Symmetric ECC with Variable Key using Chaotic Map

Abstract

Elliptic Curve Cryptography (ECC) lately obtained a lot of care in cryptography science because it is more secure than the other cryptography methods and it is consider as one of the most significant cryptography technique. The ECC offers same security with smaller key comparing with the RSA (approximately 160 bits vs. 1024 bits), hence, this will decreases processor overhead, lowering power consumption, increase processing speed, enhance the storage efficiency, requires smaller certificates and it is good in bandwidth saving. The ECC uses high level mathematical operations. The ECC is an algebraic structure in finite fields and it is differ than other encryption algorithm because of the cipher text is a points in Cartesian coordinates. This paper proposed a new effective implementation method for symmetric encryption over ECC by use of secret shared key between two parties and this key change for every symbol in message. This technique provides authentication, confidentiality and non-repudiation.