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 discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the d...This paper discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the degree of completeness and other cryptographic criteria. For resilient Boolean functions, a method to enhance the degree of completeness is proposed, while the nonlinearity and the algebraic degree do not decrease. Moreover, two constructions of resilient functions are provided, which have optimal degree of completeness, high nonlinearity, and high algebraic degree.展开更多
Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered： high nonl...Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered： high nonlinearity, balancedness, strict avalanche criterion, and global avalanche characteristics. The trade-off among these criteria is a difficult problem and has attracted many researchers. In this paper, two construction methods are provided to obtain balanced Boolean functions with high nonlinearity. Besides, the constructed functions satisfy strict avalanche criterion and have good global avalanche characteristics property. The algebraic immunity of the constructed functions is also considered.展开更多
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 Key Basic Research Program of China(No.2013CB834204)
文摘This paper discusses the degree of completeness of cryptographic functions, which is one of the cryptographic criteria should be considered in the design of stream ciphers. We establish the relationships between the degree of completeness and other cryptographic criteria. For resilient Boolean functions, a method to enhance the degree of completeness is proposed, while the nonlinearity and the algebraic degree do not decrease. Moreover, two constructions of resilient functions are provided, which have optimal degree of completeness, high nonlinearity, and high algebraic degree.
基金This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 61373008, 11201359, 61562069）, the Natural Science Basic Research Plan in Shaanxi Province of China （Grant No. 2012JM8013）, the 111 Project （Grant No. B08038）, and the Science and Technology on Communication Security Laboratory （Grant No. 9140C110203140C11049）.
文摘Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered： high nonlinearity, balancedness, strict avalanche criterion, and global avalanche characteristics. The trade-off among these criteria is a difficult problem and has attracted many researchers. In this paper, two construction methods are provided to obtain balanced Boolean functions with high nonlinearity. Besides, the constructed functions satisfy strict avalanche criterion and have good global avalanche characteristics property. The algebraic immunity of the constructed functions is also considered.
