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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 259))

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Abstract

This paper presents 1-Error Linear Complexity Test (1-ELCT) which is based on Linear Complexity Test—LCT described in (Rukhin et al., NIST Special Publication 800–822, 2001). 1-ELCT is improved version of Bit Flipping Linear Complexity Test (BFLCT). In BFLCT, it is checked that wether the sequence remains random or not after flipping one bit with respect to the LCT. 1-ELCT is for block length of the form \( M = 2^{q} ,\;q \in {\mathbb{N}}\,\& \;q > 8 \) and it is of practical use for binary sequences of length 106.

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References

  1. Massey, J.L.: Shift register synthesis and BCH decoding. IEEE Trans. Inf. Theor. 15(1), 122–127 (1969)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  4. Lauder, G.B., Paterson, K.G.: Computing the error linear complexity spectrum of a binary sequence of period 2n. IEEE Trans. Inf. Theor. 49(1), 273–2803 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Ding, C., Xiao, G., Shan, W.: The Stability Theory of Stream Ciphers. Springer, Heidelberg (1992)

    Google Scholar 

  6. Kaida, T., Uehara, S., Imamura, K.: An algorithm for the k-error linear complexity of sequences over GF(p m) with period pn, p a prime. Inf. Comput. 151, 134–147 (1999) Academic Press

    Google Scholar 

  7. Kaida, T.: On the generalized Lauder-Paterson algorithm and profiles of the k-error linear complexity for exponent periodic sequences. In: Proceedings of SETA 2004, Volume LNCS 3486, pp. 166–178. Spinger, Berlin (2005)

    Google Scholar 

  8. Wei, S.: An efficient algorithm for determining the k-error linear complexity of binary sequences with periods 2p n. JCSNS Int. J. Comput. Sci. Netw. Sec. 8(4), 221 (2008)

    Google Scholar 

  9. Alecu, A., Salagean, A.M.: A genetic algorithm for computing the k-error linear complexity of cryptographic sequences. In: 2007 IEEE Congress on Evolutionary Computation, pp. 3569–3576 (2007)

    Google Scholar 

  10. Zhou, J.: An algorithm for the k-error linear complexity of a sequence with period 2p n over GF(q). In: IEEE Proceedings of IWSDA’07, pp. 104–108 (2007)

    Google Scholar 

  11. Salagean, A.: On the computation of the linear complexity and k-error linear complexity of binary sequences with period a power of two. IEEE Trans. Inf. Theor. 51(3), 1145–1150 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Rukhin, A., et al.: A statistical test suite for random and psuedo random number generators for cryptographic applications. NIST Spec. Publ. 800–822 (with revisions dated 15 May 2001)

    Google Scholar 

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Acknowledgments

We would like to thank Dr. P. K. Saxena, Dr. S. S. Bedi and Ms. Neelam Verma for their support. Also we are thankful to Dr. Indivar Gupta for his valuable suggestions.

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Correspondence to Hetal G. Borisagar .

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© 2014 Springer India

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Borisagar, H.G., Mishra, P.R., Gaba, N. (2014). 1-Error Linear Complexity Test for Binary Sequences. In: Pant, M., Deep, K., Nagar, A., Bansal, J. (eds) Proceedings of the Third International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 259. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1768-8_21

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  • DOI: https://doi.org/10.1007/978-81-322-1768-8_21

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  • Print ISBN: 978-81-322-1767-1

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