用两种方法求解环上的ECC [ε]，ε4=0

IF 0.7 Q2 MATHEMATICS Tbilisi Mathematical Journal Pub Date : 2021-08-01 DOI:10.32513/tmj/19322008155

Bilel Selikh, A. Chillali, Douadi Mihoubi, N. Ghadbane

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引用次数: 0

摘要

设F3d为3d阶有限域，d为正整数，我们考虑A4:=F3d[e]=F3d[X]/(X4)是一个有限商环，其中e4=0。在本文中，我们将展示一个加密和解密的示例。首先，我们将给出环上的椭圆曲线。此外，我们还研究了算法的性质，提出了表示元素和群律的有效实现。准确地说，我们给出了一个使用两种方法和一个密钥的密码学(加密和解密)的数值例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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ECC over the ring F3d[ε],ε4=0 by using two methods

Let F3d is the finite field of order 3d with d be a positive integer, we consider A4:=F3d[e]=F3d[X]/(X4) is a finite quotient ring, where e4=0. In this paper, we will show an example of encryption and decryption. Firstly, we will present the elliptic curve over this ring. In addition, we study the algorithmic properties by proposing effective implementations for representing the elements and the group law. Precisely, we give a numerical example of cryptography (encryption and decryption) by using two methods with a secret key.

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Tbilisi Mathematical Journal MATHEMATICS-

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