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[原创]群论的一些基础知识
平凡同态就两个,太特殊了,都肯定非单非满吗? 刘绍学书上举了个,看了几回没看懂,是不是只有无限群才有非单非满,想不出来 还看到有说说实数集加群到正数1的映射是非单非满,想不出来 发现同态就是群的最重要也最难了。。。。 induced诱导出了个--------新词 交换群找子群,找正规子群比一般群容易,不容易试出啊 s4:=Sym(4);对称群S4,阶24,抽象群都可在对称群和置换群中找个同构,所以有普遍性,交换群就不在话下了 NormalSubgroups(s4) ;找出S4的正规子群 Subgroups(s4); ss:=sub< Sym(4) | (2,3,4),(1,4)(2,3),(1,3)(2,4)>;S4的正规子群ss阶为12 ss; Order(ss); Index(s4, ss) ;指标=24/12=2 s4 /ss; CosetTable(s4,ss);在S4中的陪集表 quotientgroup:= quo< Sym(4) | ss>;ss阶为12在S4中商群{(1, 2), (1, 2)},阶为2 quotientgroup; s5:=Sym(5); s5; fatherquotientgroup:= PermutationGroup< 5 | (2,1),(1,2),(2,1) >;在S5中有子群=商群{(1, 2), (1, 2)}, fatherquotientgroup; Subgroups(fatherquotientgroup);在S5中有子群=商群{(1, 2), (1, 2)}, NormalSubgroups(fatherquotientgroup) ;子群商群{(1, 2), (1, 2)}还为正规,也可不正规, S4-------S5的同态: HOM:= hom< s4 -> s5| s4.1 -> s5.1 >; HOM; S4-------S5的一种非单非满同态: S4阶12的{(2,3,4),(1,4)(2,3),(1,3)(2,4)}的正规子群的商群为商群{(1, 2), (1, 2)},阶为2 S5的阶2子群{(1, 2),(2, 1),(1, 2)}, 两者同态 Conjugacy classes of subgroups ------------------------------ [1] Order 1 Length 1 Permutation group acting on a set of cardinality 4 Order = 1 [2] Order 4 Length 1 Permutation group acting on a set of cardinality 4 Order = 4 = 2^2 (1, 4)(2, 3) (1, 3)(2, 4) [3] Order 12 Length 1 Permutation group acting on a set of cardinality 4 Order = 12 = 2^2 * 3 (2, 3, 4) (1, 4)(2, 3) (1, 3)(2, 4) [4] Order 24 Length 1 Permutation group acting on a set of cardinality 4 Order = 24 = 2^3 * 3 (3, 4) (2, 3, 4) (1, 4)(2, 3) (1, 3)(2, 4) Permutation group ss acting on a set of cardinality 4 (2, 3, 4) (1, 4)(2, 3) (1, 3)(2, 4) 12 2 Permutation group acting on a set of cardinality 2 (1, 2) (1, 2) Mapping from: Cartesian Product<{ 1 .. 2 }, GrpPerm: s4, Degree 4, Order 2^3 * 3> to { 1 .. 2 } $1 $2 -$1 1. 2 2 2 2. 1 1 1 Symmetric group s3 acting on a set of cardinality 3 Order = 6 = 2 * 3 Symmetric group quotientgroup acting on a set of cardinality 2 Order = 2 (1, 2) (1, 2) Symmetric group s5 acting on a set of cardinality 5 Order = 120 = 2^3 * 3 * 5 Permutation group fatherquotientgroup acting on a set of cardinality 5 (1, 2) (1, 2) (1, 2) Conjugacy classes of subgroups ------------------------------ [1] Order 1 Length 1 Permutation group acting on a set of cardinality 5 Order = 1 [2] Order 2 Length 1 Permutation group acting on a set of cardinality 5 Order = 2 (1, 2) Conjugacy classes of subgroups ------------------------------ [1] Order 1 Length 1 Permutation group acting on a set of cardinality 5 Order = 1 [2] Order 2 Length 1 Permutation group acting on a set of cardinality 5 Order = 2 (1, 2) Homomorphism of GrpPerm: s4, Degree 4, Order 2^3 * 3 into GrpPerm: fatherquotientgroup, Degree 5, Order 2 induced by (1, 2, 3, 4) |--> (1, 2) Kernel(HOM) ; Domain(HOM) ; Codomain(HOM); Image(HOM) ; |
