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Operations of Points on Elliptic Curve in Projective Coordinates

100%

Futa Y., Okazaki H., Mizushima D., Shidama Y.

Formalized Mathematics

2012

tom 20

nr 1

87-95

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.

Gaussian Integers

100%

Futa Y., Okazaki H., Mizushima D., Shidama Y.

Formalized Mathematics

2013

tom 21

nr 2

115-125

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 number field and a quotient field of the Gaussian integer ring are isomorphic.

Ograniczanie wyników

2 Formalized Mathematics

2 Futa Y.

2 Mizushima D.

2 Okazaki H.

2 Shidama Y.

1 2013

1 2012

Wyniki wyszukiwania

Operations of Points on Elliptic Curve in Projective Coordinates

Gaussian Integers