|
[转帖]布尔函数的WALSH谱
这书难,还是杨晓元的好懂点 Z:=Matrix(GF(2), 1 ,[1]); Z; X := RandomMatrix(GF(2), 3, 3); > X; Y := RandomMatrix(GF(2), 4, 4); > Y; KZX:=KroneckerProduct(Z, X); KZX; KZX1:=KroneckerProduct(Z, KZX); KZX1; KZX2:=KroneckerProduct(Z, KZX1); KZX2; KZX3:=KroneckerProduct(Z, KZX2); KZX3; KZX4:=KroneckerProduct(Z, KZX3); KZX4; [1] [0 1 1] [0 1 1] [0 1 0] [1 0 1 0] [1 1 0 1] [1 1 0 0] [0 0 1 0] [0 1 1] [0 1 1] [0 1 0] [0 1 1] [0 1 1] [0 1 0] [0 1 1] [0 1 1] [0 1 0] [0 1 1] [0 1 1] [0 1 0] [0 1 1] [0 1 1] [0 1 0] Z:=Matrix(GF(2), 1 ,[1]); Z; X := RandomMatrix(GF(2), 2, 2); > X; Y := RandomMatrix(GF(2), 4, 4); > Y; 沃尔什转换矩阵: KXY:=KroneckerProduct(X, Y); KXY; KXY1:=KroneckerProduct(X, KXY); KXY1; KXY2:=KroneckerProduct(X, KXY1); KXY2; [1] [1 1] [0 1] [0 0 1 1] [1 0 0 1] [0 0 0 0] [1 1 0 0] [0 0 1 1 0 0 1 1] [1 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0] [1 1 0 0 1 1 0 0] [0 0 0 0 0 0 1 1] [0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0] [0 0 0 0 1 1 0 0][0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1] [1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1] [0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0] [0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1] [1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1] [0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0] 逆针 [1 0 0 0 1 0 0 0] [0 1 1 0 0 1 1 0] [1 0 1 1 1 0 1 1] [1 1 1 1 1 1 1 1] [0 0 0 0 1 0 0 0] [0 0 0 0 0 1 1 0] [0 0 0 0 1 0 1 1] [0 0 0 0 1 1 1 1][1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0] [0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0] [1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0] [0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1] [0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1] [1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0] [0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0] [1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1] [1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0] [0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1] [0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1] 转换式与反转换式只差了一个常数,这是由于沃尔什转换矩阵的反矩阵就是自己的转置矩阵乘上一个常数 Transpose(KXY); [1 1 1 1 0 0 0 0] [0 1 0 0 0 0 0 0] [1 0 1 1 0 0 0 0] [1 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] 序数顺序(沃尔什顺序) 双积顺序(培力顺序) 自然顺序(哈德码得顺序) W[m,n] Sequency Ordering(Walsh Ordering) Dyadic Ordering(Paley Ordering) Natural Ordering (Hadamard Ordering) 双积顺序的二进制编号是序数顺序的格雷码编码 G:格雷码 B:二进制码 G(N) = B(n+1) XOR B(n) 自然顺序的二进制编号是双积顺序的位元反转。 沃尔什转换矩阵的每个列是互相正交的 SwapColumns(KXY, 1, 2) ; SwapColumns(KXY, 2, 3) ; SwapColumns(KXY, 3, 4) ; [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0] |
|
[求助]软件代码被DES加密,已知许多组明文和加密代码,如何得到密钥?
