Elliptic Curve Cryptography-A new approach to Public Key Cryptography

Elliptic curve cryptography (ECC) is an approach to public key Cryptography based on the algebraic structure of Elliptic curves over finite field. Elliptic curves are also used in several integer factorization algorithms that have applications in cryptography. An elliptic curve in cryptography was suggested independently by Neal Koblitz and Victor S. Millar in 1985. Elliptic curve cryptography algorithms entered wide use in 2004 to 2005.Cryptography comes from Greek words meaning “hidden writing”. Cryptography converts readable data or clear text into encoded data called cipher text. By definition cryptography is the science of hiding information so that unauthorized users cannot read it. It involves Encryption and decryption of messages. Encryption is the process of converting a Plain text into cipher text and decryption is the process of getting back the original Message from the encrypted text. ECC is a newer approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields, and considered a s a marvelous technique with low key size for the use r, and hard exponential time challenge for an intruder to break into the system. In ECC a 16 0 bits key, provides the same security as RSA [1] 1024 bits key, thus lower computation f aster cryptographic power is required. The advantage of elliptic curve cryptosystems is the absence of sub exponential time algorithms, for attack. As ECC uses less key size to provide more security, and for this advantage it is used to perform operations, running on smaller chips or m ore compact software. The public key cryptography- based r emote authentication schemes are not suitable for mobile devices, because of the limitation in the bandwidth, computational strength, power availability or storage in mobile devices. Elliptic Curve cryptography is very difficult to understand by attacker because it relies on Elliptic Curve Discrete Logarithm Problem known as ECDLP. So it is difficult to break.