Multiplicative complexity of polynomial multiplication over finite fields

Authors:
Michael Kaminski;Nader H. Bshouty
Affiliations:
Technion-Israel Institute of Technology, Haifa, Israel;Technion-Israel Institute of Technology, Haifa, Israel
Venue:
Journal of the ACM (JACM)
Year:
1989

Citing 4
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A lower bound on the complexity of polynomial multiplication over finite fields

STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science

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Abstract

Let Mq(n) denote the number of multiplications required to compute the coefficients of the product of two polynomials of degree n over a q-element field by means of bilinear algorithms. It is shown that Mq(n) ≱ 3n - o(n). In particular, if q/2 n ⪇ q + 1, we establish the tight bound Mq(n) = 3n + 1 [q/2].The technique we use can be applied to analysis of algorithms for multiplication of polynomials modulo a polynomial as well.