arXiv: Number Theory | 2019
Values of rational functions in small subgroups of finite fields and the identity testing problem from powers
Abstract
Motivated by some algorithmic problems, we give lower bounds on the size of the multiplicative groups containing rational function images of low-dimensional affine subspaces of a finite field~$\\mathbb{F}_{q^n}$ considered as a linear space over a subfield $\\mathbb{F}_q$. We apply this to the recently introduced algorithmic problem of identity testing of hidden polynomials $f$ and $g$ over a high degree extension of a finite field, given oracle access to $f(x)^e$ and $g(x)^e$