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Fujii, K. (2014-2016) Public-Key Cryptography and Its Decoding by Quantum Computation (in Japanese). Lecture Note at Yokohama City University, Yokohama, 39.

has been cited by the following article:

• 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.