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[分享]GCHQ、M15/M16/英国密码管理机构
原来是CASSAR+1 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z sgd-------+1--------the ozrrvnqc---+1----password hr--------+1 is bhsx------city ne--------od mdv-------new sgd-------+1--------the azrd--------base irs kdssdq--------jst letter sgdm----------then sgd---------the bntmsqx---------country ne---------is sgd----------the mdv------------new azrd--------base 2mc kdssdq--------2nd letter sgdm------then sgd------the rzed-----safe bnlahmzshnm------combination entqsg------fourth kdssdg-------letter ne --------of sgd ------the vddj---------week ne-------of sqzudk----travel SGD ozrrvnqc NE SGD BHSX OF SGD MDV AZRD IRS KDSSDQ SGDM SGD BNTMSQX NE SGD MDV AZRD 2MC KDSSDQ SGDM SGD 3QC MTLADQ the password is:THE city of THE new base (1st letter) then the country is the new base (2nd letter) then the 3rd number NE SGD RZED BNLAHMZSHNM SGDM SGD ENTQSG KDSSDQ NE SGD CZX NE SGD VDDJ NE SQZUDK of the safe combination THEN THE FOURTH LETTER of the DAY OF THE week of travel EXETER NRGLP ------EXETERBRRDEAUXmonday easter day anqcdztw--------BORDEAUX 1----monday FRANCEBORDEAUX96521MONDAY FRANCEBORDEAUX96521MONDAY27THJUNE BORDEAUXFRANCE96521MONDAY27THJUNE EXETERTHEUNITEDKINGDOMMONDAY |
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[讨论]希望开展时空平衡算法(彩虹表及完美表)的学习和研究
反对!就没穴位这种存在!和电脑都能连到一起,您老真是能忽悠 中医害人啊,精神上害人和孔儒一样 你到蒙古看看蒙医藏医,和中医一样蒙古大夫,撒满教女神婆怎麽忽悠人 |
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[原创]群论的一些基础知识
H1 := PermutationGroup< 13|(3,5)(4,6),(1,3,5),(2,4,6) ,(3,4)>; H1; H2 := PermutationGroup< 13 | (1,5)(3,4),(1,2,3,5)(4,6)>; H2; NormalSubgroups(H1); H1/H2; Permutation group H1 acting on a set of cardinality 13 (3, 5)(4, 6) (1, 3, 5) (2, 4, 6) (3, 4) Permutation group H2 acting on a set of cardinality 13 (1, 5)(3, 4) (1, 2, 3, 5)(4, 6) Conjugacy classes of subgroups ------------------------------ [1] Order 1 Length 1 Permutation group acting on a set of cardinality 13 Order = 1 Id($) [2] Order 360 Length 1 Permutation group acting on a set of cardinality 13 Order = 360 = 2^3 * 3^2 * 5 (2, 3)(4, 6) (1, 3, 4, 