# Classification of all the minimal bilinear algorithms for computing the coefficients of the product of two polynomials modulo a polynomial

## Abstract

In view of the results of Theorems III.1 and Theorem III.2, all the minimal bilinear algorithms for computing the coefficients of *R*(*u*)*S*(*u*) mod *Q*(*u*)^{ l } have multiplications of the form *R*(*α*_{j})*S*(*α*_{j}) hence the algorithm requires large coefficients (as in *l*=1). Therefore using the identity *R*(*u*)*S*(*u*)=*R*(*u*)*S*(*u*) mod *P*(*u*) where *degP*(*u*)=2*n* − 1 with distinct irreducible, but not necessarily only linear, factors, does not reduce the large coefficients generated by the algorithm. In order to achieve better "practical" algorithms, non-minimal algorithms should be studied. In addition, classification of all the minimal algorithms for computing the coefficients of *R*(*u*)*S*(*u*) mod *Q*(*u*)^{ l } remains open.

## Keywords

Bilinear Form Discrete Fourier Transform Bilinear Mapping Minimal Algorithm Zero Divisor## Preview

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