Multi-Valued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields

Begum, Nasima; Nogami, Yasuyuki; Uehara, Satoshi; Moleros-Zaragoza, Robert H.

doi:10.1587/transfun.e100.a.922

Cited by 4 publications

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…T NTU A is called an ℓ-ary generalized NTU sequence. If A = 0, then T NTU 0 is an ℓ-ary NTU sequence [26,25]. The autocorrelation distribution of T NTU A have been explicitly obtained in [27, 3.3].…”

Section: Generalized Ntu Sequencesmentioning

confidence: 99%

“…In this section, we survey properties of the generalized NTU sequences. For details, see [26,25,27].…”

Section: Generalized Ntu Sequencesmentioning

confidence: 99%

“…They showed the period, periodic autocorrelation and linear complexity of the NTU sequence. The studies on generalization of the sequences have made progress in recent years [4,28,27,25,20,3,17,2,32]. In particular, Nogami et al [27] proposed a generalization of the NTU sequence (this sequence is referred to as the generalized NTU sequence), and showed the period and periodic autocorrelation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Linear Complexity of Geometric Sequences Defined by Cyclotomic Classes and Balanced Binary Sequences Constructed by the Geometric Sequences

Tsuchiya

Ogawa

Nogami

et al. 2018

IEICE Trans. Fundamentals

Self Cite

View full text Add to dashboard Cite

Pseudorandom number generators are required to generate pseudorandom numbers which have good statistical properties as well as unpredictability in cryptography. An m-sequence is a linear feedback shift register sequence with maximal period over a finite field. M-sequences have good statistical properties, however we must nonlinearize m-sequences for cryptographic purposes. 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, and showed the period and periodic autocorrelation. In this paper, we first investigate linear complexity of the geometric sequences. In the case that the Chan-Games formula which describes linear complexity of geometric sequences does not hold, we show the new formula by considering the sequence of complement numbers, Hasse derivative and cyclotomic classes. Under some conditions, we can ensure that the geometric sequences have a large linear complexity from the results on linear complexity of Sidel'nikov sequences. The geometric sequences have a long period and large linear complexity under some conditions, however they do not have the balance property. In order to construct sequences that have the balance property, we propose interleaved sequences of the geometric sequence and its complement. Furthermore, we show the periodic autocorrelation and linear complexity of the proposed sequences. The proposed sequences have the balance property, and have a large linear complexity if the geometric sequences have a large one.

show abstract

Section: Generalized Ntu Sequencesmentioning

confidence: 99%

“…In this section, we survey properties of the generalized NTU sequences. For details, see [26,25,27].…”

Section: Generalized Ntu Sequencesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Linear Complexity of Geometric Sequences Defined by Cyclotomic Classes and Balanced Binary Sequences Constructed by the Geometric Sequences

Tsuchiya

Ogawa

Nogami

et al. 2018

IEICE Trans. Fundamentals

Self Cite

View full text Add to dashboard Cite

show abstract

“…In another related work [18], the authors proposed an approach for generating a multi-value sequence and evaluated its linear complexity property. The authors discussed binary sequence generation procedure along with its linear complexity like crucial property [19].…”

Section: B Related Workmentioning

confidence: 99%

Pseudo Random Ternary Sequence and Its Autocorrelation Property Over Finite Field

Ali¹,

Ali²,

Habib³

et al. 2017

IJCNIS

Self Cite

View full text Add to dashboard Cite

Abstract-In this paper, the authors have proposed an innovative approach for generating a pseudo random ternary sequence by using a primitive polynomial, trace function, and Legendre symbol over odd characteristics field. Let p be an odd prime number, F p be an odd characteristic prime field, and m be the degree of the primitive polynomial  .fx Let  be its zero and a primitive element in pA This paper mathematically explains the properties of the proposed ternary sequence such as period and autocorrelation. Additionally, these properties are also justified based on some experimental results.

show abstract

“…NTU sequences have several nice properties such as long period, three-valued autocorrelation, and maximum linear complexity. Thereafter, NTU sequences were generalized to -valued generalized NTU sequences by adding a fixed value to each element of q-ary m-sequences before reducing to values (see [8], [9]). In this paper, we focus on the binary generalized NTU sequences, for which mathematical definitions are given as follows.…”

Section: Introductionmentioning

confidence: 99%

Combinatorial Structures Behind Binary Generalized NTU Sequences

2023

IEICE Trans. Fundamentals

View full text Add to dashboard Cite

This paper concentrates on a class of pseudorandom sequences generated by combining q-ary m-sequences and quadratic characters over a finite field of odd order, called binary generalized NTU sequences. It is shown that the relationship among the sub-sequences of binary generalized NTU sequences can be formulated as combinatorial structures called Hadamard designs. As a consequence, the combinatorial structures generalize the group structure discovered by Kodera et al. (IEICE Trans. Fundamentals, vol.E102-A, no.12, pp.1659-1667, 2019 and lead to a finite-geometric explanation for the investigated group structure.

show abstract

Multi-Valued Sequences Generated by Power Residue Symbols over Odd Characteristic Fields

Cited by 4 publications

References 9 publications

Linear Complexity of Geometric Sequences Defined by Cyclotomic Classes and Balanced Binary Sequences Constructed by the Geometric Sequences

Linear Complexity of Geometric Sequences Defined by Cyclotomic Classes and Balanced Binary Sequences Constructed by the Geometric Sequences

Pseudo Random Ternary Sequence and Its Autocorrelation Property Over Finite Field

Combinatorial Structures Behind Binary Generalized NTU Sequences

Contact Info

Product

Resources

About