Linear Complexity of Least Significant Bit of Polynomial Quotients

ZHAO Chun'e; MA Wenping; YAN Tongjiang; SUN Yuhua

doi:10.1049/cje.2016.10.008

Volume 26 Issue 3

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ZHAO Chun'e, MA Wenping, YAN Tongjiang, et al., “Linear Complexity of Least Significant Bit of Polynomial Quotients,” Chinese Journal of Electronics, vol. 26, no. 3, pp. 573-578, 2017, doi: 10.1049/cje.2016.10.008

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ZHAO Chun'e, MA Wenping, YAN Tongjiang, et al., “Linear Complexity of Least Significant Bit of Polynomial Quotients,” Chinese Journal of Electronics, vol. 26, no. 3, pp. 573-578, 2017, doi: 10.1049/cje.2016.10.008

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Linear Complexity of Least Significant Bit of Polynomial Quotients

doi: 10.1049/cje.2016.10.008

1.
State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China;
2.
College of Sciences, China University of Petroleum, Qingdao 266555, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61170319, No.61072140, No.61373171), the 111 Project (No.B08038), the Specialized Research Fund for the Doctoral Program of Higher Education (No.20100203110003), the Fujian Provincial Key Laboratory of Network Security and Cryptology Research Fund (Fujian Normal University) (No.15002), the Shandong Provincial Natural Science Foundation of China (No.ZR2014FQ005), the Fundamental Research Funds for the Central Universities (No.15CX08011A, No.15CX02065A, No.15CX02060A, No.15CX05060A, No.16CX02013A), and the Applied Basic Research Program of Qingdao (No.16-5-1-5-jch).

Received Date: 2015-02-17
Rev Recd Date: 2015-07-24
Publish Date: 2017-05-10

Abstract

Abstract

Binary sequences with large linear complexity have been found many applications in communication systems. We determine the linear complexity of a family of p²-periodic binary sequences derived from polynomial quotients modulo an odd prime p. Results show that these sequences have high linear complexity, which means they can resist the linear attack method.
- Cryptography,
- Polynomial quotient,
- Fermat quotient,
- Pseudo-random sequences,
- Linear complexity

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References(17)

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