Polynomial Interpolation of the Discrete Logarithm

Recently, Coppersmith and Shparlinski proved several results on the interpolation of the discrete logarithm in the finite prime field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{F}p$$ \end{document} by polynomials modulo p and modulo p-1, respectively. In this paper most of these results are extended to arbitrary \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\mathbb{F}p^r$$ \end{document}.