CryptoDB
On Exponential Sums, Nowton identities and Dickson Polynomials over Finite Fields
Authors: | |
---|---|
Download: | |
Abstract: | Let $\mathbb{F}_{q}$ be a finite field, $\mathbb{F}_{q^s}$ be an extension of $\mathbb{F}_q$, let $f(x)\in \mathbb{F}_q[x]$ be a polynomial of degree $n$ with $\gcd(n,q)=1$. We present a recursive formula for evaluating the exponential sum $\sum_{c\in \mathbb{F}_{q^s}}\chi^{(s)}(f(x))$. Let $a$ and $b$ be two elements in $\mathbb{F}_q$ with $a\neq 0$, $u$ be a positive integer. We obtain an estimate of the exponential sum $\sum_{c\in \mathbb{F}^*_{q^s}}\chi^{(s)}(ac^u+bc^{-1})$, where $\chi^{(s)}$ is the lifting of an additive character $\chi$ of $\mathbb{F}_q$. Some properties of the sequences constructed from these exponential sums are provided also. |
BibTeX
@misc{eprint-2010-22940, title={On Exponential Sums, Nowton identities and Dickson Polynomials over Finite Fields}, booktitle={IACR Eprint archive}, keywords={foundations /}, url={http://eprint.iacr.org/2010/039}, note={ xwcao@nuaa.edu.cn 14633 received 23 Jan 2010}, author={Xiwang Cao and Lei Hu}, year=2010 }