http://www.sciengines.com/products/computers-and-clusters/copacobana-s3-1000.html 打破小于单日的DES SciEngines是自豪地宣布,他们的大规模并行架构RIVYERA已经取得了自2008年以来的一个单一的硬件加速服务器的最高速度为56位DES解密。 2006年开始与第三方科学出版物实现了超过65亿美元的第二个使用赛灵思Spartan - 3 1000的FPGA上SciEngines COPACOBANA键的吞吐量。 2008年7月15日报道SciEngines打破DES使用COPACOBANA设置一个单一的一天的平均时间。 2009年,我们实现了吞吐量超过280亿美元的使用128赛灵思Spartan - 3 5000 FPGA的一个RIVYERA单3胡硬件加速服务器的关键。不过,我们感到非常自豪地宣布,我们达到每秒292亿个密钥,我们的RIVYERA机器的总功耗降低75%。 由16 RIVYERA S3 - 5000 FPGA卡,配备了8 FPGA的每个SciEngines“大规模并行高性能计算平台。据报道,本机消耗低于850峰瓦的功率。它可以适合于任何现成的货架,占领不超过3HU以上。 该系统是德国制造“的质量”。 在一般情况下,数据加密标准(DES)是在1998年以来的首次定制的硬件攻击打破,并已取代更现代化的标准,如三重DES,AES,RSA。不过DES仍然在使用。 SciEngines COPACOBANA隐窝算法使用一个攻击蛮力攻击在2006年的非政府客户提供第一个已知的的经济实惠的解决方案,作为参考系统的加密研究中的重要作用。 格尔德菲佛说:“我们当前和即将推出的产品仍然酒吧来衡量当前的密码分析算法和第三部分产品。”SciEngines有限责任公司,SciEngines有限责任公司首席执行官。“我们的解决方案在硬件和软件提供更高的性能和消耗更少的,完全可伸缩的标准架构的能量比我们设法消除古典集群计算和混合运算加速器,使用PC一样的PCI - Express总线系统的瓶颈。DES和密码分析是市场SciEngines机有独特的性能证明了自己的市场之一,另一些则自然科学,如天气预报和物理以及模拟海洋。FPGA提供了在这些市场上最好的性能价格比,GPU和CPU的集群相比。“ “DES是一个很好的例子,2006年单一COPACOBANA S3 - 1000在蛮力攻击对DES提供了3000多台电脑的性能。斯特凡Baumgart,首席硬件工程师在大规模并行硬件的专家说:“COPACOBANA V4 - SX35和RIVYERA的第一架原型机2008年,我们能够提供性能更比为4.3倍。 “2009年我们的头号现成的硬件加速点击蛮力个人键恢复解决方案。现在介绍RIVYERA更大的观众,2010,RIVYERA提供最简单的使用设计过的个人键恢复工具的每一个访问。我们的方法允许恢复丢失的DES密钥用一个简单的点击。我们的硬件加速算法自动分析的56位加密的文件,搜索使用蛮力的关键,并返回已测试,以赌他正确的关键的关键候选人。“ SciEngines“基于FPGA的平台技术,能够处理超过292亿每秒键,利用128的FPGA。这意味着已采取超过一百年,一台PC或PC上的群集或混合配备GPU或FPGA的PCI - Express卡的计算机集群几个月一键恢复,可以实现在一个单一的一天。 关于SciEngines SciEngines是建立在视觉上,我们能满足在科学和工程计算的需要。虽然高性能计算(HPC)和FPGA技术并不是新的,我们认为两者的结合是一个有吸引力的替代买不起或无法访问的超级计算机。基于FPGA的大规模并行高性能计算机的设计规模到大规模并行水平有利的成本性能比和功率性能比单一的FPGA。 我们的专家在现场可编程门阵列(FPGA)的发展。 SciEngines产品,如自然科学,加密技术,信号处理和科学计算处理应用。欲了解更多信息,访问www.sciengines.com。 Undo edits =============== 两名以色列密码专家发明了一种新的方法来破解des,微分密码分析法. RSA中的S和biham,只要采样247个对明密文 都是软硬兼施,先要看书《能量分析攻击》,买示波器 http://bbs.pediy.com/showthread.php?t=132752 http://ieeexplore.ieee.org/xpl/freeabs_all.jsp?reload=true&arnumber=5389567 http://www.cs.technion.ac.il/~biham/ |
|
[求助]软件代码被DES加密,已知许多组明文和加密代码,如何得到密钥?
