Elliptic Curves Cryptographic Techniques

Abstract

The security issues are very important for information technology applications now a day such as ATM and Smart cards. One of the recent public key cryptosystems is Elliptic Curves Cryptography. The group of the elliptic curve points forms an Abelian group, that is a suitable choice for constructing the Elliptic Curve Discrete Logarithm Problem (ECDLP). This led to create cipher system based on the difficulty of its solution. That is open a new windows for treatment with special groups and new operations. This paper provides three proposed techniques as a modification of ElGamal cryptosystem based on the elliptic curves, as well as, implement these techniques, compute the computational complexity of these methods compared to the original methods, compare these methods with the original methods in running time of several messages have different sizes. A great reduction in calculation time is resulted, also these techniques makes the cipher text more confused than cipher text which resulted from original techniques