6)(2, 5) [3] Order 720 Length 1 Permutation group acting on a set of cardinality 13 Order = 720 = 2^4 * 3^2 * 5 (1, 4, 6, 2, 5) (2, 3) Permutation group acting on a set of cardinality 2 Id($) Id($) Id($) (1, 2) 小群表: Size Construction Notes 1 SymmetricGroup(1) Trivial 2 SymmetricGroup(2) Also CyclicPermutationGroup(2) 3 CyclicPermutationGroup(3) Prime order 4 CyclicPermutationGroup(4) Cyclic 4 KleinFourGroup() Abelian, non-cyclic 5 CyclicPermutationGroup(5) Prime order 6 CyclicPermutationGroup(6) Cyclic 6 SymmetricGroup(3) Non-abelian, also DihedralGroup(3) 7 CyclicPermutationGroup(7) Prime order 8 CyclicPermutationGroup(8) Cyclic 8 D1=CyclicPermutationGroup(4) D2=CyclicPermutationGroup(2) G=direct product permgroups([D1,D2]) Abelian, non-cyclic 8 D1=CyclicPermutationGroup(2) D2=CyclicPermutationGroup(2) D3=CyclicPermutationGroup(2) G=direct product permgroups([D1,D2,D3]) Abelian, non-cyclic 8 DihedralGroup(4) Non-abelian 8 PermutationGroup(["(1,2,5,6)(3,4,7,8)", "(1,3,5,7)(2,8,6,4)" ]) Quaternions The two generators are I and J 9 CyclicPermutationGroup(9) Cyclic 9 D1=CyclicPermutationGroup(3) D2=CyclicPermutationGroup(3) G=direct product permgroups([D1,D2]) Abelian, non-cyclic 10 CyclicPermutationGroup(10) Cyclic 10 DihedralGroup(5) Non-abelian 11 CyclicPermutationGroup(11) Prime order 12 CyclicPermutationGroup(12) Cyclic 12 D1=CyclicPermutationGroup(6) D2=CyclicPermutationGroup(2) G=direct product permgroups([D1,D2]) Abelian, non-cyclic 12 DihedralGroup(6) Non-abelian 12 AlternatingGroup(4) Non-abelian, symmetries of tetrahedron 12 PermutationGroup(["(1,2,3)(4,6)(5,7)", "(1,2)(4,5,6,7)"]) Non-abelian Semi-direct product Z3 o Z4 13 CyclicPermutationGroup(13) Prime order 14 CyclicPermutationGroup(14) Cyclic 14 DihedralGroup(7) Non-abelian 15 CyclicPermutationGroup(15) Cyclic |
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[原创]群论的一些基础知识
HOM:= hom< H2 -> H1 | H2.1 -> H1.1 >; HOM; Homomorphism of GrpPerm: H2, Degree 10, Order 3^2 into GrpPerm: H1, Degree 10, Order 2^4 * 3^2 * 5 induced by (1, 5, 3) |--> (3, 5)(4, 6) HOM:= hom< H1 -> H2 | H1.1 -> H2.1 >; HOM; Homomorphism of GrpPerm: H1, Degree 10, Order 2^4 * 3^2 * 5 into GrpPerm: H2, Degree 10, Order 3^2 induced by (3, 5)(4, 6) |--> (1, 5, 3) 非单非满同态互逆?!?