on algebra has not been given as far as we know. Undergraduates or non-experts can master the addition of elliptic curves through this paper. After mastering it they should challenge the elliptic curve cryptography.

Elliptic Curve, Addition, Associative Law, MATHEMATICA, Elliptic Curve Cryptography

Fujii, K. and Oike, H. (2017) An Algebraic Proof of the Associative Law of Elliptic Curves. Advances in Pure Mathematics, 7, 649-659. doi: 10.4236/apm.2017.712040.