模运算

The method this paper discussed was based following theoretic analysis: Square and multiplication of large integer are two basic operations in modular exponential m_ary algorithm. The main operations of m_ary algorithm of point multiplication in elliptic curve encryption were doublings and point addition. The steps of m_ary algorithm in point multiplication was similar to modular exponential.

其基于以下理论分析：模幂m_ary算法的基本运算为大数乘法，其中包括大数平方算法和一般大数乘法；椭圆曲线加密算法中点乘的m_ary算法步骤与模幂的m_ary算法相同，后者的基本运算为倍乘和加法。

The window method is also used to reduce significantly the number of modular multiplications needed for completing modular exponentiation.

在设计中还采用了窗口法减少模幂运算过程中所需进行的模乘运算次数，大大提高了处理速度。

The window method is used to significantly reduce the number of modular multiplications needed for completing the modular exponentiation.

在设计中还采用了窗口法减少模幂运算过程中所需进行的模乘运算次数，大大提高了处理速度。

The large numer exponentiation algorithms is the key of RSA cryptography system,which is performed by a series of modular multiplication.

RSA算法的核心运算是大整数模幂运算，而模幂运算是由一系列的模乘运算构成。

Inthe paper, the blind inspection is executed by using modular arithmetic, namely, modulus 2arithmetic.(The result is 0 or 1). A algorithm with high transparency and robustness is realizedby smartly combining this arithmetic with binary chaotic sequence.

文中利用模数运算实现了音频水印的盲检测，即利用模2 运算，模2 取余(所得结果为0 或1)，很巧妙地将这种运算与二值化的混沌水印序列相结合，实现了一种不可感知度高，嵌入量大的高鲁棒性水印算法。

The implementation processes of those two algorithms on smart card with cryptographic coprocessor are explained separately. The implementation process of RSA includes modular exponentiation and modular multiplication. The process of ECC includes the selection of base field and coordinates, scalar multiplication and field operation.

本文分别阐述了两者在带有加密协处理器的智能卡平台上的实现过程，包括RSA算法中模幂运算、模乘运算的实现；ECC算法中基域的选择、坐标系的选择、标量乘法和域算术运算的实现。

A good use of the integer type, the biggest 9999990 to support the decimal integer, It can perform large integers, plus or minus, multiplication, addition and modular, with a big round of the largest factions, extended Euclidean algorithm, the Chinese remainder theorem algorithm, Miller - Rabin primality testing algorithm, random generation of arbitrary integer spaces such as libraries, This kind of dynamic library has been used for commercial software, the reliability and speed is affirmed.

一个很好用的大整数的类，最大可支持9999990位的十进制整数，可进行大整数的加、减、乘、除和取模运算，并带有求大整数的最大公因数、扩展Euclidean算法、中国剩余定理算法、Miller-Rabin素性测试算法、随机生成任意位的大整数等函数库，这个类的动态库曾用于商业软件之中，其可靠性和速度是得到确认的。

Based on the system feedback archetype mode theory, the dissertation introduce the upper limit stepwise generation and elimination method of the system pullulate upper limit mode, construct the five upper limit archetype mode such as: market demand upper limit archetype mode, human resource upper limit archetype mode; fund upper limit archetype modes; technology innovation upper limit archetype mode; government support upper limit archetype mode ;By combining the five upper limit archetype mode ,we can attain a electronic information industry developmental pattern system upper limit archetype mode.

利用系统科学反馈基模分析理论，提出了系统成长上限模型上限逐步生成与消除法，通过构建江西电子信息产业市场需求成长上限子基模、人力资源不足成长上限子基模、政府支持有限成长上限子基模、资金不足成长上限子基模、创新能力不足成长上限子基模等5个基模，并对其做并运算，得到了江西电子信息产业系统成长上限基模，刻画了资金、市场、技术创新、人才与政府支持相互制约的关联关系。

At last, it"s studied the consistency of unsigned ones complement addition with bit-wise exclusive-OR and addition modulo 2". The formula of consistency probability is proposed.

随后，本文研究了进位返加运算与逐位模2加运算及模2~n加运算的相容性问题，给出了其相容概率的计算公式。

It"s revealed that the consistency probability of unsigned ones complement addition with bit-wise exclusive-OR is very greater than the ideal value 2~", though it is very small, and the consistency probability of unsigned ones complement addition with addition modulo 2 is 2/3 approximately, hence it is very large.

结论表明，进位返加运算与逐位模2加运算的相容概率尽管很小，但远大于理想值2~；进位返加运算与模2~n加运算的相容概率很大，近似为2／3。

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。