Affine–Hill cipher from Hadamard-type Fibonacci–Mersenne and Fibonacci-balancing p-sequences
Elahe Mehraban, Thomas Aaron Gulliver, Evren Hınçal · Notes on Number Theory and Discrete Mathematics · 2025
In this paper, we define two new sequences using the generalized Mersenne numbers, Fibonacci p-numbers, and m-balancing numbers. These sequences are constructed using the Hadamard-type product of their characteristic polynomials. The determinants and combinatorial and exponential representations of these new sequences are given. As an application, they are with used to generate keys for encryption for the Affine–Hill cipher using an elliptic curve and self-invertible matrix.