polynomial basis

noun2

1. •
   A basis of a polynomial ring (said ring being viewed either as a vector space over the field of coefficients or as a free module over the ring of coefficients).
2. •
   Specifically, a basis, of the form {1, α, ..., αⁿ⁻¹}, of a finite extension F_(qⁿ) of a Galois field F_q, where α is a primitive element of F_(qⁿ) (i.e., a root of a degree-n primitive polynomial over F_q).

   • In this case, the GF(2ᵐ) multiplication is implemented in hardware using three algorithms for polynomial basis (PB) and three for gaussian normal basis (GNB). — 2010