New cyclic groups based on the generalized order-k Pell sequences in the Heisenberg group and their application in cryptography

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-03-23 DOI:10.1007/s00200-024-00649-3

引用次数: 0

Abstract

In this paper, we consider the finite groups $$\begin{aligned} H_{(t,l,m)}=\langle a,b,c | a^t=b^l=c^m=1, [a,b]=c, [a,c]=[b,c]=1\rangle . \end{aligned}$$ We obtain the generalized order-k Pell sequences and study their periods. We prove the period of the order-k Pell sequence divided the period of the generalized order-k Pell sequence in the Heisenberg group. Then, the generalized order-k Pell sequence in Heisenberg group are used to define new cyclic groups. As an application, these groups are used in encryption algorithms.

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基于海森堡群中广义 K 阶佩尔序列的新循环群及其在密码学中的应用

Abstract In this paper, we consider the finite groups $$\begin{aligned} H_{(t,l,m)}=\langle a,b,c | a^t=b^l=c^m=1, [a,b]=c, [a,c]=[b,c]=1\rangle .\end{aligned}$$ 我们得到广义的阶 k 佩尔序列并研究它们的周期。我们证明了阶-k 佩尔序列的周期除以海森堡群中广义阶-k 佩尔序列的周期。然后，海森堡群中的广义阶k佩尔序列被用来定义新的循环群。作为一种应用，这些群被用于加密算法中。

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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来源期刊

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.