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Research Article | Open Access

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

Elahe Mehraban1,2,3( ), T. Aaron Gulliver4, Salah Mahmoud Boulaaras5( ), Kamyar Hosseini1,6, Evren Hincal1,2,3
Mathematics Research Center, Near East University TRNC, Mersin 10, 99138 Nicosia, Turkey
Department of Mathematics, Near East University TRNC, Mersin 10, 99138 Nicosia, Turkey
Faculty of Art and Science, University of Kyrenia, TRNC, Mersin 10, 99320 Kyrenia, Turkey
Department of Electrical and Computer Engineering, University of Victoria, Victoria, BC, V8W 2Y2, Canada
Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia
Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon
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Abstract

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 Diffie-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.

Keywords

Mersenne numbersPell pnumbersDiffie-Hellman key exchangepublic keyprivate keysequence analysis
CLC number: 11K31, 11C20, 68P25, 68R01, 68P30, 15A15

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AIMS Mathematics
Volume 9 Issue 5,
May 2024
Pages 13537-13552
DOI: 10.3934/math.2024660

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Cite this article:
Mehraban E, Aaron Gulliver T, Boulaaras SM, et al. New sequences from the generalized Pell p −numbers and mersenne numbers and their application in cryptography. AIMS Mathematics, 2024, 9(5): 13537-13552. https://doi.org/10.3934/math.2024660

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Received: 20 January 2024
Revised: 29 March 2024
Accepted: 03 April 2024
Published: 15 May 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)