逆元

The algorithm is based on a modification of Euclid s algorithm.

在扩展欧几里得算法的基础上提出了有限域乘法逆元的计算方法。

The operation laws including:commutative law, associative law, cancellation law, unity of operation, inverse element, and distributive law between two operations,here we just omit them.

这些运算律包括：交换律，结合律，消去律，运算单位元，运算逆元，两个运算之间的分配律等，在此不再一一说明详细过程。

Conversely, if ''S'' is a subgroup of ''G'', then it obeys the axioms of a group.

因此，满足了闭包、单位元和逆元公理，而结合律是继承来的，所以''S''是子群。

The S box was constituted with the multiplication inverse element affined transformation in GF(2) of all elements of limited field GF(28),with S box s nonlinear byte changed,ciphered text attained the ideal status of the even of difference and the linear of deviation,and increased the capability of the AES algorithm of anti beating the difference cipher of analysis and linear cipher of analysis.

S盒由有限域G F(28)上所有元素的乘法逆元及在域G F(2)上的仿射变换构成，经过S盒的非线性字节代换，密文的差分均匀性和线性偏差都达到较理想的状态，提高了A E S算法抗击差分密码分析及线性密码分析的能力。

The inverse polynomial and the invertible affine transformation exist by the finite field, linear algebra and matrix theory. The invertible affine transformation and the inversion in are easily realized by using lookup table. An algorithm can be used to get the inverse element of modulo .

本文运用有限域、线性代数和矩阵理论，论证了逆多项式和逆仿射的存在性，并且应用查表法简捷地实现了中元素的求逆和逆仿射变换；设计了一个易于在在计算机上实现的算法，来求形如的多项式模时的逆元，该多项式的系数在上。

Then the affine permutation in the process of S-box construction was combined with an inverse mapping in order to construct all kinds of S-boxes, such as 8×8、4×4、6×6 and m×n S-boxes, and the avalanche probabilities of these S-boxes were analyzed in the light of variance, and some rules were obtained from the analysis, which will help to find safer S-boxes.

然后通过将有限域上的乘法逆元与一个可逆仿射变换相结合构造了一批8×8、6×6和4×4的S盒，并从方差的角度分析了S盒的雪崩概率，同时总结出部分结论。

The author mainly realized the method of generating the large random numbers and judging the prime number using Lehmann means,then three pairs of secure key with different lengths (256 bits,512 bits,1024 bits) was generated to meet the demand of different security grade. In encryption module,modular multiplication arithmetic of large number was realized adopting addition chaining. In decryption module,extended Euclid was used to get inverse,and the Chinese remainder theorem was used to realize decryption,which increased the speed of decryption greatly.

作者主要实现了大随机数的生成、采用整除小素数和勒曼测试法判定素数，可以生成三种不同长度的密钥对(256位、512位、1024位)来满足不同的加密安全等级的需求；加密模块中，选用了二进制序列的乘法方法，实现了大数模幂乘运算；解密模块中，引用了扩展的欧几里德法求逆元，并采用中国剩余定理实现解密过程，大大提高了解密速度。

Image scrambling transform ; Doolittle decomposition ; Crout decomposition ; Gauss-Jordan elimination ; inverse transform ; multiplication inversion

图像置乱变换；杜里特尔分解；克劳特分解；高斯-约当消去；逆变换；乘法逆元

The apparatus further includes a quad-symbol mapper which quad-maps the systematic symbol streams to one symbol stream, a channel interleaver which independently interleaves the quad-mapped systematic symbol stream and the parity symbol streams, quad-demaps the quad-mapped systematic symbol stream, interlaces symbols in parity symbol streams, and serial-concatenates the quad-demapped systematic symbol stream to the interlaced parity symbol streams.

该设备还包括：四码元映射器，其将系统码元流四映射到一个码元流；信道交织器，其独立地交织四映射的系统码元流和奇偶码元流，对四映射的系统码元流进行四逆映射，交错奇偶码元流中的码元，并且将四逆映射的系统码元流串行连接为交错的奇偶码元流。

Is negative yuan, against the yuan, Yin Yao, expressed the other side of contradictions.

1是负元、逆元、阴爻，表示矛盾的另一面。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新