Work

Cryptography using Fibonacci–Mersenne and Fibonacci-balancing p-sequences with a self-invertible matrix and the Affine–Hill cipher

Year: 2025

Type: article

Abstract: In this paper, we define two new sequences using the Fibonacci p-numbers, the generalized Mersenne numbers, and m-balancing numbers. These sequences are obtained from the corresponding characteristic polynomials. The determinants and combinatorial and exponential representations of these new sequences are given. As an application, we provide two algorithms using these new sequences with self-invertible matrices and the Affine–Hill cipher.

Source: Notes on Number Theory and Discrete Mathematics

DOI: 10.7546/nntdm.2025.31.4.792-818

Authors: Elahe Mehraban, T. Aaron Gulliver, Ömür Deveci, Evren Hincal

Institutions: Near East University, University of Victoria, Kafkas University

Language: English

Topic: Advanced Mathematical Theories and Applications

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4416046898

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