New Bit Parallel Multiplier With Low Space Complexity for All Irreducible Trinomials Over GF(2(n))
Koc and Sunar proposed an architecture of the Mastrovito multiplier for the irreducible trinomial f(x) = x(n) + x(k) + 1, where k not equal n/2 to reduce the time complexity. Also, many multipliers based on the Karatsuba-Ofman algorithm (KOA) was proposed that sacrificed time efficiency for low space complexity. In this paper, a new multiplication formula which is a variant of KOA presented. We also provide a straightforward architecture of a non-pipelined bit-parallel multiplier using the new formula. The proposed multiplier has lower space complexity than and comparable time complexity to previous Mastrovito multipliers' for all irreducible trinomials.
irreducible trinomial bit-parallel multiplier finite field mastrovito multiplication polynomial basis