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Efficient Computation of Point Multiplication in the Implementation of Elliptic Curve Cryptography

  1. Bh . Padma
  2. D. Chandravathi

Abstract

In recent times, elliptical curves have been used for public-key cryptographic and signature schemes in information security. The security provided by elliptic curve cryptographic protocols, either using signature or public-key encryption, is entirely based on the discrete logarithm problem. The discrete logarithm problem says that for a given a point Q that is a certain multiple k of a fixed point P, how to find the value of k in a reasonably amount of time. The difficulty of the discrete logarithm problem can only be exploited if scalar multiplications are easy to obtain. But fortunately, a point multiplication can always be computed in linear time, nonetheless this operation needs to be optimized as much as possible. Because of there is much concentration on reducing the speed of the scalar multiplication, several methods have been developed for improvisation. This paper describes implementations and test results of Elliptic Curve Cryptography (ECC). The paper deals with the problem of improving the performance of point multiplication using Binary method and Addition - Subtraction method. These methods reduce the number of point doublings and point additions in the computation. Also this paper insists the application of these two proposed methods for point multiplication.

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