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.
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