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Asymptotic lower bound on the algebraic immunity of random balanced multi-output Boolean functions
| 1. | LAGA, Universities of Paris 8 and Paris 13, CNRS, France |
| 2. | Department of Algebraic and number theory, University of Sciences and Technology, Houari Boumedienne, Algiers, Algeria, and University of Kasdi Merbah, Ouargla, Algeria |
References:
| [1] |
F. Armknecht, C. Carlet, P. Gaborit, S. Kunzli, W. Meier and O. Ruatta, Efficient computation of algebraic immunity for algebraic and fast algebraic attacks, in "Advances in Cryptology-EUROCRYPT 2006,'' Springer-Verlag, (2006), 147-164. |
| [2] |
C. Carlet, A method of construction of balanced functions with optimum algebraic immunity, in "Proceedings of the International Workshop on Coding and Cryptography,'' World Scientific Publishing Co., 2008. |
| [3] |
C. Carlet, Boolean functions for cryptography and error correcting codes, in "Boolean Models and Methods in Mathematics, Computer Science, and Engineering'' (eds. Y. Crama and P. Hammer), Cambridge Univ. Press, (2010), 257-397. |
| [4] |
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,'' Springer-Verlag, (2008), 425-440. |
| [5] |
N. Courtois and W. Meier, Algebraic attacks on stream ciphers with linear feedback, in "Proceedings of Eurocrypt 2003,'' Springer, (2003), 345-359; An extended version is available at http://www.cryptosystem.net/stream/ |
| [6] |
D. K. Dalai, K. C. Gupta and S. Maitra, Cryptographically significant Boolean functions: Construction and analysis in terms of algebraic immunity, in "Fast Software Encryption 2005,'' Springer, (2005), 98-111.
doi: 10.1007/11502760_7. |
| [7] |
F. Didier, A new bound on the block error probability after decoding over the erasure channel, IEEE Trans. Inform. Theory, 52 (2006), 4496-4503.
doi: 10.1109/TIT.2006.881719. |
| [8] |
K. Feng, Q. Liao and J. Yang, Maximal values of generalized algebraic immunity, Des. Codes Crypt., 50 (2009), 243-252.
doi: 10.1007/s10623-008-9228-0. |
| [9] |
R. G. Gallager, "Information Theory and Reliable Communication,'' John Wiley and Sons Inc., New York, 1968. |
| [10] |
M. Liu, Y. Zhang and D. Lin, Perfect algebraic immune functions, in "Advances in Cryptology,'' Springer, (2012), 172-189. |
| [11] |
F. J. Macwilliams And N. J. Sloane, "The theory of Error-Correcting Codes,'' Amsterdam, North Holland, 1977. |
| [12] |
W. Meier, E. Pasalic and C. Carlet, Algebraic attacks and decomposition of Boolean functions, in "Advances in Cryptology EUROCRYPT 2004,'' Springer-Verlag, (2004), 474-491.
doi: 10.1007/978-3-540-24676-3_28. |
| [13] |
V. K. Wei, Generalized Hamming weights for linear codes, IEEE Trans. Inform. Theory, 37 (1991), 1412-1418.
doi: 10.1109/18.133259. |
show all references
References:
| [1] |
F. Armknecht, C. Carlet, P. Gaborit, S. Kunzli, W. Meier and O. Ruatta, Efficient computation of algebraic immunity for algebraic and fast algebraic attacks, in "Advances in Cryptology-EUROCRYPT 2006,'' Springer-Verlag, (2006), 147-164. |
| [2] |
C. Carlet, A method of construction of balanced functions with optimum algebraic immunity, in "Proceedings of the International Workshop on Coding and Cryptography,'' World Scientific Publishing Co., 2008. |
| [3] |
C. Carlet, Boolean functions for cryptography and error correcting codes, in "Boolean Models and Methods in Mathematics, Computer Science, and Engineering'' (eds. Y. Crama and P. Hammer), Cambridge Univ. Press, (2010), 257-397. |
| [4] |
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,'' Springer-Verlag, (2008), 425-440. |
| [5] |
N. Courtois and W. Meier, Algebraic attacks on stream ciphers with linear feedback, in "Proceedings of Eurocrypt 2003,'' Springer, (2003), 345-359; An extended version is available at http://www.cryptosystem.net/stream/ |
| [6] |
D. K. Dalai, K. C. Gupta and S. Maitra, Cryptographically significant Boolean functions: Construction and analysis in terms of algebraic immunity, in "Fast Software Encryption 2005,'' Springer, (2005), 98-111.
doi: 10.1007/11502760_7. |
| [7] |
F. Didier, A new bound on the block error probability after decoding over the erasure channel, IEEE Trans. Inform. Theory, 52 (2006), 4496-4503.
doi: 10.1109/TIT.2006.881719. |
| [8] |
K. Feng, Q. Liao and J. Yang, Maximal values of generalized algebraic immunity, Des. Codes Crypt., 50 (2009), 243-252.
doi: 10.1007/s10623-008-9228-0. |
| [9] |
R. G. Gallager, "Information Theory and Reliable Communication,'' John Wiley and Sons Inc., New York, 1968. |
| [10] |
M. Liu, Y. Zhang and D. Lin, Perfect algebraic immune functions, in "Advances in Cryptology,'' Springer, (2012), 172-189. |
| [11] |
F. J. Macwilliams And N. J. Sloane, "The theory of Error-Correcting Codes,'' Amsterdam, North Holland, 1977. |
| [12] |
W. Meier, E. Pasalic and C. Carlet, Algebraic attacks and decomposition of Boolean functions, in "Advances in Cryptology EUROCRYPT 2004,'' Springer-Verlag, (2004), 474-491.
doi: 10.1007/978-3-540-24676-3_28. |
| [13] |
V. K. Wei, Generalized Hamming weights for linear codes, IEEE Trans. Inform. Theory, 37 (1991), 1412-1418.
doi: 10.1109/18.133259. |
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