The Linear Complexity of a New Class of Generalized Cyclotomic Sequence of Order q with Period 2pm

Yan WANG; Gaina XUE; Shunbo LI; Feifei HUI

doi:10.11999/JEIT180884

Volume 41 Issue 9

Sep. 2019

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Yan WANG, Gaina XUE, Shunbo LI, Feifei HUI. The Linear Complexity of a New Class of Generalized Cyclotomic Sequence of Order q with Period 2pm[J]. Journal of Electronics & Information Technology, 2019, 41(9): 2151-2155. doi: 10.11999/JEIT180884

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Yan WANG, Gaina XUE, Shunbo LI, Feifei HUI. The Linear Complexity of a New Class of Generalized Cyclotomic Sequence of Order q with Period 2p^m[J]. Journal of Electronics & Information Technology, 2019, 41(9): 2151-2155. doi: 10.11999/JEIT180884

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The Linear Complexity of a New Class of Generalized Cyclotomic Sequence of Order q with Period 2p^m

doi: 10.11999/JEIT180884

School of Science, Xi’an University of Architecture and Technology, Xi’an 710055, China

Funds: The National Natural Science Foundation of China (11471255), The Natural Science Project of Xi’an University of Architecture and Technology (1609718034), The Talent Fund of Xi’an University of Architecture and Technology (RC1338)

Received Date: 2018-09-18
Rev Recd Date: 2019-06-06

Available Online: 2019-06-28

Publish Date: 2019-09-10

Abstract

Abstract

Based on the theory of Ding - generalized circle, a new class of generalized cyclotomic sequences of $ 2{p^m}$ ($ p$ odd prime and m>1) with arbitrary prime order is constructed in this paper. The polynomial cyclotomic classes are analysed by algebra number theory method. Moreover, the linear complexity of the new sequences are determined, which losely related to the division of quadratic residual classes and quadratic non-residual classes. Results show that the linear complexity of this kind of sequence is much larger than half of the period, hence, can fight Berlekamp-Massey’s security application attack that is a pseudo-random sequence with good properties in the sense of cryptography.
- Generalized cyclotomic sequence,
- Linear complexity,
- Secondary residual class,
- Berlekamp-Massey (B-M) algorithm

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References(16)

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