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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。

The effect of"Modulation Saturation"is proposed and the effective solution is also obtained.

提出了"调制饱和"效应的概念及解决这一效应的可行的方法。

The used adsorbents could be regenerated in 24 h by 0.1 molL^(-1) of sodium hydroxide.

用0.1 molL^(-1)的NaOH对吸附饱和后的吸附剂进行解吸处理24 h,可以有效地恢复其吸附性能。

In the middle are the mono- unsaturated fats such as olive and peanut oils.

处于中间位置的是一元化不饱和脂肪,如橄榄油和花生油。

The more ω-9 Mono Unsaturated Fatty Acid has, the higher oil stability is.

9单元不饱和脂肪酸愈高,油品稳定性愈高。

Standards: Acid Value is within 3 mg KOH / g, and ω-9 Mono Unsaturated Fatty Acid is more than 79%.

标准:酸价3 mg KOH/g以内;ω-9单元不饱和脂肪酸79%以上等级标准。

Use heart-healthy mono- and polyunsaturated fats, like olive, canola and safflower oil, instead.

使用对心脏健康有益的单或多不饱和脂肪如橄榄油,蓖麻油,红花油等替代。

This test is a measure of the unsaturated linkages in a fat and is determined by reacting the fat with a solution of iodine monochloride in a mixture of acetic acid and CCU, liberating excess iodine with KI, and titrating with Na2S203.

这个试验是不饱和键的测量,它由脂肪与一氯化碘在乙酸与CCU的混合物的溶液反应进行测量,用KI除多余的碘,用硫代硫酸钠滴定。

Do we see diversity, or monoculture and a saturation of the market by its most powerful players?

或是市场反被那些垄权者推动的一体化所饱和了呢?

Surface mottle of BMC parts is one of common quality defects.

饱和聚酯树脂模塑料压制件表面颜色不均匀是常见的质量难题之一。

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This paper discusses design and realizable methods of remote test output interface from logical design angle.

本文从逻辑设计的角度讨论遥测输出接口的设计及实现方法。

This also 星体投射plies to buildings, structures and geological features.

这也适用于建筑物和地质特征。

We all hope for a better life.

我们都希望好的生活。