试了5个都是 很大的40320/5040阶的 : H1 := PermutationGroup< 14|(3,5,7)(4,6,7),(1,3,5,7),(2,4,6,7),(3,4,5),(4,2),(11,3),(3,6)>; H1; H2 := PermutationGroup< 14 | (1,5,3,7)(3,6),(2,4,6,7)(4,2),(11,3)>; H2; N:=NormalSubgroups(H1) ; N; N1:=NormalSubgroups(H2) ; N1; Order(H1); Order(H2); Index(H1, H2) ; CosetTable(H1,H2); HOM:= hom< H2 -> H1 | H2.1 -> H1.1 >; HOM; HOM:= hom< H1 -> H2 | H1.1 -> H2.1 >; HOM; Permutation group H1 acting on a set of cardinality 14 (3, 5, 4, 6, 7) (1, 3, 5, 7) (2, 4, 6, 7) (3, 4, 5) (2, 4) (3, 11) (3, 6) Permutation group H2 acting on a set of cardinality 14 (1, 5, 6, 3, 7) (4, 6, 7) (3, 11) Conjugacy classes of subgroups ------------------------------ [1] Order 1 Length 1 Permutation group acting on a set of cardinality 14 Order = 1 Id($) [2] Order 20160 Length 1 Permutation group acting on a set of cardinality 14 Order = 20160 = 2^6 * 3^2 * 5 * 7 (1, 3)(2, 11)(4, 7)(5, 6) (2, 3, 7, 11, 5) [3] Order 40320 Length 1 Permutation group acting on a set of cardinality 14 Order = 40320 = 2^7 * 3^2 * 5 * 7 (1, 2) (1, 4, 3)(2, 6, 11, 5, 7) Conjugacy classes of subgroups ------------------------------ [1] Order 1 Length 1 Permutation group acting on a set of cardinality 14 Order = 1 Id($) [2] Order 2520 Length 1 Permutation group acting on a set of cardinality 14 Order = 2520 = 2^3 * 3^2 * 5 * 7 (1, 3, 11) (1, 4, 5)(3, 7)(6, 11) [3] Order 5040 Length 1 Permutation group acting on a set of cardinality 14 Order = 5040 = 2^4 * 3^2 * 5 * 7 (1, 3) (1, 4, 5, 6)(3, 7, 11) 40320 5040 8 Mapping from: Cartesian Product<{ 1 .. 8 }, GrpPerm: H1, Degree 14, Order 2^7 * 3^2 * 5 * 7> to { 1 .. 8 } $1 $2 $3 $4 $5 $6 $7 -$1 -$2 -$3 -$4 1. 1 1 2 1 2 1 1 1 1 3 1 2. 4 2 4 5 1 2 2 5 2 1 6 3. 6 7 1 3 3 3 3 4 5 4 3 4. 3 4 3 4 4 4 6 2 4 2 4 5. 2 3 5 6 5 5 5 6 6 5 2 6. 5 5 6 2 6 8 4 3 7 6 5 7. 7 6 7 7 7 7 7 7 3 7 7 8. 8 8 8 8 8 6 8 8 8 8 8 Homomorphism of GrpPerm: H2, Degree 14, Order 2^4 * 3^2 * 5 * 7 into GrpPerm: H1, Degree 14, Order 2^7 * 3^2 * 5 * 7 induced by (1, 5, 6, 3, 7) |--> (3, 5, 4, 6, 7) Homomorphism of GrpPerm: H1, Degree 14, Order 2^7 * 3^2 * 5 * 7 into GrpPerm: H2, Degree 14, Order 2^4 * 3^2 * 5 * 7 induced by (3, 5, 4, 6, 7) |--> (1, 5, 6, 3, 7) |
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[已解决][求助]一文本的加密方法
CMD.EXE字符表: 蔼 U853C B0AA 碍 U788D BOAD 爱 U7231 80AE 筹 U7B79 83EF 村 U6751 84E5 鲼 蝠鲼(fú fèn)是软骨鱼纲、蝠鲼科几个海产属鱼类的统称。体扁平,有强大的胸鳍,类似 翅膀,在海洋中巡游,胸鳍前有两个薄、窄、似耳朵的突起,可以向 ... 鲼GB2312里没这字。。。 