Systematic design of original and modified Mastrovito multipliers for general irreducible polynomials

This paper considers the design of bit-parallel dedicated finite field mult ipliers using standard basis. An explicit algorithm is proposed for efficie nt construction of Mastrovito product matrix, based on which we present a s ystematic design of Mastrovito multiplier applicable to GF(2(m)) generated by an arbitrary irreducible polynomial. This design effectively exploits th e spatial correlation of elements in Mastrovito product matrix to reduce th e complexity. Using a similar methodology, we propose a systematic design o f modified Mastrovito multiplier, which is suitable for GF(2(m))generated b y high-Hamming weight irreducible polynomials. For both original and modifi ed Mastrovito multipliers, the developed multiplier architectures are highl y modular, which is desirable for VLSI hardware implementation. Applying th e proposed algorithm and design approach. we study the Mastrovito multiplie rs for several special irreducible polynomials, such as trinomial and equal ly-spaced-polynomial, and the obtained complexity results match the best kn own results. Moreover, we have discovered several new special irreducible p olynomials which also lead to low-complexity Mastrovito multipliers.