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.
Highlights
Mizar [1] is an advanced project of the Mizar Society, led by Andrzej Trybulec, which formalizes mathematics
The security of the elliptic curve cryptosystem (ECC) is based on the computational complexity of the elliptic curve discrete logarithm problem, in which s is computed from sP
We introduced our formalization of the definitions and theorems related to an elliptic curve over a finite prime field Fp
Summary
Mizar [1] is an advanced project of the Mizar Society, led by Andrzej Trybulec, which formalizes mathematics. The Mizar proof checker operates on both Windows and UNIX environments and registers proven definitions and theorems in the Mizar Mathematical Library (MML). We formalize the definitions and theorems related to an elliptic curve over a finite prime field [3]. The security of the ECC is based on the computational complexity of the elliptic curve discrete logarithm problem, in which s is computed from sP (multiplication of a scalar s and a point P). The formalization of mathematical definitions and theorems of the elliptic curve is not yet included in the MML. The definitions and theorems in this paper are described as formalizations in Mizar and have been verified for correctness using the Mizar proof checker
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