The Arithmetic Of elliptic Curve for Prime Curve Secp-384r1 using One Variable Polynomial Division for Security of Transport Layer Protocol

In this paper, we present a new method for solving multivariate polynomial elliptic curve equations over a finite field. The arithmetic of elliptic curve is implemented using the mathematical function trace of finite fields. We explain the approach which is based on one variable polynomial division. This is achieved by identifying the plane p with the extension of and transforming elliptic curve equations as well as line equations arising in point addition or point doubling into one variable polynomial. Hence the intersection of the line with the curve is analogous to the roots of the division between these polynomials. Hence this is the different way of computing arithmetic of elliptic curve.Transport layer security provides end-to-end security services for applications that use a reliable transport layer protocol such as TCP. Two Protocols are dominant today for providing security at the transport layer, the secure socket layer (SSL) protocol and transport layer security (TLS) protocol. One of the goals of these protocols is to provide server and client authentication, data confidentiality and data integrity. The above goals are achieved by establishing the keys between server and client, the algorithm is called elliptic curve digital signature algorithm (ECDSA) and elliptic curve Diffie-Hellman (ECDH). These algorithms are implemented using standard for efficient cryptography(SEC) prime field elliptic curve secp-384r1 currently specified in NSA Suite B Cryptography. The algorithm is verified on elliptic curve secp-384r1and is shown to be adaptable to perform computation.