多转换些字看规律,连4进6进,64进都看看 IntegerToString(0x853c,2); IntegerToString(0xb0aa,2); IntegerToString(0x853c,10); IntegerToString(0xb0aa,10); IntegerToString(0x788d,2); IntegerToString(0xb0ad,2); IntegerToString(0x788d,10); IntegerToString(0xb0ad,10); IntegerToString(0x7231,2); IntegerToString(0x80ae,2); IntegerToString(0x7231,10); IntegerToString(0x80ae,10); IntegerToString(0x7231,2); IntegerToString(0x80ae,2); IntegerToString(0x7231,10); IntegerToString(0x80ae,10); 1000010100111100 1011000010101010 34108 45226 111100010001101 1011000010101101 30861 45229 111001000110001 1000000010101110 29233 32942 111001000110001 1000000010101110 29233 32942 http://www.4qx.net/Unicode_Conversion.php 在线看编码: 筹/蔼 村/碍 鲼/爱 艇/肮 丨/奥 耿/坝 容/罢 盯/摆 檫/败 巢/板 九/办 槽/绊 狞/绑 旖/剥 嫫/饱 本文来源:http://www.4qx.net/Unicode_Conversion.php |
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[已解决][求助]一文本的加密方法
http://www.unicode.org/charts/PDF/Unicode-6.0/ http://www.knowsky.com/resource/gb2312tbl.htm http://blog.163.com/ldq_691012/blog/static/12815072009031824920/ GB2312: code +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +A +B +C +D +E +F B0A0 啊 阿 埃 挨 哎 唉 哀 皑 癌 蔼 矮 艾 碍 爱 隘 B0B0 鞍 氨 安 俺 按 暗 岸 胺 案 肮 昂 盎 凹 敖 熬 翱 B0C0 袄 傲 奥 懊 澳 芭 捌 扒 叭 吧 笆 八 疤 巴 拔 跋 B0D0 靶 把 耙 坝 霸 罢 爸 白 柏 百 摆 佰 败 拜 稗 斑 B0E0 班 搬 扳 般 颁 板 版 扮 拌 伴 瓣 半 办 绊 邦 帮 B0F0 梆 榜 膀 绑 棒 磅 蚌 镑 傍 谤 苞 胞 包 褒 剥 code +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +A +B +C +D +E +F B3A0 场 尝 常 长 偿 肠 厂 敞 畅 唱 倡 超 抄 钞 朝 B3B0 嘲 潮 巢 吵 炒 车 扯 撤 掣 彻 澈 郴 臣 辰 尘 晨 B3C0 忱 沉 陈 趁 衬 撑 称 城 橙 成 呈 乘 程 惩 澄 诚 B3D0 承 逞 骋 秤 吃 痴 持 匙 池 迟 弛 驰 耻 齿 侈 尺 B3E0 赤 翅 斥 炽 充 冲 虫 崇 宠 抽 酬 畴 踌 稠 愁 筹 B3F0 仇 绸 瞅 丑 臭 初 出 橱 厨 躇 锄 雏 滁 除 楚 code +0 +1 +2 +3 +4 +5 +6 +7 +8 +9 +A +B +C +D +E +F B1A0 薄 雹 保 堡 饱 宝 抱 报 暴 豹 鲍 爆 杯 碑 悲 B1B0 卑 北 辈 背 贝 钡 倍 狈 备 惫 焙 被 奔 苯 本 笨 B1C0 崩 绷 甭 泵 蹦 迸 逼 鼻 比 鄙 笔 彼 碧 蓖 蔽 毕 B1D0 毙 毖 币 庇 痹 闭 敝 弊 必 辟 壁 臂 避 陛 鞭 边 B1E0 编 贬 扁 便 变 卞 辨 辩 辫 遍 标 彪 膘 表 鳖 憋 B1F0 别 瘪 彬 斌 濒 滨 宾 摈 兵 冰 柄 丙 秉 饼 炳 繁简都有的18030 ai 伌佁僾凒叆呆哀哎唉啀嗌嗳嘊噫噯埃堨塧壒娭娾嫒嬡嵦愛懓懝戹挨捱敱敳昹暧曖欸毐溰溾濭爱瑷璦癌皑皚皧瞹矮砨砹硋硙碍磑礙艾蔼薆藹誒譪譺诶賹躷銰鎄鑀锿閊閡阨阸隘霭靄靉餲馤騃魞鱛鱫鴱 chou 丑丒仇侴俦偢儔吜嚋妯婤嬦帱幬怞惆愁懤抽搊搐杻杽栦椆檮殠焘燽燾牰犨犫畴疇瘳皗盩瞅矁稠筹篘簉籌紬絒綢绸臭臰菗薵裯詶謅讎讐踌躊遚酧酬醜醻鈕雔雠雦霌魗鮘鯈 |
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[原创]群论的一些基础知识
看能不能造个非单非满同态: H2是H1的真子群(正规),如果H2和H1的一个商群H1/N相同,找个和这商群同构,再找个包括这群的大群,就能成H1->H2非单非满同态 H1 := PermutationGroup< 10|(3,5)(4,6),(1,3,5),(2,4,6) ,(3,4)>; H1; H2 := PermutationGroup< 10 | (1,5,3),(2,4,6)>; H2; N:=NormalSubgroups(H1) ; N; N1:=NormalSubgroups(H2) ; N1; Order(H1); Order(H2); Index(H1, H2) ; CosetTable(H1,H2); Permutation group H1 acting on a set of cardinality 10 (3, 5)(4, 6) (1, 3, 5) (2, 4, 6) (3, 4) Permutation group H2 acting on a set of cardinality 10 (1, 5, 3) (2, 4, 6) Conjugacy classes of subgroups ------------------------------ [1] Order 