An Algebraic Proof of the Associative Law of Elliptic Curves

Authors: Kazuyuki Fujii, Hiroshi Oike

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.


Journal: Advances in Pure Mathematics

DOI: 10.4236/apm.2017.712040 (PDF)
Paper Id: 80983 (metadata)

See also: Comments to Paper

About scirp

(SCIRP: is an academic publisher of open access journals. It also publishes academic books and conference proceedings. SCIRP currently has more than 200 open access journals in the areas of science, technology and medicine. Readers can download papers for free and enjoy reuse rights based on a Creative Commons license. Authors hold copyright with no restrictions. SCIRP calculates different metrics on article and journal level. Citations of published papers are shown based on Google Scholar and CrossRef. Most of our journals have been indexed by several world class databases. All papers are archived by PORTICO to guarantee their availability for centuries to come.
This entry was posted in APM. Bookmark the permalink.

Leave a Reply

Your email address will not be published. Required fields are marked *