Maiorana-McFarland's Bent函数零化子空间维数  

Dimensions of Vector Spaces of Annihilators for Maiorana-McFarland's Bent Functions

作　　者：张凤荣[1,2] 胡予濮[2] 马华[3] 谢敏[2] 周宇[4] 

机构地区：[1]中国矿业大学计算机科学与技术学院,江苏徐州221116 [2]计算机网络与信息安全教育部重点实验室(西安电子科技大学),西安710071 [3]西安电子科技大学理学院,西安710071 [4]中国电子科技集团公司第三十研究所保密通信重点实验室,成都610041

出　　处：《计算机研究与发展》2012年第6期1243-1247,共5页Journal of Computer Research and Development

基　　金：国家自然科学基金项目(60833008;60832001);国家"九七三"重点基础研究发展计划基金项目(2007CB311201);保密通信重点实验室基金项目(9140C110201110C1102);中央高校基本科研业务费专项资金项目(K50510010015)

摘　　要：在流密码和分组密码的设计中,所用布尔函数应该具有好的密码学性质来抵抗已知的各种有效攻击.布尔函数的低次零化子空间维数与其补函数低次零化子空间维数之和是评价该函数抵抗代数攻击能力的一个重要参数.根据Maiorana-McFarlands(M-M)Bent函数和布尔置换之间的一一对应关系,给出了一组布尔函数组并证明了它们是线性无关的.借助所给的线性无关布尔函数组和布尔置换中向量函数非零线性组合均是平衡函数的特性,给出了一类特殊M-M Bent函数低次零化子空间的维数与其补函数低次零化子空间的维数之和的一个上限.就这类特殊M-M Bent函数而言,该上限低于已知的限.进一步给出了适合所有M-M Bent函数的新上限.It is known that Boolean functions used in stream and block ciphers should have good cryptographic properties to resist the existing efficient attacks. The number of linearly independent low degree annihilators of a given Boolean function and of its complement function is an important parameter for evaluating the complexity of algebraic attacks on the systems using this Boolean function. The dimensions of vector spaces of annihilators for Boolean functions have received much attention in Cryptographic literature. According to one-to-one correspondence between Maiorana- McFarland＇s （M-M） Bent functions and Boolean permutations, a family of Boolean functions are presented. Moreover, it is shown that the presented family of Boolean functions is linearly independent. In addition~ it is known that every nonzero linear combination of a Boolean permutation is a balanced Boolean function. On the basis of the above facts, a new upper bound on the dimension of vector spaces of annihilators with prescribed degrees of a special M-M Bent function and of its complement is proposed. As far as the special M-M Bent functions are concerned, the new upper bound is less than the known ones. Furthermore, the new upper bound for all M-M Bent functions can be obtained.

关 键 词：流密码 布尔函数 BENT函数 代数次数 代数免疫度 

分 类 号：TN918.1[电子电信—通信与信息系统] TP309[电子电信—信息与通信工程]