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Autocorrelation Values of New Generalized Cyclotomic Sequences of Order Six Over \(Z_{pq}\)

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Information Security and Cryptology (Inscrypt 2013)

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Abstract

Let \(p, q\) \((p<q)\) be two odd primes with \(gcd(p-1,q-1)=6\). In this paper, based on the Whiteman generalized cyclotomy, new generalized cyclotomic sequences with order six and length \(pq\) are constructed. We first calculate the autocorrelation values of these sequences and get conditions of \(p\) and \(q\) such that they are four-valued. Besides, we find some specific examples such that the autocorrelation function takes on only a few values.

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Notes

  1. 1.

    We only list part of the results, many others can be found by a computer calculation.

References

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Acknowledgment

The authors would like to thank the anonymous reviewers for their helpful comments. This work is supported by the National Grand Fundamental Research 973 Program of China(Grant No. 2013CB338002, 2013CB338003), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDA06010701), IIE’s Research Project on Cryptography (Grant No. Y3Z0016102), and the programs of the National Natural Science Foundation of China (Grant No. 60833008, 60603018, 61173134, 91118006, 61272476).

Author information

Authors and Affiliations

  1. Trusted Computing and Information Assurance Laboratory, Institute of Software, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Xinxin Gong

  2. Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100093, People’s Republic of China

    Bin Zhang

  3. Institute of Software, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Dengguo Feng

  4. China College of Sciences, China University of Petroleum, Beijing, China

    Tongjiang Yan

Authors
  1. Xinxin Gong
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  2. Bin Zhang
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  3. Dengguo Feng
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  4. Tongjiang Yan
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Corresponding author

Correspondence to Xinxin Gong .

Editor information

Editors and Affiliations

  1. Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  2. University of Texas, San Antonio, Texas, USA

    Shouhuai Xu

  3. Columbia University, New York, New York, USA

    Moti Yung

Appendix

Appendix

We list in Table 1 part of the results in Example 1, and Table 2 part of the results in Example 2.

Table 1. Some result that \(A{C_s}(w) = -1\) for each \(w \in Z_{pq}^*\)
Full size table
Table 2. some results that \(A{C_s}(w)\) is four, five or six-valued
Full size table

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Gong, X., Zhang, B., Feng, D., Yan, T. (2014). Autocorrelation Values of New Generalized Cyclotomic Sequences of Order Six Over \(Z_{pq}\) . In: Lin, D., Xu, S., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2013. Lecture Notes in Computer Science(), vol 8567. Springer, Cham. https://doi.org/10.1007/978-3-319-12087-4_6

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  • DOI: https://doi.org/10.1007/978-3-319-12087-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12086-7

  • Online ISBN: 978-3-319-12087-4

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