A construction of Boolean functions with good cryptographic properties

References

• A. Braeken and B. Preneel, On the algebraic immunity of symmetric Boolean functions, in Progress in Cryptology – Indocrypt 2005, S. Maitra, C.E.V. Madhavan, and R. Venkatesan, eds., LNCS 3797, Springer-Verlag, Bangalore, 2005, pp. 35–48.
   Google Scholar
• R.E. Bryant, On the complexity of VLSI implementation and graph representations of Boolean functions with application to integer multiplication, IEEE Trans. Comput. 40(2) (1991), pp. 205–213. doi: 10.1109/12.73590
   Web of Science ®Google Scholar
• R.E. Bryant, Symbolic manipulation with ordered binary decision diagrams, ACM Comput. Surv. 24(3) (1992), pp. 293–318. doi: 10.1145/136035.136043
   Web of Science ®Google Scholar
• C. Carlet, Comment on constructions of cryptographically significant Boolean functions using primitive polynomials, IEEE Trans. Inform. Theory 57(7) (2011), pp. 4852–4853. doi: 10.1109/TIT.2011.2146170
   Web of Science ®Google Scholar
• C. Carlet, On secondary constructions of resilient and bent functions, Coding, Cryptography and Combinatorics, Progress in Computer Science and Applied Logic, Vol. 23, Birkhauser-Verlag, Basel, 2004, pp. 3–28.
   Google Scholar
• C. Carlet, On the higher order nonlinearities of algebraic immune functions, in Advances in Cryptology – CRYPTO 2006, C. Dwork, ed., LNCS 4117, Springer-Verlag, Santa Barbara, CA, 2006, pp. 584–601.
   Google Scholar
• C. Carlet, D.K. Dalai, K.C. Gupta, and S. Maitra, Algebraic immunity for cryptographically significant Boolean functions: Analysis and construction, IEEE Trans. Inform. Theory 52(7) (2006), pp. 3105–3121. doi: 10.1109/TIT.2006.876253
   Web of Science ®Google Scholar
• C. Carlet, H. Dobbertin, and G. Leander, Normal extensions of bent functions, IEEE Trans. Inform. Theory 50(11) (2004), pp. 2880–2885. doi: 10.1109/TIT.2004.836681
   Web of Science ®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.P. Pieprzyk, ed., LNCS 5350, Springer-Verlag, Melbourne, Australia, 2008, pp. 425–440.
   Google Scholar
• C. Carlet and K. Feng, An infinite class of balanced vectorial Boolean functions with optimum algebraic immunity and good nonlinearity, in IWCC 2009, Y.M. Chee, C. Li, S. Ling, H. Wang, and C. Xing, eds., LNCS 5557, Springer-Verlag, Zhangjiajie, China, 2009, pp. 1–11.
   Google Scholar
• N. Courtois, Fast algebraic attacks on stream ciphers with linear feedback, in Advances in Cryptology – CRYPTO 2003, D. Boneh, ed., LNCS 2729, Springer-Verlag, Santa Barbara, CA, 2003, pp. 176–194.
   Google Scholar
• N. Courtois and W. Meier, Algebraic attacks on stream ciphers with linear feedback, in Advances in Cryptology – EUROCRYPT 2003, E. Biham, ed., LNCS 2656, Springer-Verlag, Warsaw, Poland, 2003, pp. 345–359.
   Google Scholar
• T.W. Cusick and P. Stănică, Cryptographic Boolean Functions and Applications, Elsevier, Academic Press, San Diego, CA, 2009.
   Google Scholar
• D.K. Dalai, K.C. Maitra, and S. Maitra, Cryptographically significant Boolean functions: Construction and analysis in terms of algebraic immunity, in Proceedings of FSE 2005, H. Gilbert and H. Handschuh, eds., LNCS 3557, Springer-Verlag, Paris, 2005, pp. 98–111.
   Google Scholar
• D.K. 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. doi: 10.1007/s10623-005-6300-x
   Web of Science ®Google Scholar
• S. Gangopadhyay and D. Sharma, On construction of non-normal Boolean functions, Aust. J. Comb. 38 (2007), pp. 267–272.
   Google Scholar
• P. Hawkes and G.G. Rose, Rewriting variables: The complexity of fast algebraic attacks on stream ciphers, in Advances in Cryptology – CRYPTO 2004, M. Franklin, ed., LNCS 3152, Springer-Verlag, Santa Barbara, CA, 2004, pp. 390–406.
   Google Scholar
• M. Krause, BDD-based cryptanalysis of keystream generators, in Advances in Cryptology – EUROCRYPT 2002, L.R. Knudsen, ed., LNCS 2332, Springer-Verlag, Amsterdam, The Netherlands, 2002, pp. 222–237.
   Google Scholar
• M. Krause and D. Stegemann, Reducing the space complexity of BDD-based attacks on keystream generators, Fast Software Encryption, LNCS 4047, 13th International Workshop, FSE 2006, Springer, Graz, Austria, 15–17 March 2006, pp. 163–178.
   Google Scholar
• 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, X. Lai, and K. Chen, eds., LNCS 4284, Springer-Verlag, Shanghai, China, 2006, pp. 84–98.
