Table of Contents Author Guidelines Submit a Manuscript
Security and Communication Networks
Volume 2017, Article ID 6268230, 9 pages
https://doi.org/10.1155/2017/6268230
Research Article

1-Resilient Boolean Functions on Even Variables with Almost Perfect Algebraic Immunity

1School of Electronics and Information, Northwestern Polytechnical University, Shaanxi, China
2Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China
3Westone Cryptologic Research Center, Beijing, China
4Department of Computer Science and Technology, East China Normal University, Shanghai, China
5National Engineering Laboratory for Wireless Security, Xi’an University of Posts and Telecommunications, Xi’an, China

Correspondence should be addressed to Yu Yu; kh.uyuy@uyuy and Xiangxue Li; nc.ude.unce.sc@ilxx

Received 15 November 2016; Accepted 12 June 2017; Published 14 September 2017

Academic Editor: Pedro García-Teodoro

Copyright © 2017 Gang Han 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. C. Carlet, “Boolean functions for cryptography and error correcting codes,” in Boolean Methods And Models in Mathematics, Computer Science, And Engineering, Y. Crama and P. Hammer, Eds., pp. 257–397, Cambridge University Press, Cambridge, UK, 2010. View at Google Scholar
  2. C. Carlet, D. K. Dalai, K. C. Gupta, and S. Maitra, “Algebraic immunity for cryptographically significant boolean functions: analysis and construction,” Institute of Electrical and Electronics Engineers. Transactions on Information Theory, vol. 52, no. 7, pp. 3105–3121, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  3. N. T. Courtois and W. Meier, “Algebraic attacks on stream ciphers with linear feedback,” in Advances in cryptology—EUROCRYPT 2003, vol. 2656 of Lecture Notes in Comput. Sci., pp. 345–359, Springer, Berlin, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  4. T. W. Cusick and P. Stanica, Cryptographic Boolean functions and applications, Academic Press, San Diego, CA, USA, 2009. View at MathSciNet
  5. T. Siegenthaler, “Correlation-immunity of nonlinear combining functions for cryptographic applications,” Institute of Electrical and Electronics Engineers. Transactions on Information Theory, vol. 30, no. 5, pp. 776–780, 1984. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. A. Canteaut and M. Trabbia, “Improved fast correlation attacks using parity-check equations of weight 4 and 5,” in Eurocrypt 2000, LNCS 1807, vol. 1807, pp. 573–588, Springer-Verlag, 2000. View at Google Scholar
  7. G. Z. Xiao and J. L. Massey, “A spectral characterization of correlation-immune combining functions,” Institute of Electrical and Electronics Engineers. Transactions on Information Theory, vol. 34, no. 3, pp. 569–571, 1988. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. S. Maitra and P. Sarkar, “Highly nonlinear resilient functions optimizing Siegenthaler's inequality,” in Advances in cryptology---{CRYPTO} '99 (SANta Barbara, {CA}), vol. 1666 of Lecture Notes in Comput. Sci., pp. 198–215, Springer, Berlin, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  9. C. Carlet and K. Feng, “An infinite class of balanced functions with optimal algebraic immunity, good immunity to fast algebraic attacks and good nonlinearity,” in Advances in cryptology---{ASIACRYPT} 2008, vol. 5350 of Lecture Notes in Comput. Sci., pp. 425–440, Springer, Berlin, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. N. T. Courtois and W. Meier, “Algebraic attacks on stream ciphers with linear feedback,” in Advances in cryptology—EUROCRYPT 2003, vol. 2656, pp. 345–359, Springer, Berlin, Germany, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  11. W. Meier, E. Pasalic, and C. Carlet, “Algebraic attacks and decomposition of Boolean functions,” in Advances in Cryptology—EUROCRYPT 2004, vol. 3027, pp. 474–491, Springer, Berlin, Germany, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  12. D. K. Dalai, S. Maitra, and S. Sarkar, “Basic theory in construction of boolean functions with maximum possible annihilator immunity,” Designs, Codes and Cryptography, vol. 40, no. 1, pp. 41–58, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  13. N. Li, L. Qu, W.-F. Qi, G. Feng, C. Li, and D. Xie, “On the construction of Boolean functions with optimal algebraic immunity,” IEEE Transactions on Information Theory, vol. 54, no. 3, pp. 1330–1334, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. N. Li and W.