|
- 2015
Hamming约束集的计数问题
|
Abstract:
摘要 构造一个应用于流密码并且具有良好性质的布尔函数是一个非常困难的问题. 最近, Tu和Deng基于一个关于二进制串分布(我们称之为Hamming约束集)的组合猜想的正确性, 构造了两类具有良好性质的布尔函数. 越来越多的学者致力于Tu-Deng猜想的证明. 本文用一种新方法给出某些Hamming约束集的计数公式, 从而部分地证明Tu-Deng猜想.
[1] | Carlet C, Ding C S. Highly nonlinear mappings[J]. Journal of Complexity, 2004, 20(2/3):205-244. |
[2] | Siegenthaler T. Correlation immunity of non-linear combining functions for cryptographic applications[J]. IEEE Transaction on Information Theory, 1984, 30:776-780. |
[3] | Langevin P, Leander G. Monomial bent functions and Stickelberger's theorem[J]. Finite Fields and Their Appilications, 2008, 14:727-742. |
[4] | Cohen G, Flori J P. On a general combinatorial conjecture invovling addition mod 2<sup>k</sup>-1[J/OL].[2014-12-20]. Cryptology ePrint Archive. http://eprint.iacr.org/2011/400.pdf. |
[5] | Matsui M. Linear cryptanalysis method for DES cipher[C]//Helleseth T. Advances in Cryptology-EUROCRYPT 1993. Springer, Berlin Heidelberg, 1994, 765:386-397. |
[6] | Courtois N T, Meier W. Algebraic attacks on stream ciphers with linear feedback[C]//Biham E. Advances in Cryptology-EUROCRYPT 2003. Springer, Berlin Heidelberg, 2003, 2656:345-359. |
[7] | Courtois N T. Fast algebraic attacks on stream ciphers with linear feedback[C]//Boneh D. Advances inCryptology-CRYPTO 2003. Springer, Berlin Heidelberg, 2003, 2729:176-194. |
[8] | Xie Y H, Hu L. A matrix construction of Boolean functions with maximum algebraic immunity[J]. Journal of Systems Science and Complexity, 2012, 25:792-801. |
[9] | Tu Z R, Deng Y P. A conjucture about binary strings and its applications on constructing Boolean functions with optimal algebraic immunity[J]. Designs, Codes and Cryptography, 2011, 60:1-14. |
[10] | Tu Z R, Deng Y P. Boolean functions optimizing most of the cryptographic criteria[J]. Discrete Applied Mathematics, 2012, 160:427-435. |
[11] | Flori J P, Randriam H, Cohen G, et al. On a conjecture about binary strings distribution[C]//Carlet C, Pott A. Sequences and Their Applications-SETA 2010. Springer, Berlin Heidelberg, 2010, 6338:346-358. |
[12] | <p> Golomb S W, Gong G. Signal design for good correlation for wireless communication, cryptography and radar[M]. New York:Cambridge University Press, 2005. |
[13] | Pei D Y, Qin W L. The correlation of a Boolean function with its variables[C]//Roy B, Okamoto E. Progress in Cryptology-INDOCRYPT 2000. Springer, Berlin Heidelberg, 2000, 1977:1-8. |
[14] | Katz J, Lindell Y. Introduction to modern cryptography[M]. Washington DC:CRC PRESS, 2007. |
[15] | Carlet C, Feng K Q. An infinite class of balanced functions with optimal algebraic immunity, good immunity to fast algebraic attacks and good nonlinearity[C]//Pieprzyk J. Advances in Cryptology-ASIACRYPT 2008. Springer, Berlin Heidelberg, 2008, 5350:425-440. |
[16] | Tu Z R. Design and analysis of Boolean functions under algebraic attacks[D]. Beijing:Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 2009 (in Chinese). |
[17] | Cusick T W, Li Y, Stanica P. On a combinatorial conjecture[J/OL].[2014-12-20]. Crypology ePrint Archive. http://eprint.iacr.org/2009/554.pdf. |
[18] | Huang K, Li C, Fu S J. Note on the Tu-Deng conjecture[J]. Computer Science, 2012, 39:6-9 (in Chinese).</p> |