An Arithmetic over GF (2^5) Tt Implement in ECC

Abstract

The potential for the use of the discrete logarithm problem in public-key cryptosystems has been recognized by Diffe and Hellman in 1976. Although the discrete logarithm problem as first employed by them 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. In this paper an efficient arithmetic for operations over elements of GF(2 5 ) represented in normal basis is presented. The arithmetic is applicable in public-key cryptography.