模运算

The finite field arithmetic is the base of cryptography and modular inversion is the kernel arithmetic operation.

有限域的运算是密码学的基础，而在有限域的所有运算中模逆运算是最核心也是最复杂的运算。

According to the demand of high magnetic field power supply, reference is increased with a set ramp rate and stops at a set stable value, so reference system is composed of digital setting and digit to analog converting circuit. But the stability of reference is mostly guaranteed by the performance of D/A circuit, so D/A circuit is particularly studied in reference system. The scheme of D/A circuit, the selection of DAC and its voltage reference, hardware anti-jamming design and PCB design are discussed in detail, and software of remote control and PLC are discussed in brief. Zero-flux DC current transformer well satisfies the demands of the high stability of Load current detection unit, so the principle of zero-flux DC current transformer is analyzed; in the mean time a project which detects the long term stability is designed. During 8 hours, analog signal which is detected with high precision digit multimeter is recorded in computer at 1HZ frequency by GPIB communication. The drift error source and related parameters are explained in the compare-amplify part. Detailed subtraction circuit is designed; also amplifier chip and periphery components are selected and verified according to the theory of error analysis.

根据强磁场电源的需求，参考源应按照软件设定的斜率逐渐上升到设定稳态值，则参考源系统应由数字给定和数模转换电路两大部分组成，而参考源的稳定度主要依靠完成数模转换功能的模拟电路的性能来保证，因此本文对参考源系统的研究以数模转换电路为重点，分别从电路方案的确定、数模转换芯片及其基准电压源的选取和验证、电路板硬件抗干扰和PCB设计几方面进行了论述，然后对数字给定部分的远控组态和PLC程序设计作了简要介绍；采用零磁通原理的直流电流转换器很好地满足了对负载电流检测单元高稳定度的需求，本文详细分析了零磁通检测的原理，并在选定此种类型电流转换器的基础上设计了一套检测长期稳定度的方案，8小时内以1秒为采样周期，通过计算机Labview程序和高精度数字电压表的GPIB通讯，将被高精度数字电压表数字化后的模拟信号采样值连续记录至计算机中；比较放大环节简要阐述了漂移产生的原因和相关参数指标，确定了具体的减法电路形式，并根据误差分析理论对运算放大器和外围元器件进行了选取和验证。

A modular exponentiation for very large integers is one of the most common fundamental operations in many public-key cryptosystems.

模乘幂运算是公钥密码体制中最常用的基本运算，提高其运算速度可有效地提高公钥密码算法的加解密效率。

RSA scheme is composed of large bit-length modular multiplication and modular exponentiation in principle.

基本上，RSA密码系统是由高位元数的模乘法运算以及模指数运算所组成。

Based on the foregoing strategy, we choose Inverse Modified Discrete Cosine Transform and Polyphase Synthesis Filterband of the MP3 decoder by an ASIC implementation. Moreover, to further reduce the hardware cost, we use CORDIC-based calculations and merging some arithmetic operations to replace the original ones of IMDCT and PSF.

基於前述的原则及由运算量的统计分析，我们选定「反转修正式离散余弦转换(Inverse Modified Discrete Cosine Transform， IMDCT)」与「多相位合成滤波频带(Polyphase Synthesis Filterband， PSF)」使用ASIC方式实现，同时为了有效降低这两个模组的硬体成本，我们导入「座标轴旋转数位计算机」及合并运算方式取代原始算术运算，使得新的计算式有效降低原IMDCT约74%之乘法及约49%加法运算，而在多相位合成滤波频带的反离散余弦转换也有降低约33.4%之乘法及约24.6%之加法运算。

Big numbers operation will take time, especially modular inverse operation and modular power operation for big numbers.

大数运算是很费时间的，尤其是大整数的模逆和模幂运算。

By using the index equation modular φ as transformation, the speed of encryption and decryption is further increased. By dividing information into groups, using multiple transformation, and eliminating the superincreasing property, the new scheme becomes more secure.

这种体制用模φ的指数方程进行变换运算，使得加解密过程的运算速度进一步提高；信息经过分组和多次模变换处理；避免了超递增序列的弱点，使其具有更强的保密性。

As to arithmetic operations of fuzzy numbers,the arithmetic rules of fuzzynumbers based on generalized t-norms are introduced,which extend greatlythe implication of the arithmetic rules of noninteractive fuzzy numbers andgeneralize the arithmetic rules of fuzzy numbers of Dubois-Prade.

在模糊数算术运算方面，给出基于广义t-模的模糊数算术运算规则，该规则极大地拓展了非相互作用模糊数算术运算的范围与含义，对Dubois-Prade意义下的模糊数算术运算是一个很好的推广。

Disjunction normal form theorem in the modal logic system S5 is inductively proved, which can be used for representing complex modal formulas by means of conjunction and disjunction of simplest modal formulas with depth at most 1 in the system S5. As application, it is proved that a knowledge base could answer KB-queries if and only if it could answer queries of non-modal propositions and their negations, which is a basic problem on knowledge base.

研究了模态逻辑系统S5中的析取范式定理的归纳证明，给出了在S5中用深度至多等于1的最简模态公式通过析取与合取运算表示含有多重模态词的公式的方法，作为范式定理的应用，讨论了知识库中的一个基本问题，证明了知识库能够回答KB命题式问题的充要条件是该知识库能够回答相关的非模态命题及其否定命题的问题。

According to the requirement of die designing, the die parting face and the gutter is designed. By Boolean calculation, the blocker, finisher , cut-off die and stripper are generated.

根据锻模设计要求，设计了分模面、毛边槽，通过布尔运算，生成了预锻模、终锻模、切边模实体和卸料板。

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。