Efficient And Low-Complexity Hardware Architecture Of Gaussian Normal Basis Multiplication Over Gf(2(M)) For Elliptic Curve Cryptosystems

In this paper, an efficient high-speed architecture of Gaussian normal basis (GNB) multiplierover binary finite field GF(2(m)) is presented. The structure is constructed by using some regular modules for computation of exponentiation by powers of 2 and low-cost blocks for multiplication by normal elements of the binary field. For the powers of 2 exponents, the modules are implemented by some simple cyclic shifts in the normal basis representation. As a result, the multiplier has a simple structure with a low critical path delay. The efficiency of the proposed multiplier is examined in terms of area and time complexity based on its implementation on Virtex-4 field programmable gate array family and also its application specific integrated circuit design in 180 nm complementary metal-oxide-semiconductor technology. Comparison results with other structures of the GNB multiplier verify that the proposed architecture has better performance in terms of speed and hardware utilisation.