-F. Qi, “Construction and analysis of Boolean functions of 2t + 1 variables with maximum algebraic immunity,” in Advances in cryptology—ASIACRYPT 2006, vol. 4284, pp. 84–98, Springer, Berlin, Heidelberg, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  15. Z. Tu and Y. Deng, “A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity,” Designs, Codes and Cryptography. An International Journal, vol. 60, no. 1, pp. 1–14, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. X. Zeng, C. Carlet, J. Shan, and L. Hu, “More balanced Boolean functions with optimal algebraic immunity and good nonlinearity and resistance to fast algebraic attacks,” Institute of Electrical and Electronics Engineers. Transactions on Information Theory, vol. 57, no. 9, pp. 6310–6320, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. N. T. Courtois, “Fast algebraic attacks on stream ciphers with linear feedback,” in Advances in cryptology—CRYPTO 2003, vol. 2729 of Lecture Notes in Comput. Sci., pp. 176–194, Springer, Berlin, Germany, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  18. X. Li, Q. Zhou, H. Qian, Y. Yu, and S. Tang, “Balanced 2p-variable rotation symmetric Boolean functions with optimal algebraic immunity, good nonlinearity, and good algebraic degree,” Journal of Mathematical Analysis and Applications, vol. 403, no. 1, pp. 63–71, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  19. S.-S. Pan, X.-T. Fu, and W.-G. Zhang, “Construction of 1-resilient Boolean functions with optimal algebraic immunity and good nonlinearity,” Journal of Computer Science and Technology, vol. 26, no. 2, pp. 269–275, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. M. Liu, Y. Zhang, and D. Lin, “Perfect algebraic immune functions,” in Advances in cryptology—ASIACRYPT 2012, vol. 7658 of Lecture Notes in Comput. Sci., pp. 172–189, Springer, Heidelberg, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  21. P. Camion and A. Canteaut, “Correlation-immune and resilient functions over a finite alphabet and their applications in cryptography,” Designs, Codes and Cryptography, vol. 16, no. 2, pp. 121–149, 1999. View at Publisher · View at Google Scholar · View at MathSciNet
  22. J. Seberry, X.-M. Zhang, and Y. Zheng, “On constructions and nonlinearity of correlation immune functions (extended abstract),” in Eurocrypt 1993, LNCS 765, pp. 181–199, 1994. View at Google Scholar
  23. M. Hermelin and K. Nyberg, “Correlation Properties of the Bluetooth Combiner,” in Information Security and Cryptology - ICISC’99, vol. 1787, pp. 17–29, Springer Berlin Heidelberg, Berlin, Heidelberg, 2000. View at Publisher · View at Google Scholar
  24. P. Camion, C. Carlet, P. Charpin, and N. Sendrier, “On correlation-immune functions,” in Advances in cryptology—CRYPTO '91, vol. 576 of Lecture Notes in Comput. Sci., pp. 86–100, Springer, Berlin, Santa Barbara, CA, USA, 1992. View at Publisher · View at Google Scholar · View at MathSciNet
  25. M. Liu, D. Lin, and D. Pei, “Fast algebraic attacks and decomposition of symmetric Boolean functions,” Institute of Electrical and Electronics Engineers. Transactions on Information Theory, vol. 57, no. 7, pp. 4817–4821, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. D. Tang, C. Carlet, and X. Tang, “Highly nonlinear Boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks,” Institute of Electrical and Electronics Engineers. Transactions on Information Theory, vol. 59, no. 1, pp. 653–664, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. M. Liu and D. Lin, “Almost perfect algebraic immune functions with good nonlinearity,” in Proceedings of the 2014 IEEE International Symposium on Information Theory, ISIT 2014, pp. 1837–1841, usa, July 2014. View at Publisher · View at Google Scholar · View at Scopus
  28. Y. Zhang, M. Liu, and D. Lin, “On the immunity of rotation symmetric Boolean functions against fast algebraic attacks,” Discrete Applied Mathematics. The Journal of Combinatorial Algorithms, Informatics and Computational Sciences, vol. 162, pp. 17–27, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. T. Siegenthaler, “Decrypting a Class of Stream Ciphers Using Ciphertext Only,” IEEE Transactions on Computers, vol. C-34, no. 1, pp. 81–85, 1985. View at Publisher · View at Google Scholar · View at Scopus
  30. G. Cohen and J. P. Flori, “On a generalized combinatorial conjecture involving addition mod 2k,” Tech. Rep. 1., 2011. View at Google Scholar
  31. Y. Du, F. Zhang, and M. Liu, “On the resistance of Boolean functions against fast algebraic attacks,” in Information security and cryptology—ICISC 2011, vol. 7259 of Lecture Notes in Comput. Sci., pp. 261–274, Springer, Heidelberg, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  32. P. Hawkes and G. G. Rose, “Rewriting variables: the complexity of fast algebraic attacks on stream ciphers,” in Advances in cryptology—CRYPTO 2004, vol. 3152, pp. 390–406, Springer, Berlin, 2004. View at Publisher · View at Google Scholar · View at MathSciNet