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2012•Journal of Automated ReasoningOpen access

Formalization of Definitions and Theorems Related to an Elliptic Curve Over a Finite Prime Field by Using Mizar

Yuichi Futa, Hiroyuki Okazaki, Yasunari Shidama

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Abstract

In this paper, we introduce our formalization of the definitions and theorems related to an elliptic curve over a finite prime field. The elliptic curve is important in an elliptic curve cryptosystem whose security is based on the computational complexity of the elliptic curve discrete logarithm problem.

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What this paper is about

In this paper, we introduce our formalization of the definitions and theorems related to an elliptic curve over a finite prime field. The elliptic curve is important in an elliptic curve cryptosystem whose security is based on the computational complexity of the elliptic curve discrete logarithm problem.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we introduce our formalization of the definitions and theorems related to an elliptic curve over a finite prime field. The elliptic curve is important in an elliptic curve cryptosystem whose security is based on the computational complexity of the elliptic curve discrete logarithm problem.

Key concepts: Hessian form of an elliptic curve, Modular elliptic curve, Schoof's algorithm, Elliptic curve, Elliptic curve point multiplication, Tripling-oriented Doche–Icart–Kohel curve, Mathematics, Prime (order theory)

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