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Based on a new representation of GF(2^n), we present two multipliers for all irreducible trinomials. Space complexities of the multipliers match the best results. The time complexity of one multiplier is T_A + (1 + \left\lceil {\log _2 n}\right\rceil )T_X for all irreducible trinomials, where T_A and T_X are the delay of one 2-input AND and XOR gates, respectively.
Finite field, multiplication, polynomial basis, irreducible trinomial.
Haining Fan, Yiqi Dai, "Fast Bit-Parallel GF(2^n) Multiplier for All Trinomials", IEEE Transactions on Computers, vol. 54, no. , pp. 485-490, April 2005, doi:10.1109/TC.2005.64
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