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Cryptography and Communications

Erschienen in:

03.01.2019

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

verfasst von: Yana Liang, Jiali Cao, Xingfa Chen, Shiping Cai, Xiang Fan

Erschienen in: Cryptography and Communications | Ausgabe 5/2019

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Abstract

During the last two decades, many kinds of periodic sequences with good pseudorandom 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-GCS₈ 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 on the linear complexity for any order d, which is high enough to resist attacks of the Berlekamp–Massey algorithm. Finally, we include SageMath codes to illustrate the validity of our result by examples.

Vorheriger Artikel A novel maximum distance separable code to generate universal identifiers

Nächster Artikel Further results on permutation trinomials with Niho exponents

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Titel: Linear complexity of Ding-Helleseth generalized cyclotomic sequences of order eight
verfasst von: Yana Liang
Jiali Cao
Xingfa Chen
Shiping Cai
Xiang Fan
Publikationsdatum: 03.01.2019
Verlag: Springer US
Erschienen in: Cryptography and Communications / Ausgabe 5/2019
Print ISSN: 1936-2447
Elektronische ISSN: 1936-2455
DOI: https://doi.org/10.1007/s12095-018-0343-0

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