Linear complexity of binary Whiteman generalized cyclotomic sequences of order 2k

Yan, Tao; Du, Xiaoni; Xiao, Gao; Huang, Xiaolong

doi:10.1016/j.ins.2008.11.006

Cited by 25 publications

(13 citation statements)

References 13 publications

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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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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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“…There are many kinds of generalized cyclotomic sequences, binary and non-binary, of different lengths. One family of them are based on Whiteman's generalized cyclotomy [20], of length pq for distinct odd primes p and q, with a high linear complexity precisely determined when gcd(p−1, q −1) = 2 k [6,1,22]. However, the imbalance (with q −p−1 more 1's than 0's in each period) makes them improper for applications.…”

Section: Introductionmentioning

confidence: 99%

Linear complexity of Ding-Helleseth generalized cyclotomic sequences of order eight

et al. 2019

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During the last two decades, many kinds of periodic sequences with good pseudo-random properties have been constructed from classical and generalized cyclotomic classes, and used as keystreams for stream ciphers and secure communications. Among them are a family DH-GCS d of generalized cyclotomic sequences on the basis of Ding and Helleseth's generalized cyclotomy, of length pq and order d = gcd(p − 1, q − 1) for distinct odd primes p and q. The linear complexity (or linear span), as a valuable measure of unpredictability, is precisely determined for DH-GCS 8 in this paper. Our approach is based on Edemskiy and Antonova's computation method with the help of explicit expressions of Gaussian classical cyclotomic numbers of order 8. Our result for d = 8 is compatible with Yan's low bound (pq − 1)/2 of the linear complexity for any order d, which means high enough to resist security attacks of the Berlekamp-Massey algorithm. Finally, we include SageMath codes to illustrate the validity of our result by examples.

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“…In 1962, the concept of generalized cyclotomy with respect to pq was first proposed by Whiteman [5] , and Ding [6] proved these sequences have several randomness properties. 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.…”

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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Linear complexity of binary Whiteman generalized cyclotomic sequences of order 2k

Cited by 25 publications

References 13 publications

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

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

Linear complexity of Ding-Helleseth generalized cyclotomic sequences of order eight

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

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