Abstract :
Over the past 30 years, Public Key Cryptography (PKC) has become a mainstay for secure communications
over the Internet and throughout many forms of communications. Many algorithms have been implemented to
improve the performance communication system and networks. Existing cryptographic algorithms such as RSA,
DSA, and DES are providing high level of security with lager key size. It tends to high computational and
communication overhead. In order to improve the performance of algorithm, new public key technique is built on
the arithmetic of elliptic curves known as Elliptic Curve Cryptography (ECC). This paper will provide the
mathematical background, types of curve, encryption and decryption algorithm, and various implementations.
Finally, it shows the comparison tables which will prove the security level of ECC compared with other cryptography
algorithm. This paper also examines the use of ECC in many constrained environments.
Keyword :
Public key cryptography, Elliptic Curve Cryptography, Rivert Shamir Adelman, Elliptic Curve, Elliptic Curve Discrete Logarithm Problem, Cryptosystem.