Symmetric 2-Adic Complexity of Ding-Helleseth Generalized Cyclotomic Sequences of Period pq

Edemskiy, Vladimir; Wu, Chenhuang

doi:10.1007/978-3-030-71852-7_21

Cited by 5 publications

(3 citation statements)

References 19 publications

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“…Let us recall a method of Edemskiy and Antonova [10,11] to compute the linear complexity of DH-GCS d .…”

Section: Computation Methodsmentioning

confidence: 99%

“…(Also see [12] for a unified approach to Whiteman's and Ding-Helleseth's generalized cyclotomy.) The linear complexity of DH-GCS d when d = 2, 4, 6 is explicitly determined in [2,23,11], and ensured by Yan [21] to be at least (pq − 1)/2 for any order d. We contribute to this line by calculating the linear complexity of DH-GCS 8 , using the computation method of Edemskiy and Antonova [10,11] with the help of Gaussian classical cyclotomic numbers.…”

Section: Introductionmentioning

confidence: 99%

“…The Ding-Helleseth generalized cyclotomic sequence of order d (DH-GCS d ) with respect to (p, q, g) is defined (cf. [2,23,11]) as the sequence s ∞ = (s i ) i 0 = (s 0 , s 1 , s 2 , . .…”

Section: Introductionmentioning

confidence: 99%

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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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“…Let us recall a method of Edemskiy and Antonova [10,11] to compute the linear complexity of DH-GCS d .…”

Section: Computation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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Symmetric 2-adic complexity of Tang–Gong interleaved sequences from generalized GMW sequence pair

Yang,

He,

Zeng

et al. 2024

Des. Codes Cryptogr.

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4-adic complexity of quaternary cyclotomic sequences and Ding-Helleseth sequences with period pq

Edemskiy

2022

2022 IEEE International Symposium on Information Theory (ISIT)

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Symmetric 2-Adic Complexity of Ding-Helleseth Generalized Cyclotomic Sequences of Period pq

Cited by 5 publications

References 19 publications

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

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

Symmetric 2-adic complexity of Tang–Gong interleaved sequences from generalized GMW sequence pair

4-adic complexity of quaternary cyclotomic sequences and Ding-Helleseth sequences with period pq

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