零化子

Besides, through the method of concatenation, the upper bound of algebraic immunity and the form of the annihilators of any generalized boolean function were also determined.

此外，还通过级联函数的方法确定了任意广义布尔函数的代数免疫的上界和零化子的形式。

From this,two algorithms to find low degree annihilators of a Boolean function are present:complete searching and stochastic searching.The complete one can not only get all the low degree annihilators of a Boolean function,but also get the algebraic immunity of the function.

利用完全搜索法可以得到布尔函数的所有低次零化子，同时还可以确定该布尔函数的代数免疫度；利用随机搜索法能快速得到布尔函数的任意一个低次零化子。

Balls can be killed with annihilator bonuses, so collect as many of them as you can to prolong your game.

球可以被杀死的零化子奖金，所以收集到许多人因为你可以延长你的游戏。

If the worst comes to the worst, use the portable annihilator in your helmet.

如果最坏的最坏的情况下，使用便携式零化子您头盔。

Balls can be killed with annihilator bonuses, so collect as many of them as you can to prolong you r game.

球可以被杀死的零化子奖金，所以收集到许多人因为你可以延长你的游戏。

Theorem 2.2.44 Let R be a reduced left morphic ring, if R satisfies ascending chain condition on right annihilators, then every maxmal left ideal of R is a direct summmand of R.

定理2.2.44设R是约化的左morphic环，若R对右零化子满足升链条件，则R的每一个极大左理想L都是R的一个直和项。

At last,we give the definition of FGT rings which is the extension of cogenerator rings.

在第二章中，我们由FGT -内射模的启发引入了CT -内射模的概念，在这一章我们知道ann -自内射环其实就是CT -内射环，只是ann -自内射环是从零化子的角度来讨论，而CT -内射是从循环无挠模的角度来进行讨论的，同时也给出了一些等价条件。

Moreover, we define weak principally quasi-injective modules and study Jacobson radical of endomorphism ring of weak principally quasi-injective modules.

另外我们还在主拟内射R-模的基础上定义了弱主拟内射R-模，利用零化子对弱主拟内射模上自同态环的Jacobson根的性质进行了讨论。

Using the concept of Boolean functions and combinatorics theory comprehensively, we investigate the construction on annihilators of Boolean functions and the algebraic immunity of symmetric Boolean functions in cryptography:Firstly, we introduce two methods of constructing the annihilators of Boolean functions, Construction I makes annihilators based on the minor term expression of Boolean function, meanwhile we get a way to judge whether a Boolean function has low degree annihilators by feature matrix. In Construction II, we use the subfunctions to construct annihilators, we also apply Construction II to LILI-128 and Toyocrypt, and the attacking complexity is reduced greatly. We study the algebraic immunitiy of (5,1,3,12) rotation symmetric staturated best functions and a type of constructed functions, then we prove that a new class of functions are invariants of algebraic attacks, and this property is generalized in the end.Secondly, we present a construction on symmetric annihilators of symmetric Boolean functions.

本文主要利用布尔函数的相关概念并结合组合论的相关知识，对密码学中布尔函数的零化子构造问题以及对称布尔函数代数免疫性进行了研究，主要包括以下两方面的内容：首先，给出两种布尔函数零化子的构造方法，构造Ⅰ利用布尔函数的小项表示构造零化子，得到求布尔函数f代数次数≤d的零化子的算法，同时得到通过布尔函数的特征矩阵判断零化子的存在性：构造Ⅱ利用布尔函数退化后的子函数构造零化子，将此构造方法应用于LILI-128，Toyocrypt等流密码体制中，使得攻击的复杂度大大降低；通过研究(5，1，3，12)旋转对称饱和最优函数的代数免疫和一类构造函数的代数免疫，证明了一类函数为代数攻击不变量，并对此性质作了进一步推广。

It is shown that if L is a subalgebra of a Lie color algebra Q, then Q is an algebra of quotients of L if and only if Q is ideally absorbed into L.

利用没有非零零化子的理想对Lie color代数的商代数进行刻画，证明了：若L为Lie color代数Q的子代数，则Q为L的商代数当且仅当Q理想吸收于L。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。