TY - GEN

T1 - Linear complexity of generalized NTU sequences

AU - Tsuchiya, Kazuyoshi

AU - Ogawa, Chiaki

AU - Nogami, Yasuyuki

AU - Uehara, Satoshi

N1 - Funding Information:
The authors would like to thank the anonymous reviewers for helpful comments and suggestions. This research was supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (A) Number 16H01723.

PY - 2017/11/3

Y1 - 2017/11/3

N2 - Pseudorandom number generators are required to generate pseudorandom numbers which have not only good statistical properties but also unpredictability in cryptography. A geometric sequence is a sequence given by applying a nonlinear feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a geometric sequence whose nonlinear feedforward function is given by the Legendre symbol, and showed the period, periodic autocorrelation and linear complexity of the sequence. Furthermore, Nogami et al. proposed a generalization of the sequence (this sequence is referred to as the generalized NTU sequence), and showed the period and periodic autocorrelation. In this paper, we investigate the linear complexity of the generalized NTU sequences. Under some conditions, we can ensure that generalized NTU sequences have large linear complexity from the results on linear complexity of Sidel'nikov sequences.

AB - Pseudorandom number generators are required to generate pseudorandom numbers which have not only good statistical properties but also unpredictability in cryptography. A geometric sequence is a sequence given by applying a nonlinear feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a geometric sequence whose nonlinear feedforward function is given by the Legendre symbol, and showed the period, periodic autocorrelation and linear complexity of the sequence. Furthermore, Nogami et al. proposed a generalization of the sequence (this sequence is referred to as the generalized NTU sequence), and showed the period and periodic autocorrelation. In this paper, we investigate the linear complexity of the generalized NTU sequences. Under some conditions, we can ensure that generalized NTU sequences have large linear complexity from the results on linear complexity of Sidel'nikov sequences.

KW - generalized NTU sequence

KW - geometric sequence

KW - linear complexity

KW - pseudorandom number generator

UR - http://www.scopus.com/inward/record.url?scp=85040598670&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040598670&partnerID=8YFLogxK

U2 - 10.1109/IWSDA.2017.8095739

DO - 10.1109/IWSDA.2017.8095739

M3 - Conference contribution

AN - SCOPUS:85040598670

T3 - 2017 8th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2017

SP - 74

EP - 78

BT - 2017 8th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2017

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 8th International Workshop on Signal Design and Its Applications in Communications, IWSDA 2017

Y2 - 24 September 2017 through 28 September 2017

ER -