Trace representation of some generalized cyclotomic sequences of length pq

Du, Xiaoni; Yan, Tao; Xiao, Gao

doi:10.1016/j.ins.2007.11.023

Cited by 15 publications

(9 citation statements)

References 15 publications

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“…By the defining pairs of the Legendre sequence, Du et al determined the trace representation and linear complexity of the generalized cyclotomic sequence of length pq with arbitrary order. It can be seen that Bai et al's conclusion is a special case when the order is two [11]. Kim et al [12] found a general trace representation of Lengendre sequences with any prime period.…”

Section: Introductionmentioning

confidence: 94%

Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two

Zhao

Jia

et al. 2021

Mathematics

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Linear complexity is an important property to measure the unpredictability of pseudo-random sequences. Trace representation is helpful for analyzing cryptography properties of pseudo-random sequences. In this paper, a class of new Ding generalized cyclotomic binary sequences of order two with period pq is constructed based on the new segmentation of Ding Helleseth generalized cyclotomy. Firstly, the linear complexity and minimal polynomial of the sequences are investigated. Then, their trace representation is given. It is proved that the sequences have larger linear complexity and can resist the attack of the Berlekamp–Massey algorithm. This paper also confirms that generalized cyclotomic sequences with good randomness may be obtained by modifying the characteristic set of generalized cyclotomy.

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Section: Introductionmentioning

confidence: 94%

Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two

Zhao

Jia

et al. 2021

Mathematics

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“…The (Whiteman) generalized cyclotomic classes were applied to constructing binary sequences in numerous references, see, e.g., [8][9][10][11][12][13][14][15]. In this article, we will extend the constructions of binary sequences to sequences of k symbols.…”

Section: Constructionsmentioning

confidence: 99%

Pseudo-Randomness of Certain Sequences of k Symbols with Length pq

Chen

2011

J. Comput. Sci. Technol.

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Chen ZX, Du XN, Wu CH. Pseudo-randomness of certain sequences of k symbols with length pq. JOURNAL OF COM-PUTER SCIENCE AND TECHNOLOGY 26(2): 276- AbstractThe theory of finite pseudo-random binary sequences was built by C. Mauduit and A. Sárközy and later extended to sequences of k symbols (or k-ary sequences). Certain constructions of pseudo-random sequences of k symbols were presented over finite fields in the literature. In this paper, two families of sequences of k symbols are constructed by using the integers modulo pq for distinct odd primes p and q. The upper bounds on the well-distribution measure and the correlation measure of the families sequences are presented in terms of certain character sums over modulo pq residue class rings. And low bounds on the linear complexity profile are also estimated.

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“…Later, sequences of order four [7] and order 2 k (where k > 1) [8] were proven to possess high linear complexity and ideal balance. Du et al [9] completely solved the problem of the linear complexity of a generalized sequence of order p m by using trace theory. Recently, Chang and Li [10] generalized the length of a Whiteman' sequence to 2pq, and derived the linear complexity of this sequence.…”

Section: Introductionmentioning

confidence: 99%

On the linear complexity of new generalized cyclotomic binary sequences of order two and period pqr

Liu¹,

Yang²,

et al. 2016

Tinshhua Sci. Technol.

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Periodic sequences over finite fields, constructed by classical cyclotomic classes and generalized cyclotomic classes, have good pseudorandom properties. The linear complexity of a period sequence plays a fundamental role in the randomness of sequences. Let p, q, and r be distinct odd primes with gcd(p-1, q-1)=gcd(p-1, r -1)=gcd(q-1, r -1)=2. In this paper, a new class of generalized cyclotomic sequence with respect to pqr over GF(2) is constructed by finding a special characteristic set. In addition, we determine its linear complexity using cyclotomic theory. Our results show that these sequences have high linear complexity, which means they can resist linear attacks.

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Trace representation of some generalized cyclotomic sequences of length pq

Cited by 15 publications

References 15 publications

Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two

Linear Complexity and Trace Representation of New Ding Generalized Cyclotomic Sequences with Period pq and Order Two

Pseudo-Randomness of Certain Sequences of k Symbols with Length pq

On the linear complexity of new generalized cyclotomic binary sequences of order two and period pqr

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