TITLE:
An Algebraic Proof of the Associative Law of Elliptic Curves
AUTHORS:
Kazuyuki Fujii, Hiroshi Oike
KEYWORDS:
Elliptic Curve, Addition, Associative Law, MATHEMATICA, Elliptic Curve Cryptography
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.7 No.12,
December
12,
2017
ABSTRACT: 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.