Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric（RotS） function is special. For a Rots n variables function f（x1, x2, …, xn） we have f（ρn^k （x1, x2, …x...Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric（RotS） function is special. For a Rots n variables function f（x1, x2, …, xn） we have f（ρn^k （x1, x2, …xn））=f（x1, x2, …, xn） for k=0, 1, …, n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.展开更多
For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions.The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptogr...This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions.The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties.The proposed method is algebraic in nature.As a by-product,the authors correct and generalize the corresponding results of Stanica and Maitra(2008).Further,the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li(2006),and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky(1994).展开更多
It is proved that if a nonlinear system possesses some group-symmetry, then under certain transversality it admits solutions with the corresponding symmetry. The method is due to Mawhin＇s guiding function one.
基金Supported by the National Natural ScienceFoundation of China (90104035)
文摘Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric（RotS） function is special. For a Rots n variables function f（x1, x2, …, xn） we have f（ρn^k （x1, x2, …xn））=f（x1, x2, …, xn） for k=0, 1, …, n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.
基金Supported by the National Natural Science Foundation of China ( 60603012)the Foundation of Hubei Provincial Department of Education, China (D200610004)
文摘For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
基金supported by the National Natural Science Foundation of China under Grant Nos.11071285 and 61121062973 Project under Grant No.2011CB302401the National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences
文摘This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions.The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties.The proposed method is algebraic in nature.As a by-product,the authors correct and generalize the corresponding results of Stanica and Maitra(2008).Further,the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li(2006),and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky(1994).
基金Supported by National Basic Research Program of China(grant No.2013CB834100)National Natural Science Foundation of China(grant No.11171132),and National Natural Science Foundation of China(grant No.11201173)
文摘It is proved that if a nonlinear system possesses some group-symmetry, then under certain transversality it admits solutions with the corresponding symmetry. The method is due to Mawhin＇s guiding function one.
