Paper 2010/039
On Exponential Sums, Nowton identities and Dickson Polynomials over Finite Fields
Xiwang Cao and Lei Hu
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.
Metadata
 Available format(s)
 Category
 Foundations
 Publication info
 Published elsewhere. Unknown where it was published
 Contact author(s)
 xwcao @ nuaa edu cn
 History
 20100126: received
 Short URL
 https://ia.cr/2010/039
 License

CC BY
BibTeX
@misc{cryptoeprint:2010/039, author = {Xiwang Cao and Lei Hu}, title = {On Exponential Sums, Nowton identities and Dickson Polynomials over Finite Fields}, howpublished = {Cryptology ePrint Archive, Paper 2010/039}, year = {2010}, note = {\url{https://eprint.iacr.org/2010/039}}, url = {https://eprint.iacr.org/2010/039} }