Affine–Hill cipher from Hadamard-type Fibonacci–Mersenne and Fibonacci-balancing p-sequences

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.