Definition and Implementation of an Elliptic Curve Cryptosystem using a New Message Mapping Scheme

Abstract

Elliptic curve cryptography (ECC) is strongly requested for encryption and decryption processes since its guarantees high level of data security, insured by small key sizes that usually lead to fast algorithms. Such processes can only deal with points on elliptic curves on which the message has to be mapped. In this paper, we define a new message mapping algorithm coupled with Elgamal encryption based on an elliptic curve defined over a finite prime field. The established algorithm will be implemented and discussed for a chosen plaintext corresponding to an integer message. Our numerical tests demonstrate that the execution time of the message mapping, encryption, reverse message mapping and decryption, increase linearly versus data sizes. These results are promising for the design of fast and secure cryptosystems desirable for implementations on constrained environments.