扩展广义斐波那契矩阵在修正椭圆曲线密码中的密钥实现

IF 0.2 Q4 MATHEMATICS

JP Journal of Algebra Number Theory and Applications Pub Date : 2023-10-27 DOI:10.17654/0972555523025

Vaishali Billore, Naresh Patel, Hemant Makwana

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引用次数: 0

摘要

本文在ECC和ElGamal中提出了一种基于递归矩阵作为密钥的改进加密技术。对于加密，我们考虑了类似于[5]的映射和ElGamal技术，其中明文矩阵是由与椭圆曲线上的字母对应的点构建的。在键空间的创建中，研究了扩展广义斐波那契矩阵，它是矩阵的一个序列。考虑扩展的广义Fibonacci矩阵是令人愉快的，因为它只需要四个参数(整数)，而不是所有的矩阵项。我们建议的系统具有很大的键空间，并且由于使用递归矩阵而更加有效。因此，它将时间和空间的复杂性降到最低。此外，它是安全和鲁棒的，因为它是基于具有挑战性的数论问题，即椭圆曲线离散对数问题。收稿日期:2023年7月4日修稿日期:2023年9月15日收稿日期:2023年9月26日

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IMPLEMENTATION OF EXTENDED GENERALIZED FIBONACCI MATRICES AS A KEY IN MODIFIED ELLIPTIC CURVE CRYPTOGRAPHY

In this paper, we present a modified cryptographic technique based on the use of recursive matrices as the key in ECC and ElGamal. For encryption, we take into account mapping similar to [5] and the ElGamal technique, in which a plaintext matrix is built from points that correspond to the letters on elliptic curves. The extended generalized Fibonacci matrices, which are a sequence of matrices, have been considered in the creation of key space. The consideration of extended generalized Fibonacci matrices is delightful because it just requires four parameters (integers) as opposed to all of the matrix entries. Our suggested system has a vast key space and is more effective because of the use of a recursive matrix. As a result, it minimizes the complexity of both time and space. Additionally, it is secure and robust since it is based on the challenging number theory issue known as the elliptic curve-discrete logarithm issue. Received: July 4, 2023Revised: September 15, 2023Accepted: September 26, 2023

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来源期刊

JP Journal of Algebra Number Theory and Applications MATHEMATICS-

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期刊介绍： The JP Journal of Algebra, Number Theory and Applications is a peer-reviewed international journal. Original research papers theoretical, computational or applied, in nature, in any branch of Algebra and Number Theory are considered by the JPANTA. Together with the core topics in these fields along with their interplay, the journal promotes contributions in Diophantine equations, Representation theory, and Cryptography. Realising the need of wide range of information for any emerging area of potential research, the journal encourages the submission of related survey articles as well.