Abstract
Recently, binary sequences generated by chaotic maps have been widely studied. In particular, the logistic map is used as one of the chaotic map. However, if the logistic map is implemented by using unite precision computer arithmetic, rounding is required. In order to avoid rounding, Miyazaki, Araki, Uehara and Nogami proposed the logistic map over finite fields, and show some properties of sequences generated by the logistic map over finite fields. In this paper, we show some properties of periods of sequences generated by the logistic map over finite fields with control parameter four. In particular, we show conditions for parameters and initial values to have a long period, and asymptotic properties for periods by numerical experiments.
| Original language | English |
|---|---|
| Title of host publication | 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 155-159 |
| Number of pages | 5 |
| ISBN (Electronic) | 9781467383080 |
| DOIs | |
| Publication status | Published - Apr 22 2016 |
| Event | 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015 - Bengaluru, India Duration: Sep 13 2015 → Sep 18 2015 |
Other
| Other | 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015 |
|---|---|
| Country | India |
| City | Bengaluru |
| Period | 9/13/15 → 9/18/15 |
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Keywords
- Hyperbola
- Legendre symbol
- logistic map over finite fields
- long period sequences
- square map
ASJC Scopus subject areas
- Computer Networks and Communications
- Signal Processing
Cite this
Periods of sequences generated by the logistic map over finite fields with control parameter four. / Tsuchiya, Kazuyoshi; Nogami, Yasuyuki.
7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015. Institute of Electrical and Electronics Engineers Inc., 2016. p. 155-159 7458394.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Periods of sequences generated by the logistic map over finite fields with control parameter four
AU - Tsuchiya, Kazuyoshi
AU - Nogami, Yasuyuki
PY - 2016/4/22
Y1 - 2016/4/22
N2 - Recently, binary sequences generated by chaotic maps have been widely studied. In particular, the logistic map is used as one of the chaotic map. However, if the logistic map is implemented by using unite precision computer arithmetic, rounding is required. In order to avoid rounding, Miyazaki, Araki, Uehara and Nogami proposed the logistic map over finite fields, and show some properties of sequences generated by the logistic map over finite fields. In this paper, we show some properties of periods of sequences generated by the logistic map over finite fields with control parameter four. In particular, we show conditions for parameters and initial values to have a long period, and asymptotic properties for periods by numerical experiments.
AB - Recently, binary sequences generated by chaotic maps have been widely studied. In particular, the logistic map is used as one of the chaotic map. However, if the logistic map is implemented by using unite precision computer arithmetic, rounding is required. In order to avoid rounding, Miyazaki, Araki, Uehara and Nogami proposed the logistic map over finite fields, and show some properties of sequences generated by the logistic map over finite fields. In this paper, we show some properties of periods of sequences generated by the logistic map over finite fields with control parameter four. In particular, we show conditions for parameters and initial values to have a long period, and asymptotic properties for periods by numerical experiments.
KW - Hyperbola
KW - Legendre symbol
KW - logistic map over finite fields
KW - long period sequences
KW - square map
UR - http://www.scopus.com/inward/record.url?scp=84978499129&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84978499129&partnerID=8YFLogxK
U2 - 10.1109/IWSDA.2015.7458394
DO - 10.1109/IWSDA.2015.7458394
M3 - Conference contribution
AN - SCOPUS:84978499129
SP - 155
EP - 159
BT - 7th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2015
PB - Institute of Electrical and Electronics Engineers Inc.
ER -