Бессалов, Анатолій Володимирович and Третьяков, Дмитрий Борисович and Цыганкова, Оксана Валентиновна
(2014)
*A new approuch to calculation of exact number of Edwards curve over prime field*
Сучасний захист інформації (3).
pp. 11-15.

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A_Bessalov._D_Tretyakov_O_Tsygankova_SZI_3_IS_DUT_NTUU.doc - Published Version Download (217kB) |

## Abstract

New properties of the cryptoresistant Edwards curves over prime fields accepted for cryptographic appendices are considered. The conditions of existence of curves in an initial form of y2 = x3 + ax + b isomorphic to Edwards's curves are found. Dependence of parameter d of Edwards curve x2 + y2 = 1 + d x2 y2 from parameters a and b of an elliptic curve in an initial form is determined. The new proof of exact formulas of calculation of number of curves of Edwards, isomorphic to initial curves with nonzero parameters a and b is provided. It differs from the proof provided in the previous work

Item Type: | Article |
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Uncontrolled Keywords: | cryptosystem, initial form of an elliptic curve, Edwards's curve, torsion curve, curve parameters, isomorphism, square, not square. |

Subjects: | Articles in journals > Збірники наукових праць |

Divisions: | Institutes > Institute of Society > Chair of Information Technologies and Mathematics > Chair of Computer Science |

Depositing User: | професор Анатолій Володимирович Бессалов |

Date Deposited: | 08 Jun 2015 05:22 |

Last Modified: | 15 Dec 2017 11:37 |

URI: | http://elibrary.kubg.edu.ua/id/eprint/9835 |

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