一類新的周期為2pm的q階二元廣義分圓序列的線性復雜度
doi: 10.11999/JEIT180884
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西安建筑科技大學理學院 西安 710055
基金項目: 國家自然科學基金(11471255)，西安建筑科技大學自然科學專項(1609718034)，西安建筑科技大學人才基金(RC1338)
The Linear Complexity of a New Class of Generalized Cyclotomic Sequence of Order q with Period 2pm
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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)
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摘要: 該文基于Ding-廣義分圓理論，將周期為
$ 2{p^m}$ ($ p$ 為奇素數(shù)，$ m$ 為正整數(shù))廣義分圓序列的研究推廣到任意素數(shù)階情形，構造了一類新序列。通過數(shù)論方法分析多項式廣義分圓類，確定并計算線性復雜度與序列的2次剩余類和2次非剩余類的劃分緊密相關。結果表明該類序列的線性復雜度遠遠大于周期的一半，能抗擊應用Berlekamp-Massey(B-M)算法的安全攻擊，是密碼學意義上性質(zhì)良好的偽隨機序列。-
關鍵詞:
- 廣義分圓序列 /
- 線性復雜度 /
- 2次剩余類 /
- Berlekamp-Massey算法
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. -
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