New sequences from the generalized Pell p - numbers and mersenne numbers and their application in cryptography

被引：4

作者：

Mehraban, Elahe ^{[1
,2
,3
]}

Gulliver, T. Aaron ^{[4
]}

Boulaaras, Salah Mahmoud ^{[5
]}

Hosseini, Kamyar ^{[1
,6
]}

Hincal, Evren ^{[1
,2
,3
]}

机构：

[1] Near East Univ TRNC, Math Res Ctr, Mersin 10, TR-99138 Nicosia, Turkiye

[2] Near East Univ TRNC, Dept Math, Mersin 10, TR-99138 Nicosia, Turkiye

[3] Univ Kyrenia, Fac Art & Sci, Mersin 10, TR-99320 Kyrenia, TRNC, Turkiye

[4] Univ Victoria, Dept Elect & Comp Engn, Victoria, BC V8W 2Y2, Canada

[5] Qassim Univ, Coll Sci, Dept Math, Buraydah 51452, Saudi Arabia

[6] Lebanese Amer Univ, Dept Comp Sci & Math, Beirut, Lebanon

来源：

AIMS MATHEMATICS | 2024年 / 9卷 / 05期

关键词：

Mersenne numbers; Pell p - numbers; Diffie-Hellman key exchange; public key; private key; sequence analysis; FIBONACCI; MATRICES;

D O I：

10.3934/math.2024660

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents the generalized Pell p - numbers and provides some related results. A new sequence is defined using the characteristic polynomial of the Pell p - numbers and generalized Mersenne numbers. Two algorithms for Di ffi e-Hellman key exchange are given as an application of these sequences. They are illustrated via numerical examples and shown to be secure against attacks. Thus, these new sequences are practical for encryption and constructing private keys.

引用

页码：13537 / 13552

页数：16

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