Set of Points on Elliptic Curve in Projective Coordinates

• Autorzy: Yuichi Futa , Hiroyuki Okazaki , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

In this article, we formalize a set of points on an elliptic curve over GF(p). Elliptic curve cryptography [10], whose security is based on a difficulty of discrete logarithm problem of elliptic curves, is important for information security.

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2011
• Tom: 19
• Numer: 3
• Strony: 131-138

Daty

wydano

2011-01-01

online

2012-04-26

Twórcy

autor

Yuichi Futa

• Shinshu University, Nagano, Japan

autor

Hiroyuki Okazaki

• Shinshu University, Nagano, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

Bibliografia

• Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
• Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• Józef Białas. Group and field definitions. Formalized Mathematics, 1(3):433-439, 1990.
• Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
• Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
• Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.
• Krzysztof Hryniewiecki. Basic properties of real numbers. Formalized Mathematics, 1(1):35-40, 1990.
• G. Seroussi I. Blake and N. Smart. Elliptic Curves in Cryptography. Number 265 in London Mathematical Society Lecture Note Series. Cambridge University Press, 1999.
• Eugeniusz Kusak, Wojciech Leończuk, and Michał Muzalewski. Abelian groups, fields and vector spaces. Formalized Mathematics, 1(2):335-342, 1990.
• Rafał Kwiatek. Factorial and Newton coefficients. Formalized Mathematics, 1(5):887-890, 1990.
• Konrad Raczkowski and Paweł Sadowski. Equivalence relations and classes of abstraction. Formalized Mathematics, 1(3):441-444, 1990.
• Christoph Schwarzweller. The ring of integers, euclidean rings and modulo integers. Formalized Mathematics, 8(1):29-34, 1999.
• Christoph Schwarzweller. The binomial theorem for algebraic structures. Formalized Mathematics, 9(3):559-564, 2001.
• Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
• Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
• Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
• Wojciech A. Trybulec. Groups. Formalized Mathematics, 1(5):821-827, 1990.
• Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
• Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
• Edmund Woronowicz and Anna Zalewska. Properties of binary relations. Formalized Mathematics, 1(1):85-89, 1990.

Identyfikatory

DOI

10.2478/v10037-011-0021-6