Low-complexity modified Mastrovito multipliers over finite fields GF(2M)

This paper considers the design of low-complexity dedicated finite field multipliers. A modified Mastrovito multiplication scheme is proposed in this paper, which has a complexity proportional to (m-1-pwt), where pwt is the Hamming weight of the underlying irreducible polynomial. With this modified multiplier and the original Mastrovito multiplier, low-complexity parallel multipliers for finite fields GF(2 ^M) can be designed with complexity proportional to min{pwt, m-1-pwt}, hence are good for irreducible polynomials of both low and high Hamming weights. This completes the design space and offers more freedom on polynomial selection. It is shown that this generalized Mastrovito multiplier generally has the lowest complexity, smallest latency and consumes the least power, compared with other standard-basis and dual-basis multipliers