  Importance of Elliptic Curves in Cryptography was independently proposed by
Neal Koblitz and Victor Miller in 1985.Since then, Elliptic curve cryptography
or ECC has evolved as a vast field for public key cryptography (PKC) systems.
In PKC system, we use separate keys to encode and decode the data. Since one of
the keys is distributed publicly in PKC systems, the strength of security
depends on large key size. The mathematical problems of prime factorization and
discrete logarithm are previously used in PKC systems. ECC has proved to
provide same level of security with relatively small key sizes. The research in
the field of ECC is mostly focused on its implementation on application
specific systems. Such systems have restricted resources like storage,
processing speed and domain specific CPU architecture.
