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)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
xwcao @ nuaa edu cn
History
2010-01-26: received
Short URL
https://ia.cr/2010/039
License
Creative Commons Attribution
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}
}
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