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Gaussian integer is one of basic algebraic integers. In this article we formalize some definitions about Gaussian integers [27]. We also formalize ring (called Gaussian integer ring), Z-module and Z-algebra generated by Gaussian integer mentioned above. Moreover, we formalize some definitions about Gaussian rational numbers and Gaussian rational number field. Then we prove that the Gaussian rational...
In this paper, we introduce formal definitions and theorems in the Mizar proof checking system for the Gaussian integer ring and the Z-module constructed from Gaussian integers, as well as for Gaussian rational numbers and the Gaussian rational field. We then prove that the Gaussian rational field and the quotient field of the Gaussian integer ring are isomorphic. We prove the correctness of our formalization...
In this article, we formalize operations of points on an elliptic curve over GF(p). Elliptic curve cryptography [7], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security. We prove that the two operations of points: compellProjCo and addellProjCo are unary and binary operations of a point over the elliptic curve.
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