Multiplication rules for polynomials

Faster Multiplication for Long Binary Polynomials

We set new speed records for multiplying long polynomials over finite fields of characteristic two. Our multiplication algorithm is based on an additive FFT (Fast Fourier Transform) by Lin, Chung, and Huang in 2014 comparing to previously best results based on multiplicative FFTs. Both methods have similar complexity for arithmetic operations on underlying finite field; however, our implementat...

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field

Fast Polynomials Multiplication Using FFT

Legendre Polynomials and Complex Multiplication, I Legendre Polynomials and Complex Multiplication, I

The factorization of the Legendre polynomial of degree (p− e)/4, where p is an odd prime, is studied over the finite field Fp. It is shown that this factorization encodes information about the supersingular elliptic curves in Legendre normal form which admit the endomorphism √ −2p, by proving an analogue of Deuring’s theorem on supersingular curves with multiplier √ −p. This is used to count th...

Multiplication of Polynomials over Finite Fields

We prove the 2.5n − o (n ) lower bound on the number of multiplications/divisions required to compute the coefficients of the product of two polynomials of degree n over a finite field by means of straight-line algorithms.