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Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

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Open Access Research Article

Implementation results on the integer Fibonacci matrix size 2×2 for key exchanging scheme

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pp. 1965–1970Vol. 29Issue 5May 2026DOI: 10.47974/JDMSC-2376 Crossmark XML
Received:
01 May 2025
Published Online:
22 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2376
Pages:
1965–1970

Abstract

In several encryption algorithms, the key exchange scheme (KES) type: Diffie-Hellman is used as a fundamental tool. In this paper, a new KES model has been proposed as an alternative contribution for using the matrix of Fibonacci numbers (IFM2×2). On the proposed model, the private keys are created as the IFMs2×2 through selecting the Fibonacci numbers (FNs) randomly over Fp, where p is a prime. The power IFMs2×2 from left (right) side is calculated (LPIFM2×2(RPIFM2×2)). These matrices are also used to compute public keys. A new algorithm of the proposed scheme, namely IFM2×2-KES, is presented in this work. New results are displayed for small parameter values, implemented in Python. The difficult computations of LPIFM2×2 and RPIFM2×2 simultaneously determine the security of the proposed algorithm. The proposed IFM2×2-KES is considered a bright point for the communication scheme.

Keywords

Subject Classifications

Primary 94A60Secondary 15AXX

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