Paper 2026/129
The ideal arithmetic correlations of $N$-ary sequences and related results
, School of Mathematics and Statistics，Fujian Normal University, Key Laboratory of Analytical Mathematics and Applications (Ministry of Education)，Fujian Normal UniversityAbstract
Arithmetic correlations represent the extension of classical correlations into the with-carry setting and serve as a critical performance criterion for pseudorandom sequences constructed via feedback with carry shift registers. The arithemetic correlation values should be as small as possible for application perspective. This paper establishes a sufficient condition for $N$-ary sequences to have ideal arithmetic correlation. Based on this characterization, it is demonstrated that $N$-ary $\ell$-sequences with a prime connection integer $p$ satisfying $p\equiv1(\textup{mod}\:N)$ exhibit ideal arithmetic correlation. Furthermore, under the condition $N^{p-1}\not\equiv1(\textup{mod}\:p^{2})$, this result is extended to the case where the connection integer is a prime power. Additionally, an upper bound is established for the arithmetic crosscorrelation of binary sequences derived from Fermat quotients with coprime periods.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Binary sequence$N$-ary sequenceArithmetic correlationsFeedback with carry shift registers
- Contact author(s)
- ffyfjnu @ 139 com
- History
- 2026-01-28: approved
- 2026-01-27: received
- See all versions
- Short URL
- https://ia.cr/2026/129
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2026/129,
author = {Feifei Yan and Pinhui Ke and Chenhuang Wu},
title = {The ideal arithmetic correlations of $N$-ary sequences and related results},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/129},
year = {2026},
url = {https://eprint.iacr.org/2026/129}
}
