Table of Contents
Journal of Discrete Mathematics
Volume 2013 (2013), Article ID 270424, 12 pages
http://dx.doi.org/10.1155/2013/270424
Research Article

Classification of Boolean Functions Where Affine Functions Are Uniformly Distributed

1Applied Statistics Unit, Indian Statistical Institute, Kolkata 700108, India
2Institute of Mathematics and Applications, Bhubaneswar 751003, India

Received 17 May 2013; Revised 22 August 2013; Accepted 11 September 2013

Academic Editor: Pantelimon Stǎnicǎ

Copyright © 2013 Ranjeet Kumar Rout et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. Slepian, “On the number of symmetry types of Boolean functions of n variables,” Canadian Journal of Mathematics, vol. 5, no. 2, pp. 185–193, 1953. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. S. W. Golomb, “On the classification of Boolean functions,” IRE Transactions on Circuit Theory, vol. 6, no. 5, pp. 176–186, 1959. View at Publisher · View at Google Scholar
  3. M. A. Harrison, “On the classification of Boolean functions by the general linear and affine groups,” Journal of the Society for Industrial and Applied Mathematics, vol. 12, no. 2, pp. 285–299, 1964. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. V. P. Correia and A. I. Reis, “Classifying n-input Boolean functions,” in Proceedings of the 7th Workshop IBERCHIP (IWS '01), pp. 58–66, Montevideo, Uruguay, March 2001.
  5. A. Braeken, Y. Borissov, S. Nikova, and B. Preneel, “Classification of Boolean functions of 6 variables or less with respect to some cryptographic properties,” in Automata, Languages and Programming, L. Caires, G. F. Italiano, L. Monteiro, C. Palamidessi, and M. Yung, Eds., vol. 3580 of Lecture Notes in Computer Science, pp. 324–334, Springer, Berlin, Germany, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. Stănică and S. H. Sung, “Boolean functions with five controllable cryptographic properties,” Designs, Codes and Cryptography, vol. 31, no. 2, pp. 147–157, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Y. V. Taranikov, “On resilient functions with maximum possible nonlinearity,” in Progress in Cryptology—INDOCRYPT 2000, B. Roy and E. Okamoto, Eds., vol. 1977 of Lecture Notes in Computer Science, pp. 19–30, Springer, 2000. View at Publisher · View at Google Scholar
  8. X.-M. Zhang and Y. Zheng, “Cryptographically resilient functions,” IEEE Transactions on Information Theory, vol. 43, no. 5, pp. 1740–1747, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. W. Millan, A. Clark, and E. Dawson, “Heuristic design of cryptographically strong balanced Boolean functions,” in Advances in Cryptology—EUROCRYPT'98, K. Nyberg, Ed., vol. 1403 of Lecture Notes in Computer Science, pp. 489–499, Springer, 1998. View at Publisher · View at Google Scholar
  10. P. P. Choudhury, S. Sahoo, and M. Chakraborty, “Characterization of the evolution of nonlinear uniform cellular automata in the light of deviant states,” International Journal of Mathematics and Mathematical Sciences, vol. 2011, Article ID 605098, 16 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  11. P. P. Choudhury, S. Sahoo, M. Chakraborty, S. K. Bhandari, and A. Pal, “Investigation of the global dynamics of cellular automata using Boolean derivatives,” Computers and Mathematics with Applications, vol. 57, no. 8, pp. 1337–1351, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. S. Sahoo, P. P. Choudhury, and M. Chakraborty, “Characterization of any non-linear Boolean function using a set of linear operators,” Journal of Orissa Mathematical Society, vol. 2, no. 1-2, pp. 111–133, 2010. View at Google Scholar
  13. P. P. Choudhury, S. Sahoo, B. K. Nayak, and Sk. S. Hassan, “Theory of Carry Value Transformation (CVT) and its application in fractal formation,” Global Journal of Computer Science and Technology, vol. 10, no. 14, pp. 98–107, 2010. View at Google Scholar
  14. S. Wolfram, A New Kind of Science, Wolfram Media, Champaign, Ill, USA, 2002. View at MathSciNet
  15. B. K. Nayak, S. Sahoo, and S. Biswal, “Cellular automata rules and linear numbers,” http://arxiv.org/abs/1204.3999.