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Efficient and low-complexity hardware architecture of Gaussian normal basis multiplication over GF(2 m ) for elliptic curve cryptosystems

Efficient and low-complexity hardware architecture of Gaussian normal basis multiplication over GF(2 m ) for elliptic curve cryptosystems

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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.

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