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 cryptog...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 St^nic~ 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
From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity（AI） of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary conditio...From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity（AI） of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed.展开更多
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 St^nic~ 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 the National Natural Science Foundation of China (10871068,61021004)DNRF-NSFC Joint (11061130539)
文摘From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity（AI） of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed.
