A New Redundant Binary Algorithm for the Elliptic Curves Cryptosystems

To improve the rate for the numerical multiplication of the points is the foundation to apply the elliptic curve cryptosystems. When the binary representation is changed into the binary redundant representations by introducing -1 in binary representation for number, the addition computing steps for the numerical multiplication of the points are decreased. In this paper a new fast redundant binary algorithm for the elliptic curves discrete logarithm problem is presented. A new binary redundant representation, which is a necessity to transformation for a very large integer, is defined, and this algorithm facilitates the speed improvement for decreasing those operations.