   Google Scholar
• N. Li, L. Qu, W. Qi, G. Feng, C. Li, and D.Q. Xie, On the construction of Boolean functions with optimal algebraic immunity, IEEE Trans. Inform. Theory 54(3) (2008), pp. 1330–1334. doi: 10.1109/TIT.2007.915914
   Web of Science ®Google Scholar
• M. Liu, Y. Zhang, and D. Lin, Perfect algebraic immune functions, in Advances in Cryptology – ASIACRYPT 2012, X. Wang, and K. Sako, eds., LNCS 7658, Springer-Verlag, Beijing, China, 2012, pp. 172–189.
   Google Scholar
• M. Lobanov, Tight bound between nonlinearity and algebraic immunity, Cryptology, ePrint Archive, 2005/441. Available at eprint.iacr.org/2005/441
   Google Scholar
• W. Meier and O. Staffelbach, Fast correlation attacks on stream ciphers, in Advances in Cryptology – EUROCRYPT 1988, D. Barstow, W. Brauer, P. Brinch Hansen, D. Gries, D. Luckham, C. Moler, A. Pnueli, G. Seegmüller, J. Stoer, N. Wirth, and C.G. Günther, eds., LNCS 330, Springer-Verlag, Davos, Switzerland, 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.L. Camenisch, eds., LNCS 3027, Springer-Verlag, Interlaken, Switzerland, 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. Inform. Theory 54(8) (2008), pp. 3656–3662. doi: 10.1109/TIT.2008.926360
   Web of Science ®Google Scholar
• E. Pasalic, A design of Boolean functions resistant to (fast) algebraic cryptanalysis with efficient implementation, Cryptogr. Commun. 4(1) (2012), pp. 25–45. doi: 10.1007/s12095-011-0057-z
   Web of Science ®Google Scholar
• E. Pasalic, Almost fully optimized infinite classes of Boolean functions resistant to (fast) algebraic cryptanalysis, in Proceedings of ICISC 2008, P.J. Lee, and J.H. Cheon, eds., LNCS 5461, Springer-Verlag, Seoul, Korea, 2009, pp. 399–414.
   Google Scholar
• E. Pasalic, S. Maitra, T. Johansson, and P. Sarkar, New constructions of resilient and correlation immune Boolean functions achieving upper bounds on nonlinearity, Workshop on Coding and Cryptography – WCC2001, Paris, France, 8–12 January 2001 [Published in Electronic Notes in Discrete Mathematics, Amsterdam, The Netherlands: Elsevier Science, Vol. 6, 2001].
   Google Scholar
• E. Pasalic and Y. Wei, On the construction of cryptographically significant Boolean functions using objects in projective geometry spaces, IEEE Trans. Inform. Theory 58(10) (2012), pp. 6681–6693. doi: 10.1109/TIT.2012.2204231
   Web of Science ®Google Scholar
• L. Qu, K. Feng, F. Liu, and L. Wang, Constructing symmetric Boolean functions with maximum algebraic immunity, IEEE Trans. Inform. Theory 55(5) (2009), pp. 2406–2412. doi: 10.1109/TIT.2009.2015999
   Web of Science ®Google Scholar
• P. Rizomiliotis, On the resistance of Boolean functions against algebraic attacks using univariate polynomial representation, IEEE Trans. Inform. Theory 56(8) (2010), pp. 4014–4024. doi: 10.1109/TIT.2010.2050801
   Web of Science ®Google Scholar
• D. Stegemann, Extended BDD-based cryptanalysis of keystream generators, 14th International Workshop on Selected Areas in Cryptography, SAC 2007, LNCS 4876, Springer, Ottawa, Canada, 16–17 August 2007, pp. 17–35.
   Google Scholar
• C. Tan and S. Goh, Several classes of even-variable balanced Boolean functions with optimal algebraic immunity, IEICE Trans. E94.A(1) (2011), pp. 165–171. doi: 10.1587/transfun.E94.A.165
   Web of Science ®Google Scholar
• D. Tang, C. Carlet, and X. Tang, Highly nonlinear Boolean functions with optimal algebraic immunity and good behavior against fast algebraic attacks, IEEE Trans. Inform. Theory 59(1) (2013), pp. 653–664. doi: 10.1109/TIT.2012.2217476
   Web of Science ®Google Scholar
• Z. Tu and Y. Deng, A conjecture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity, Des. Codes Cryptogr. 60(1) (2011), pp. 1–14. doi: 10.1007/s10623-010-9413-9
   Web of Science ®Google Scholar
• Q. Wang, T. Johansson, and H. Kan, Some results on fast algebraic attacks and higher-order non-linearities, IET Inform. Secur. 6(1) (2012), pp. 41–46. doi: 10.1049/iet-ifs.2011.0090
   Web of Science ®Google Scholar
• Q. Wang, C. Carlet, P. Stănică, and C.-H. Tan, Cryptographic properties of the hidden weighted bit function, Discrete Appl. Math., in press. Available at http://dx.doi.org/10.1016/j.dam.2014.01.010
   Web of Science ®Google Scholar
• W. Wang, M. Liu, and Y. Zhang, Comments on ‘A design of Boolean functions resistant to (fast) algebraic cryptanalysis with efficient implementation’, Cryptogr. Commun. 5(1) (2013), pp. 1–6. doi: 10.1007/s12095-012-0063-9
   Web of Science ®Google Scholar
• 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, IEEE Trans. Inform. Theory 57(9) (2011), pp. 6310–6320. doi: 10.1109/TIT.2011.2109935
   Web of Science ®Google Scholar