In this paper, we propose a modified cryptography based on the application of recursive matrices as key elements in ECC and ElGamal techniques. For encryption, we consider mapping analogous to affine Hill cipher, where a plaintext has been constructed by the points corresponding to letters on elliptic curves. Our key element for the proposed cryptography is based on the generalized Fibonacci matrices that make a large keyspace and its security strength is based on EC-DLP which is a hard problem in number theory.