http://w2.eff.org/Privacy/Crypto/Crypto_misc/DESCracker/HTML/19980716_eff_des_faq.html 1.暴力破解 2.分布式计算 通过网络联合数台计算机一起计算.可以大大缩短时间. 3.专用设备破解(破解机) 暴力破解实在是太费时间,但是个人计算机不是最快的破解工具,PC终归是一种通用设备.在1998年,EFF为了向世人证明des不是一种安全的加密方式而制造了一台专用于破解des的机器,这台机器叫做Deep Crack ,总共耗资20万美元,该机器使用1536个专用处理器,平均破解(穷举)出一个正确的key需耗时4天左右. 每秒钟可以穷举920亿个key. 4.时间与数据量折衷法. 这是马丁赫尔曼先生于1980年提出的一种可行的破解des的算法, 可以想象这样一种情况,我们有无穷多的存储器,我们预先把所有可能的key(A)和与某个明文通过这个key所得到的相应的密文(B)组成一对(A,B)存在存储器中.我们就可以通过数据库快速的找到我们需要的key,当我们有足够的存储器的时候,这是最快的方法,那么需要多少存储器呢??你可以自己算一下.:))) 当然,我们没有那么多的硬盘来村这些数据,但是马丁赫尔曼提出了一种新的算法来解决这个问题,按照一定的规则选一部分key把相应的数据对(A,B)存在硬盘中,再按照相应的算法通过数据库的搜索结果,把正确的key锁定在很小的范围内,然后在这一范围内进行穷举.按照这一方法,一台普通的微机只需要1000G的硬盘和3天左右的时间就可以找到正确的key. 5.微分密码分析法. 1990年,;两名以色列密码专家发明了一种新的方法来破解des,这就是微分密码分析法. 按照这一方法只需要对特殊的明文和密文成对采样247对,通过短时间的分析便可以得到正确的key.具体算法吗.....hehehe...:)) 6.线性分析法. 日本三菱电子1994年发明的方法,按照这一方法如果我们有2^43==8'796'093'022'208个明文和密文对(约 64'000 GB),我们可以在短时间内计算出正确的key. ============ 最早的定制硬件攻击可能已被用于恢复在第二次世界大战之谜机键Bombe。 1998年,一个自定义的硬件攻击扫荡的数据加密标准密码由电子前沿基金会。 “深裂”整机成本25万美元建立和解密DES挑战II- 2测试消息后56小时工作。唯一的其他确认的DES裂解COPACOBANA机(成本优化的并行代码断路器)建于2006年。与深裂,COPACOBANA包括商业化,可重构集成电路。 COPACOBANA成本约为10,000建立和恢复DES密钥,在平均6.4天。成本的下降,大约在EFF机25倍,是一个令人印象深刻的数字硬件的不断改善的例子。通胀率超过8年的调整,产量约30倍甚至更高的改善。自2007年以来,SciEngines有限公司,COPACOBANA两个项目的合作伙伴公司分拆已加强和发展的COPACOBANA接班人。在2008年COPACOBANA RIVYERA减少打破DES的不到一天的当前记录的时间,使用128的Spartan - 35000。[1]。一般认为[引证需要],大政府的代码,打破组织,如美国国家安全局,广泛使用,使定制的硬件攻击,但没有例子,2005年已解密[更新]。 |
|
[求助]哥们今天QQ登不上了
试了没问题啊 |
|
[转帖]几个google的彩蛋很好玩!
还是不行,节都要过了 |
|
[求助]n个元素集合的拓朴数真的没公式吗?
The answer is 29. How to get this answer? There turn out to be 9 different topologies on a three point set {1,2,3} (for definiteness' sake), and then some more topologies can be obtained from permuting the points. 1. The discrete topology; all sets are open. There is of course only 1. 2. The indiscrete topology; no sets are open except the empty set and the whole set. In the following I will not include these sets any more... There is of course only 1. 3. A topology with no isolated points (=open singletons) and 1 (non-trivial) open set consisting of a doubleton. So {{0,1}} + the trivial ones, eg. If these there are 3: "3 choose 2" ways of chosing the doubleton. 4. A topology with one isolated point, and no more open sets. There are 3 ways of chosing the isolated point. So that makes 3 more. 5. A topology with one isolated point, and the two other points also form an open set. Of this there are 3 as well. 6. A topology with one isolated point, and the other two points are in its closure, but not in each other's closure, so eg. {1}, {1,2}, {1,3} as non-trivial open sets. This topology is determined by the choice of the isolated point, so there are 3 of them. 7. A topology with one isolated point, another point is in the closure of it, but not in the closure of the third, while the third is in the closure of both the others. eg.: {1}, {1,2} as non-trivial open sets. All three points have different "roles" here, so there are 6 = 3! of these. (3 ways of picking the isolated point, and then 2 to pick the point "inbetween".) 8. A topology with 2 isolated points as only non-trivial open sets. So eg {1},{2}. There are 3 ways of picking the non-isolated point, which fixes the type, so there are 3 of these. 9. A topology with 2 isolated points, and the third one is in the closure of one of them. Eg.: {1},{2},{2,3} as non-trivial open sets. There are 3 ways of fixing the non-isolated point, and then 2 to fix the point in whose closure it is. So 6 of these in all. That's all. Eg if there are 2 open sets of 2 points, their intersection will be an isolated point, etc. A bit of thought shows that these are all the types. This gives: 2*1 + 5*3 + 2*6 = 12 + 15 + 2 = 29 topologies, divided over 9 types. |
|
[求助]n个元素集合的拓朴数真的没公式吗?
