A Scalar Multiplication Algorithm for Elliptic Curve Cryptosystem

Since the introduction of public-key cryptography by Diffe and Hellman in 1976, the potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized. Although the discrete logarithm problem as first employed by Diffe and Hellman was defined explicitly as the problem of finding logarithms with respect to a generator in the multiplicative group of the integers module a prime, this idea can be extended to arbitrary groups and in particular, to elliptic curve groups. The resulting public - key systems provide relatively small block size, high speed, and high security. This book identifies an efficient performance of a scalar multiplication, which is one of the main operation in ECC. Adopting potential concurrent property using complementary recoding for scalar multiplication and having the elements of GF(2^m), particularly in the polynomial basis (PB) to use in an elliptic curve cryptosystems, computation of scalar multiplication is done.

Autorentext

S. REVATHI. Department of Mathematics,University of Thiruvalluar, Theivanai Ammal College for Women,Villupuram-605 602.