Parallel Multipliers based on Special Irreducible PentanomialsF. Rodriguez-Henriquez and C. K. KocIEEE Transactions on Computers, 52(12):1535-1542, December 2003.AbstractThe state-of-the-art Galois field GF(2^m) multipliers offer advantageous space and time complexities when the field is generated by some special irreducible polynomial. To date, the best complexity results have been obtained when the irreducible polynomial is either a trinomial or an equally-space polynomial (ESP). Unfortunately, there exist only a few irreducible ESPs in the range of interest for most of the applications, e.g., error-correcting codes, computer algebra, and elliptic curve cryptography. Furthermore, it is not always possible to find an irreducible trinomial of degree m in this range. For those cases, where neither an irreducible trinomial or an irreducible ESP exists, the use of irreducible pentanomials has been suggested. Irreducible pentanomials are abundant, and there are several eligible candidates for a given m. In this paper, we promote the use of two special types of irreducible pentanomials. We propose new Mastrovito and weakly dual basis multiplier architectures based on these special irreducible pentanomials, and give rigorous analyses of their space and time complexity. |