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Elliptical curve cryptography (ECC) is a public key cryptosystem based on intractability of certain mathematical problems. It was first recommended by N. Koblitz and V. Miller in 1985 and is becoming accepted as a substitute to cryptosystems such as RSA and El Gamal over finite fields .Elliptical curve cryptography (ECC) can be used to generate faster, lesser, and more efficient cryptographic keys. The technology can be used in combination of RSA, and Diffie-Hellman and it is becoming widely used for mobile applications. The size of the elliptic curve determines the difficulty of the problem. The most important benefit agreed by ECC is a lesser key size, reducing storage and communication requirements. In this report, the implementation of ECC will depend on equation (y^2 = x^3 + A*x + B mod p) in which (a) and (b) variable are applied with different values and which lead to get different types of elliptical curve.
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