http://www.jstor.org/stable/2313548 http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Benoumhani/benoumhani11.pdf http://pdf.tj1.cnki.net/cjfdsearch/pdfdownloadnew.asp?encode=gb&nettype=cnet&zt=&filename=TdSpFN1ZmT3lVa4A3KDBHbysCURpUZXpUVYFWW3RXRa50Kz9EcPlESyh0Z1AnWx80L6NFUahXVGZHR=0TVDR2bCFkM0E2arIUOlJHODdWUvtWMohmds9WM2QGd5EGNstESzckWMp1ZkZ3cCVUdzU0M0JUR1Z&doi=CNKI:SUN:ZSXZ.0.2006-03-003&m=ysCURpUZXpUVYFWW3RXRa50Kz9EcPlESyh0Z1AnWx80L6NFUahXVGZHR9kFezYHaYN3VwMUOIxWTRZjM2cTWZhTS1ZTdSpFN1ZmT3lVa4A3KDBHb&filetitle=%d3%d0%cf%de%bc%af%c9%cf%c1%bd%bc%ab%cd%d8%c6%cb%b8%f6%ca%fd%b5%c4%cc%bd%cc%d6&p=CJFQ&cflag=&pager=21-24 http://www.mathchina.com/Cgi-bin/view.cgi?forum=5&topic=8250 3点集 {a,b,c} (1) {{a},{b},{c}}, (2) {{a},{b,c}},{{b},{c,a}},{{c},{a,b}} (3) {{a},{b},{b,c}},{{a},{c},{b,c}},{{b},{c},{a,c}},{{b},{a},{a,c}},{{c},{b},{a,b}},{{c},{a},{a,b}} (4) {{a},{a,b},{c,a}},{{b},{b,c},{a,b}},{{c},{c,a},{b,c}} (5) {{a},{a,b},{a,b,c}},{{a},{a,c},{a,b,c}},{{b},{b,c},{a,b,c}}, {{b},{a,b},{a,b,c}},{{c},{b,c},{a,b,c}},{{c},{a,c},{a,b,c}} (6) {{a},{a,b,c}},{{b},{a,b,c}},{{c},{a,b,c}} (7) {a,{b},{c}},{{a}.b.{c}}.{{a}.{b},c} (8) {{a,b},{a,b,c}},{{b,c},{a,b,c}},{{c,a},{a,b,c}} (9) {{a,b,c}} 除了同构,就9种了 |
|
|
|
[分享]国家保密学院
是啊,同问! |
|
[分享]LFSR和m序列
p<x> := PolynomialRing(Integers()); > f := x^38-1; > f; Rank(p); a:=Factorization(f) ; a; b:=Factorisation(f^27); b; c:=Factorisation(f^279*f); c; f1:=x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 -x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1; f1; IsIrreducible(f); IsIrreducible(f1); Degree(f); Degree(f1); Discriminant(f) ; Discriminant(f1) ; CompanionMatrix(f) ; CompanionMatrix(f1) ; F<i> := PolynomialRing(GF(5)); i := x^2-2*x+2; i; IsSeparable(F!i) ; Factorization(F!i); F<k> := PolynomialRing(GF(5)); k := x^2-3*x+2; k; IsSeparable(F!k) ; Factorization(F!k); F<g> := PolynomialRing(GF(2)); g := x^2-2*x+2; g; IsSeparable(F!g) ; Factorization(F!g); F<m> := PolynomialRing(GF(2^2)); m := x^2-2*x+2; m; IsSeparable(F!m) ; Factorization(F!m); F<n> := PolynomialRing(GF(2^103)); n := x^2-2*x+2; n; IsSeparable(F!n) ; Factorization(F!n); x^38 - 1 1 [ <x - 1, 1>, <x + 1, 1>, <x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1, 1>, <x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 1> ] [ <x - 1, 27>, <x + 1, 