Skip to main content
SpringerLink
Log in

An algorithm for the spectral immunity of binary sequence with period 2n

  • Computer Science
  • Published:
Wuhan University Journal of Natural Sciences

Abstract

To resist the fast algebraic attack and fast selective discrete Fourier transform attacks, spectral immunity of a sequence or a Boolean function was proposed. At the same time, an algorithm to compute the spectral immunity of the binary sequence with odd period N was presented, here N is a factor of 2n − 1, where n is an integer. The case is more complicated when the period is even. In this paper, we compute linear complexity of every orthogonal sequence of a given sequence using Chan-Games algorithm and k - error linear complexity algorithm. Then, an algorithm for spectral immunity of binary sequence with period N = 2n is obtained. Furthermore, the time complexity of this algorithm is proved to be O(n).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Armknecht F, Rause M. Algebraic attacks on combiners with memory [C] //Proc Advances in Cryptology — CRYPTO 2003, Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2003, 2729: 162–175.

    Google Scholar 

  2. Courtois N, Meier W. Algebraic attacks on stream ciphers with linear feedback [C] //Proc Advances in Cryptology— EUROCRYPT 2003, Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2003, 2656: 345–359.

    Google Scholar 

  3. Courtois N. Fast algebraic attacks on stream ciphers with linear feedback [C] //Proc Advances in Cryptology—CRYPTO 2003, Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2003, 2729: 176–194.

    Google Scholar 

  4. Armknecht F. Improving fast algebraic attacks [C] //Proc Fast Software Encryption 2004, Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2004, 3017: 65–82.

    Google Scholar 

  5. Armknecht F, Ars G. Introducing a new variant of fast algebraic attacks and minimizing their successive data complexsity [C] //Proc Mycrypt 2005(International Conference on Cryptology in Malaysia), Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2005, 3715: 16–32.

    Google Scholar 

  6. Hawkes P, Rose G G. Rewriting variables: The complexcity of fast algebraic attacks on stream ciphers [C] //Proc Advances in Cryptology — CRYPTO, Lecture Notes in Computer Science. Berlin: Spring-Verlag, 2004, 3152: 390–406.

    Google Scholar 

  7. Meier W, Pasalic E, Carlet C. Algebraic attacks and decom-position of Boolean functions [C]//Advances in Cryptology— EURO-CRYPT 2004, Lecture Notes in Computer Science. Berlin: Springer-Verlag, 2004, 3027: 474–491.

    Google Scholar 

  8. Dalai D K, Maitra S, Sarkar S. Basic theory in construction Boolean functions with maximum possible annihilator immunity [J]. Designs, Codes and Cryptography, 2006, 40(1): 41–58.

    Article  Google Scholar 

  9. Li N, Qi W F. Symmetric Boolean functions depending on an odd number of variables with maximum algebraic immunity [J]. IEEE Trans Inf Theory, 2006, 52(5): 2271–2273.

    Article  Google Scholar 

  10. Qu L J, Li C. On the 2m-variable symmetric Boolean functions with maximum algebraic immunity [J]. Science in China Series F: Information Sciences, 2008, 51(2): 120–127.

    Article  Google Scholar 

  11. Liao Q Y, Feng K Q, Liu F. On the 2m+1-variable symmetric Boolean functions with maximum algebraic immunity 2m-1 [J]. Science in China Series A: Mathematics, 2009, 52(1): 17–28.

    Article  Google Scholar 

  12. Qu L J, Feng K Q, Liu F, et al. Constructing symmetric boolean functions with maximum algebraic immunity [J]. IEEE Trans Inf Theory, 2009, 55(5): 2406–2412.

    Article  Google Scholar 

  13. Carlet C, Zeng X Y, Li C L, et al. Further properties of several classes of Boolean functions with optimum algebraic immunity [J]. Designs, Codes and Cryptography, 2009, 52(3): 303–338.

    Article  Google Scholar 

  14. Li C L, Zeng X Y, Su W, et al. A class of rotation symmetric Boolean functions with optimum algebraic immunity [J]. Wuhan University Journal of Natural Science, 2008, 13(6): 702–706.

    Article  Google Scholar 

  15. Liu M C, Pei D Y, Du Y S. Identification and construction of Boolean functions with maximum algebraic immunity[J]. Science in China Series F: Information Sciences, 2010, 53(7): 1379–1396.

    Article  Google Scholar 

  16. Wang Q C, Peng J, Kan H B, et al. Constructions of cryptographically significant Boolean functions using primitive polynomials[ J]. IEEE Trans Inf Theory, 2010, 56(6): 3048–3053.

    Article  Google Scholar 

  17. Gong G, Ronjom S, Helleseth T, et al. Fast discrete Fourier spectra attacks on stream ciphers[J]. IEEE Trans Inf Theory, 2011, 57(8): 5555–5565.

    Article  Google Scholar 

  18. Helleseth T, Ronjom S. Simplifying algebraic attacks with univariate analysis [C] // Information Theory and Applications Workshoo(ITA). Washington D C: IEEE Press, 2011: 1–7.

    Google Scholar 

  19. Stamp M, Martin C F. An algorithm for the k-error linear complexity of binary sequence with period 2n [J]. IEEE Trans Inf Theory, 1993, 39(4): 1398–1401.

    Article  Google Scholar 

  20. Games R A, Chan A H. A fast algorithm for determining the complexity of a binary sequence with period 2n [J]. IEEE Trans Inf Theory, 1983, 29(1): 144–146.

    Article  Google Scholar 

Download references

Acknowledgements

The author would like to thank the reviewers for their constructive comments that much improved the presentation and quality of this paper.

Author information

Authors and Affiliations

  1. Computer Science Department, China Women’s University, Beijing, 100101, China

    Zhenhua Liu

Authors
  1. Zhenhua Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhenhua Liu.

Additional information

Foundation item: Supported by the National Natural Science Foundation of China( 61300181, 61272057, 61202434, 61170270, 61100203, 61121061)

Biography: LIU Zhenhua, male, Master, Lecturer, research direction: information system.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Z. An algorithm for the spectral immunity of binary sequence with period 2n . Wuhan Univ. J. Nat. Sci. 21, 121–125 (2016). https://doi.org/10.1007/s11859-016-1147-8

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11859-016-1147-8

Key words

CLC number

Search

Navigation