A Lower Bound on the Complexity of Polynomial Multiplication over Finite Fields

  • Authors:

  • Michael Kaminski

  • Affiliations:

  • -

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 2005

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Abstract

It is shown that computing the coefficients of the product of two degree-$n$ polynomials over a q-element field by means of a quadratic algorithm requires at least $(3 + \frac{\scriptstyle (q - 1)^2}{\scriptstyle q^5 + (q - 1)^3})n - o(n)$ multiplications.