The retaining of confidentiality in data transmission with user authentication has become eminent for easy and secure communication. This is achieved by using the art of cryptology at its best. Various ciphers are developed balancing time, memory, and security. In particular, the invertible property is the basic requirement in constructing a secure cryptosystem. In this paper, an invertible block matrix is constructed over Fibonacci sequences. The sender and the recipient can derive the block matrix through the key exchanged over a secure channel for encryption and decryption. Also, an asymmetric cryptosystem is designed based on the skewed Affine cipher, which uses a bijective map over points on an elliptic curve. The developed cryptosystem is resistant to cryptanalytic attacks.

In this era, where communication over technology has become vital, the reliability of the same is of utmost need. Cryptography ensures confidentiality, user authentication, and integrity of data. One of the techniques is the Elliptic Curve Cryptography (ECC). Several classical ciphers are designed based on mathematical backgrounds. In this paper, we focus on combining Affine Cipher and ECC to magnify the security provided by an Affine cipher. Hence a skewed Affine cipher that uses multiple keys over Elliptic curves is proposed. The keys chosen are derived from the points on the specified Elliptic curve, which forms a cyclic group or a cyclic subgroup.