27>, <x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1, 27>, <x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 27> ] [ <x - 1, 280>, <x + 1, 280>, <x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1, 280>, <x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 280> ] x^18 - x^17 + x^16 - x^15 + x^14 - x^13 + x^12 - x^11 + x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1 false true 38 18 1075911801979993982060429252856123779115487368830416064610304 -5480386857784802185939 [0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] [1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0] [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1] [-1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1] x^2 - 2*x + 2 true [ <i + 1, 1>, <i + 2, 1> ] x^2 - 3*x + 2 true [ <k + 3, 1>, <k + 4, 1> ] x^2 - 2*x + 2 false [ <g, 2> ] x^2 - 2*x + 2 false [ <m, 2> ] x^2 - 2*x + 2 false [ <n, 2> ] P<x> := PolynomialRing(GF(2)); PrimePolynomials(P,2); NumberOfPrimePolynomials(P, 2); NumberOfPrimePolynomials(P, 3); P<Z> := PolynomialRing(GF(2^4)); PrimePolynomials(P,2); NumberOfPrimePolynomials(P, 2); NumberOfPrimePolynomials(P, 3); f3 := x^3+x^2+13; f3; HasPolynomialFactorization(P) ; f30 := x^30-1; f30; HasPolynomialFactorization(P) ; [ x^2 + x + 1 ] 1 2 [ Z^2 + $.1*Z + $.1^8, Z^2 + $.1^2*Z + $.1, Z^2 + $.1*Z + $.1^9, Z^2 + $.1^4*Z + $.1^2, Z^2 + $.1^6*Z + $.1^10, Z^2 + $.1^2*Z + $.1^3, Z^2 + Z + $.1^11, Z^2 + $.1^8*Z + $.1^4, Z^2 + $.1^12*Z + $.1^12, Z^2 + $.1^12*Z + $.1^5, Z^2 + $.1^7*Z + $.1^13, Z^2 + $.1^4*Z + $.1^6, Z^2 + $.1^10*Z + $.1^14, Z^2 + Z + $.1^7, Z^2 + $.1^9*Z + 1, Z^2 + $.1^9*Z + $.1^9, Z^2 + $.1^10*Z + $.1^2, Z^2 + $.1^9*Z + $.1^10, Z^2 + $.1^12*Z + $.1^3, Z^2 + $.1^14*Z + $.1^11, Z^2 + $.1^10*Z + $.1^4, Z^2 + $.1^8*Z + $.1^12, Z^2 + $.1*Z + $.1^5, Z^2 + $.1^5*Z + $.1^13, Z^2 + $.1^5*Z + $.1^6, Z^2 + Z + $.1^14, Z^2 + $.1^12*Z + $.1^7, Z^2 + $.1^3*Z + 1, Z^2 + $.1^8*Z + $.1^8, Z^2 + $.1^2*Z + $.1^10, Z^2 + $.1^3*Z + $.1^3, Z^2 + $.1^2*Z + $.1^11, Z^2 + $.1^5*Z + $.1^4, Z^2 + $.1^7*Z + $.1^12, Z^2 + $.1^3*Z + $.1^5, Z^2 + $.1*Z + $.1^13, Z^2 + $.1^9*Z + $.1^6, Z^2 + $.1^13*Z + $.1^14, Z^2 + $.1^13*Z + $.1^7, Z^2 + $.1^8*Z + 1, Z^2 + $.1^5*Z + $.1^8, Z^2 + $.1^11*Z + $.1, Z^2 + $.1^10*Z + $.1^11, Z^2 + $.1^11*Z + $.1^4, Z^2 + $.1^10*Z + $.1^12, Z^2 + $.1^13*Z + $.1^5, Z^2 + Z + $.1^13, Z^2 + $.1^11*Z + $.1^6, Z^2 + $.1^9*Z + $.1^14, Z^2 + $.1^2*Z + $.1^7, Z^2 + $.1^6*Z + 1, Z^2 + $.1^6*Z + $.1^8, Z^2 + $.1*Z + $.1, Z^2 + $.1^13*Z + $.1^9, Z^2 + $.1^3*Z + $.1^12, Z^2 + $.1^4*Z + $.1^5, Z^2 + $.1^3*Z + $.1^13, Z^2 + $.1^6*Z + $.1^6, Z^2 + $.1^8*Z + $.1^14, Z^2 + $.1^4*Z + $.1^7, Z^2 + $.1^2*Z + 1, Z^2 + $.1^10*Z + $.1^8, Z^2 + $.1^14*Z + $.1, Z^2 + $.1^14*Z + $.1^9, Z^2 + $.1^9*Z + $.1^2, Z^2 + $.1^11*Z + $.1^13, Z^2 + $.1^12*Z + $.1^6, Z^2 + $.1^11*Z + $.1^14, Z^2 + $.1^14*Z + $.1^7, Z^2 + $.1*Z + 1, Z^2 + $.1^12*Z + $.1^8, Z^2 + $.1^10*Z + $.1, Z^2 + $.1^3*Z + $.1^9, Z^2 + $.1^7*Z + $.1^2, Z^2 + $.1^7*Z + $.1^10, Z^2 + $.1^4*Z + $.1^14, Z^2 + $.1^5*Z + $.1^7, Z^2 + $.1^4*Z + 1, Z^2 + $.1^7*Z + $.1^8, Z^2 + $.1^9*Z + $.1, Z^2 + $.1^5*Z + $.1^9, Z^2 + $.1^3*Z + $.1^2, Z^2 + $.1^11*Z + $.1^10, Z^2 + Z + $.1^3, Z^2 + $.1^12*Z + 1, Z^2 + $.1^13*Z + $.1^8, Z^2 + $.1^12*Z + $.1, Z^2 + Z + $.1^9, Z^2 + $.1^2*Z + $.1^2, Z^2 + $.1^13*Z + $.1^10, Z^2 + $.1^11*Z + $.1^3, Z^2 + $.1^4*Z + $.1^11, Z^2 + $.1^5*Z + $.1, Z^2 + $.1^6*Z + $.1^9, Z^2 + $.1^5*Z + $.1^2, Z^2 + $.1^8*Z + $.1^10, Z^2 + $.1^10*Z + $.1^3, Z^2 + $.1^6*Z + $.1^11, Z^2 + $.1^4*Z + $.1^4, Z^2 + $.1^13*Z + $.1^2, Z^2 + $.1^14*Z + $.1^10, Z^2 + $.1^13*Z + $.1^3, Z^2 + $.1*Z + $.1^11, Z^2 + $.1^3*Z + $.1^4, Z^2 + $.1^14*Z + $.1^12, Z^2 + $.1^6*Z + $.1^3, Z^2 + $.1^7*Z + $.1^11, Z^2 + $.1^6*Z + $.1^4, Z^2 + $.1^9*Z + $.1^12, Z^2 + $.1^11*Z + $.1^5, Z^2 + $.1^14*Z + $.1^4, Z^2 + Z + $.1^12, Z^2 + $.1^14*Z + $.1^5, Z^2 + $.1^2*Z + $.1^13, Z^2 + $.1^7*Z + $.1^5, Z^2 + $.1^8*Z + $.1^13, Z^2 + $.1^7*Z + $.1^6, Z^2 + Z + $.1^6, Z^2 + $.1*Z + $.1^14, Z^2 + $.1^8*Z + $.1^7 ] 120 1360 x^3 + x^2 + 1 true x^30 + 1 true |
|
[转帖]异构数据库安全集成论文
主要看后几十页。。。 |
|
[原创]magma,/PARI/GP中文文档ECC初步:
像个小桌,面是四角海星,Z轴方向上都是抛物线 |
|
[原创]magma,/PARI/GP中文文档ECC初步:
就在这页面上。。。 又进步了,再贴点 Tate Pairing在ECC中ADWARDS式中的视屏:http://www.youtube.com/watch?v=nideQo-K9ME ADWARDS式中两点加如下图,还有沙盘演试: |
操作理由
RANk
{{ user_info.golds == '' ? 0 : user_info.golds }}
雪币
{{ experience }}
课程经验
{{ score }}
学习收益
{{study_duration_fmt}}
学习时长
基本信息
荣誉称号:
{{ honorary_title }}
能力排名:
No.{{ rank_num }}
等 级:
LV{{ rank_lv-100 }}
活跃值:
在线值:
浏览人数:{{ visits }}
最近活跃:{{ last_active_time }}
注册时间:{{ user_info.create_date_jsonfmt }}
勋章
兑换勋章
证书
证书查询 >
能力值