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In this paper, we first propose a novel common subexpression elimination(CSE) algorithm for matrix-vector multiplications over characteristic-2 fields.As opposed to previously proposed CSE algorithms, which usually focus oncomplexity savings due to recurrences of subexpressions, our CSE algorithmachieves two types of complexity reductions, differential savings andrecurrence savings, by taking advantage of the cancelation property ofcharacteristic-2 fields. Using our CSE algorithm, we reduce the additivecomplexities of cyclotomic fast Fourier transforms (CFFTs). Using a weightedsum of the numbers of multiplications and additions as a metric, our CFFTsachieve smaller total complexities than previously proposed CFFTs and otherFFTs, requiring both fewer multiplications and fewer additions in many cases.

Cyclotomic FFTs with Reduced Additive Complexities Based on a Novel Common Subexpression Elimination Algorithm