Article
A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
(2016)
Abstract
This paper proposes a new multi-value sequence generated by utilizing primitive element, trace, and power residue symbol over odd characteristic finite field. In detail, let p and k be an odd prime number as the characteristic and a prime factor of p-1, respectively. Our proposal generates k-value sequence T={ti | ti=fk(Tr(ωi)+A)}, where ω is a primitive element in the extension field $\F{p}{m}$, Tr(⋅) is the trace function that maps $\F{p}{m} \rightarrow \f{p}$, A is a non-zero scalar in the prime field $\f{p}$, and fk(⋅) is a certain mapping function based on k-th power residue symbol. Thus, the proposed sequence has four parameters as p, m, k, and A. Then, this paper theoretically shows its period, autocorrelation, and cross-correlation. In addition, this paper discusses its linear complexity based on experimental results. Then, these features of the proposed sequence are observed with some examples.
Disciplines
Publication Date
December 1, 2016
DOI
10.1587/transfun.E99.A.2226
Publisher Statement
This article was originally published in IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, volume E99. A, issue 12, 2016. ©2016 IEICE
This article is also available online at http://dx.doi.org/10.1587/transfun.E99.A.2226
SJSU Users: use the following link to login and access the article via SJSU databases.
Citation Information
Yasuyuki Nogami, Satoshi Uehara, Kazuyoshi Tsuchiya, Nasima Begum, et al.. "A Multi-Value Sequence Generated by Power Residue Symbol and Trace Function over Odd Characteristic Field" IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Vol. E99. A Iss. 12 (2016) p. 2226 - 2237 ISSN: 0916-8508 Available at: http://works.bepress.com/robert_morelos-zaragoza/47/