Paper 2020/160

Solving Some Affine Equations over Finite Fields

Sihem Mesnager, Kwang Ho Kim, Jong Hyok Choe, and Dok Nam Lee

Abstract

Let $l$ and $k$ be two integers such that $l|k$. Define $T_l^k(X):=X+X^{p^l}+\cdots+X^{p^{l(k/l-2)}}+X^{p^{l(k/l-1)}}$ and $S_l^k(X):=X-X^{p^l}+\cdots+(-1)^{(k/l-1)}X^{p^{l(k/l-1)}}$, where $p$ is any prime. This paper gives explicit representations of all solutions in $\GF{p^n}$ to the affine equations $T_l^{k}(X)=a$ and $S_l^{k}(X)=a$, $a\in \GF{p^n}$. For the case $p=2$ that was solved very recently in \cite{MKCL2019}, the result of this paper reveals another solution.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Preprint. MINOR revision.
Keywords
Affine equationFinite fieldZeros of a polynomialLinearized polynomial
Contact author(s)
smesnager @ univ-paris8 fr
History
2020-02-13: received
Short URL
https://ia.cr/2020/160
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2020/160,
      author = {Sihem Mesnager and Kwang Ho Kim and Jong Hyok Choe and Dok Nam Lee},
      title = {Solving Some Affine Equations over Finite Fields},
      howpublished = {Cryptology ePrint Archive, Paper 2020/160},
      year = {2020},
      note = {\url{https://eprint.iacr.org/2020/160}},
      url = {https://eprint.iacr.org/2020/160}
}
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