Construction of balanced even-variable Boolean functions with optimal algebraic immunity

References

• A. Canteaut and M. Videau, Symmetric Boolean functions, IEEE Trans. Inf. Theory 51(8) (2005), pp. 2791–2811.
   Web of Science ®Google Scholar
• C. Carlet, A method of construction of balanced functions with optimum algebraic immunity, International Workshop on Coding and Cryptology, Versailles (France), 2007, pp. 25–43.
   Google Scholar
• C. Carlet, A survey on nonlinear Boolean functions with optimal algebraic immunity suitable for stream ciphers, Vietnam J. Math. 41(4) (2013), pp. 527–541.
   Google Scholar
• 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, J. Pieprzyk, ed., Lecture Notes in Computer Science, Vol. 5350, Springer, Berlin, 2008, pp. 425–440.
   Google Scholar
• C. Carlet, X. Zeng, C. Li and L. Hu, Further properties of several classes of Boolean functions with optimum algebraic immunity, Des., Codes Cryptogr. 52(3) (2009), pp. 303–338.
   Web of Science ®Google Scholar
• N. Courtois, Fast algebraic attacks on stream ciphers with linear feedback, in Advances in Cryptology-CRYPTO 2003, D. Boneh, ed., Lecture Notes in Computer Science, Vol. 2729, Springer, Berlin, 2003, pp. 176–194.
   Google Scholar
• N. Courtois, Cryptanalysis of sfinks, in ICISC 2005, D.H. Won, S. Kim, eds., Lecture Notes in Computer Science, Vol. 3935, Springer, Berlin Heidberg, 2006, pp. 261–269.
   Google Scholar
• N. Courtois and W. Meier, Algebraic attacks on stream ciphers with linear feedback, in EUROCRYPT 2003, E. Biham, ed., Lecture Notes in Computer Science, Vol. 2656, Springer, Berlin, 2003, pp. 345–359.
   Google Scholar
• D. Dalai, S. Maitra and S. Sarkar, Basic theory in construction of Boolean functions with maximum possible annihilator immunity, Des., Codes Cryptogr. 40(1) (2006), pp. 41–58.
   Web of Science ®Google Scholar
• C. Ding, G. Xiao and W. Shan, The Stability Theory of Stream Ciphers, Lecture Notes in Computer Science, Vol. 561, Springer, Berlin, 1991, pp. 70–80.
   Google Scholar
• M. Lobanov, Tight bound between nonlinearity and algebraic immunity, Available at http://eprint.iacr.org/2005/441.
   Google Scholar
• F.J. MacWillams and N.J.A. Sloane, The Theory of Error Correcting Codes, North-Holland, Amsterdam, 1977.
   Google Scholar
• W. Meier and O. Staffelbach, Fast correlation attacks on stream ciphers, in Advances in Cryptology-EUROCRYPT 1988, C.G. Gunther, ed., Lecture Notes in Computer Science, Vol. 330, Springer, Berlin, 1988, pp. 301–314.
   Google Scholar
• W. Meier, E. Pasalic and C. Carlet, Algebraic attacks and decomposition of Boolean functions, in Advances in Cryptology-EUROCRYPT 2004, C. Cachin and J. Camenisch, eds., Lecture Notes in Computer Science, Vol. 3027, Springer, Berlin, 2004, pp. 474–491.
   Google Scholar
• S. Mesnager, Improving the lower bound on the higher order nonlinearity of Boolean functions with prescribed algebraic immunity, IEEE Trans. Inf. Theory 54 (2008), pp. 3656–3662.
   Web of Science ®Google Scholar
• W. Mihaljevic and H. Imai, Cryptanalysis of Toyocrypt-HS1 stream cipher, IEICE T. Fund. Electr. 85-A (2002), pp. 66–73.
   Google Scholar
• D. Muller, Application of Boolean algebra to switching circuit design and to error detection, IEEE Trans. Comput. 3 (1954), pp. 6–12.
   Google Scholar
• S. Reed, A class of multiple-error-correcting codes and the decoding scheme, IEEE Trans. Inf. Theory 4 (1954), pp. 38–49.
   Google Scholar
• S. Sarkar and S. Maitra, Construction of rotation symmetric Boolean functions with optimal algebraic immunity, Comput. Syst. 12 (2009), pp. 267–284.
   Google Scholar
• P. Savicky, On the bent Boolean functions that are symmetric, Eur. J. Combin. 15 (1994), pp. 407–410.
   Web of Science ®Google Scholar
• W. Su, X. Zeng and L. Hu, Construction of 1-resilient Boolean functions with optimum algebraic immunity, Int. J. Comput. Math. 88(2) (2011), pp. 222–238.
   Web of Science ®Google Scholar
• S. Su, X. Tang and X. Zeng, A systematic method of constructing Boolean functions with optimal algebraic immunity based on the generator matrix of Reed–Muller code, Des., Codes Cryptogr. 72(3) (2014), pp. 653–673.
   Web of Science ®Google Scholar
• Y. Sun, L. Li and B. Yang, Constructions of balanced Boolean functions with high nonlinearity and high algebraic degree, Int. J. Comput. Math. (2013), DOI:10.1080/00207160.2013.770147.
   Web of Science ®Google Scholar
• Q. Wang, T. Johansson and H. Kan, Some results on fast algebraic attacks and higher order nonlinearities, IET Inf. Secur. 6(1) (2012), pp. 41–46.
   Web of Science ®Google Scholar