一类多输出k阶拟Bent函数的构造及其密码学性质  

The Construction of a Class of Multi-output k-Order Quasi-Bent Functions and Their Cryptographic Properties

作　　者：刘志高[1] 张福泰[2] 

机构地区：[1]马鞍山职业技术学院,安徽马鞍山243031 [2]南京师范大学数学与计算机科学学院,江苏南京210097

出　　处：《佳木斯大学学报（自然科学版）》2010年第3期466-468,共3页Journal of Jiamusi University：Natural Science Edition

基　　金：安徽省高等学校省级优秀青年人才基金项目资助(2010SQRL223)

摘　　要：给出了多输出k阶拟Bent函数的一种构造方法.该方法通过组合两个无共同变元函数而构造出多输出k阶拟Bent函数.同时,还讨论了所构造的这类多输出k阶拟Bent函数的代数次数,非线性性,平衡性,扩散性及稳定性等密码学性质.这些性质来显示,多输出拟Bent函数是一类密码学性质良好的多输出函数.用作分组密码体制的非线性组合器时,能有效地抵抗差分分析和线性分析的攻击.另外,它还可应用于多输出前馈网等方面.A method to construct muhi -output k -order quasi -bent functions was presented, in which a class of k - order quasi - muhi - output bent functions was constructed by combining two functions without the same variables. Furthermore, some cryptographic properties of this kind of functions such as algebraic degree, nonlinearity, balance, propagation criterion and stability etc, were discussed. The discussion showed that the multi - output quasi - bent function was a class of multi - output functions with good eryptographic properties. This kind of functions could effectively resist differential analysis attack and linearity attack when it is used as nonlinear combiner in block ciphers. Furthermore, it could also be applied in multi -output feed -forward networks.

关 键 词：拟BENT函数 多输出拟Bent函数 Walsh循环谱 

分 类 号：O236.2[理学—运筹学与控制论] TN918.1[理学—数学]