Operations of Points on Elliptic Curve in Projective Coordinates

Yuichi Futa; Hiroyuki Okazaki; Daichi Mizushima; Yasunari Shidama

Formalized Mathematics (2012)

  • Volume: 20, Issue: 1, page 87-95
  • ISSN: 1426-2630

Abstract

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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.

How to cite

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Yuichi Futa, et al. "Operations of Points on Elliptic Curve in Projective Coordinates." Formalized Mathematics 20.1 (2012): 87-95. <http://eudml.org/doc/268134>.

@article{YuichiFuta2012,
abstract = {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.},
author = {Yuichi Futa, Hiroyuki Okazaki, Daichi Mizushima, Yasunari Shidama},
journal = {Formalized Mathematics},
language = {eng},
number = {1},
pages = {87-95},
title = {Operations of Points on Elliptic Curve in Projective Coordinates},
url = {http://eudml.org/doc/268134},
volume = {20},
year = {2012},
}

TY - JOUR
AU - Yuichi Futa
AU - Hiroyuki Okazaki
AU - Daichi Mizushima
AU - Yasunari Shidama
TI - Operations of Points on Elliptic Curve in Projective Coordinates
JO - Formalized Mathematics
PY - 2012
VL - 20
IS - 1
SP - 87
EP - 95
AB - 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.
LA - eng
UR - http://eudml.org/doc/268134
ER -

References

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  7. G. Seroussi I. Blake and N. Smart. Elliptic Curves in Cryptography. Number 265 in London Mathematical Society Lecture Note Series. Cambridge University Press, 1999. 
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