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Trace representation of pseudorandom binary sequences derived from Euler quotients

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Abstract

We give the trace representation of a family of binary sequences derived from Euler quotients by determining the corresponding defining polynomials. The result extends an earlier result of Z. Chen on the trace of binary sequences derived from Fermat quotients modulo a prime. However, the case of composite modulus brings some interesting twists. Trace representation can help us producing the sequences efficiently and analyzing their cryptographic properties, such as linear complexity.

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Notes

  1. In the sequel, we will use the Euler quotients \(Q_r(u)\) and related notations for \(1\le r\le {\mathfrak {r}}\) repeatedly.

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Acknowledgments

The authors wish to thank the anonymous referees and the editor for their patience in reading this manuscript and their helpful suggestions. Z. Chen was partially supported by the National Natural Science Foundation of China under Grant No. 61373140. X. Du was partially supported by the National Natural Science Foundation of China under Grants 61202395,61462077 and the Program for New Century Excellent Talents in University (NCET-12-0620).

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Authors and Affiliations

  1. Provincial Key Laboratory of Applied Mathematics, Putian University, Putian, 351100, Fujian, People’s Republic of China

    Zhixiong Chen

  2. The State Key Laboratory of Integrated Services Networks, Xidian University, Xi’an, 710071, Shaanxi, People’s Republic of China

    Zhixiong Chen & Xiaoni Du

  3. College of Mathematics and Statistics, Northwest Normal University, Lanzhou, 730070, Gansu, People’s Republic of China

    Xiaoni Du

  4. Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

    Radwa Marzouk

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  1. Zhixiong Chen
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  2. Xiaoni Du
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  3. Radwa Marzouk
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Correspondence to Zhixiong Chen.

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Chen, Z., Du, X. & Marzouk, R. Trace representation of pseudorandom binary sequences derived from Euler quotients. AAECC 26, 555–570 (2015). https://doi.org/10.1007/s00200-015-0265-4

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  • DOI: https://doi.org/10.1007/s00200-015-0265-4

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