The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this ...The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.展开更多
Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr（R（x）） with n=3r or 4r variables, where r 〉 1 is ...Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr（R（x）） with n=3r or 4r variables, where r 〉 1 is an odd integer. Our results can be used to determine the numbers of non-zero Walsh spectrum values and the nonlinearities of these functions, and estimate their resiliency orders. Especially, the value distributions can be used to deduce the tight lower bounds of the second order nonlinearity of two classes of Boolean functions. It is demonstrated that our bounds are better than the previously obtained bounds.展开更多
To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation o...To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.展开更多
Chaos control in random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase.However,controlled nodes are only viewed as passive blocks to prevent perturbation spre...Chaos control in random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase.However,controlled nodes are only viewed as passive blocks to prevent perturbation spread.We propose a new control method in which controlled nodes can exert an active impact on the network.Controlled nodes and frozen values are deliberately selected according to the information of connection and Boolean functions.Simulation results show that the number of nodes needed to achieve control is largely reduced compared to the previous method.Theoretical analysis is also given to estimate the least fraction of nodes needed to achieve control.展开更多
低延迟分组密码的设计是目前密码学研究中的热点之一,其中低延迟S盒的构造是设计中的重要研究方向.本文基于低延迟门电路和两层树型结构,搜索不同延迟水平下具有一定密码学性质的低延迟平衡布尔函数及其拓展比特置换等价类;基于将低延...低延迟分组密码的设计是目前密码学研究中的热点之一,其中低延迟S盒的构造是设计中的重要研究方向.本文基于低延迟门电路和两层树型结构,搜索不同延迟水平下具有一定密码学性质的低延迟平衡布尔函数及其拓展比特置换等价类;基于将低延迟布尔函数作为分量布尔函数构造向量布尔函数的方法,本文构造得到了不同延迟水平下的低延迟S盒,并给出延迟性质和硬件实现面积具有优势的S盒实例;此外,本文对低延迟的S盒集合与逆S盒集合匹配搜索具有双向低延迟性质的S盒,给出搜索得到的实例.与PRINCE、MANTIS等其他低延迟分组密码中使用的4 bit S盒相比,本文构造的低延迟S盒在延迟水平上相较MANTIS降低了20%,与PRINCE相比降低了33%,在硬件实现面积上相较MANTIS减少了6.68%,与PRINCE相比减少了17.69%.展开更多
文摘The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class.
基金Acknowledgments This work was supported in part by 973 Project of China （No. 2007CB311201）, the Notional Natural Science Foundation（No. 60833008, 60803149）, and the Foundation of Guangxi Key Laboratory of Information and Communication（No. 20902）.
文摘Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr（R（x）） with n=3r or 4r variables, where r 〉 1 is an odd integer. Our results can be used to determine the numbers of non-zero Walsh spectrum values and the nonlinearities of these functions, and estimate their resiliency orders. Especially, the value distributions can be used to deduce the tight lower bounds of the second order nonlinearity of two classes of Boolean functions. It is demonstrated that our bounds are better than the previously obtained bounds.
基金This work was supported by the National Natural Science Foundation of China under Grants No. 61103191, No. 61070215 the Funds of Key Lab of Fujian Province University Network Security and Cryptology under Crant No. 2011003 and the Open Research Fund of State Key Laboratory of Inforrmtion Security.
文摘To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity.
基金Supported by the National Natural Science Foundation of China under Grant Nos 60874018,60736022 and 60821091.
文摘Chaos control in random Boolean networks is implemented by freezing part of the network to drive it from chaotic to ordered phase.However,controlled nodes are only viewed as passive blocks to prevent perturbation spread.We propose a new control method in which controlled nodes can exert an active impact on the network.Controlled nodes and frozen values are deliberately selected according to the information of connection and Boolean functions.Simulation results show that the number of nodes needed to achieve control is largely reduced compared to the previous method.Theoretical analysis is also given to estimate the least fraction of nodes needed to achieve control.
文摘低延迟分组密码的设计是目前密码学研究中的热点之一,其中低延迟S盒的构造是设计中的重要研究方向.本文基于低延迟门电路和两层树型结构,搜索不同延迟水平下具有一定密码学性质的低延迟平衡布尔函数及其拓展比特置换等价类;基于将低延迟布尔函数作为分量布尔函数构造向量布尔函数的方法,本文构造得到了不同延迟水平下的低延迟S盒,并给出延迟性质和硬件实现面积具有优势的S盒实例;此外,本文对低延迟的S盒集合与逆S盒集合匹配搜索具有双向低延迟性质的S盒,给出搜索得到的实例.与PRINCE、MANTIS等其他低延迟分组密码中使用的4 bit S盒相比,本文构造的低延迟S盒在延迟水平上相较MANTIS降低了20%,与PRINCE相比降低了33%,在硬件实现面积上相较MANTIS减少了6.68%,与PRINCE相比减少了17.69%.