1 Length 1 Permutation group acting on a set of cardinality 10 Order = 1 Id($) [2] Order 360 Length 1 Permutation group acting on a set of cardinality 10 Order = 360 = 2^3 * 3^2 * 5 (2, 6)(3, 5) (1, 5)(2, 4, 3, 6) [3] Order 720 Length 1 Permutation group acting on a set of cardinality 10 Order = 720 = 2^4 * 3^2 * 5 (1, 4, 6, 2, 5) (3, 5) Conjugacy classes of subgroups ------------------------------ [1] Order 1 Length 1 Permutation group acting on a set of cardinality 10 Order = 1 [2] Order 3 Length 1 Permutation group acting on a set of cardinality 10 Order = 3 (1, 5, 3)(2, 6, 4) [3] Order 3 Length 1 Permutation group acting on a set of cardinality 10 Order = 3 (2, 4, 6) [4] Order 3 Length 1 Permutation group acting on a set of cardinality 10 Order = 3 (1, 5, 3) [5] Order 3 Length 1 Permutation group acting on a set of cardinality 10 Order = 3 (1, 5, 3)(2, 4, 6) [6] Order 9 Length 1 Permutation group acting on a set of cardinality 10 Order = 9 = 3^2 (1, 5, 3) (2, 4, 6) 720 9 80 Mapping from: Cartesian Product<{ 1 .. 80 }, GrpPerm: H1, Degree 10, Order 2^4 * 3^2 * 5> to { 1 .. 80 } $1 $2 $3 $4 -$2 -$3 1. 2 1 1 3 1 1 2. 1 2 2 4 2 2 3. 5 6 7 1 14 16 4. 8 9 10 2 21 23 5. 3 11 12 13 10 9 6. 10 14 8 15 3 19 7. 9 8 16 17 18 3 8. 4 18 19 20 7 6 9. 7 21 5 22 4 12 10. 6 5 23 24 11 4 ...... 78. 66 69 64 72 62 74 79. 80 79 79 66 79 79 80. 79 80 80 68 80 80 |
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[原创]群论的一些基础知识
把z4------z6,z6-------z4同态用手工算了,都是自同态或单同态,满同态 想找个非单非满同态看看,能不能给个例子? http://www.numberempire.com/texequationeditor/equationeditor.php z4 [0] [1 ] [2] [3 ] z6 [0] [1] [2] [3] [4] [5] x---------->[0]*x 很多组合都同态,只要z4选4个,Z6里可选1个(6种)=4*6=24种 z4选4个 ,Z6里两个=4*30=120种 z4选4个 ,Z6里3个=4*6*5*4=480种 z4选4个 ,Z6里4个=4*6*5*4*3=1440种 x---------->[3]*x,只有4种组合才同态: z4中4个都选 --------> z6 子群[0] [1 ] [2] [3 ] 一一映射组: 0-->0 1->1 2->2 3->3 z4 自身ID映射 自同构,内自同构 或0-->0 1->1 2->3 3->2 z4和 z6 子群z'4同构,可z4-----z6单射同构 或1->0 0->1 2->2 3->3 z4和 z6 子群z'4同构,可z4-----z6单射同构 或1->0 0->1 2->3 3->2 z4和 z6 子群z'4同构,可z4-----z6单射同构 φ(a+b) φ(a)+φ( b) MOD4 MOD6 (0+1) *3 =3 0*3+1*3 =3 (0+2 ) *3 =2 0*3+2 *3 =0 (0+3)*3 =1 0*3+3 *3 = 3 (1+0 )*3 =3 1*3+0 *3 =3 (1+2)*3 =3 1*3+2*3 =3 (1+3 )*3 =0 =0 (2+3)*3 =3 =3 ](3+2)*3 =3 =3 z6-------------------z4 z6中6个都选 --------> 0 1 2,3,4,5---------------->0,1,2,3 映射: [0+1 ] [3+4 ] [ 2+5 ]红 可交换(蓝) x---------->[0]*x 虽有四元素{1,2,4,5}集合在可交换运算[2+4],[1+5]符合φ(a+b) =φ(a)+φ( b) ,可[0+3]却左右不等,不是z6--z4映射,所以x---------->[0]*x 不同态 x---------->[2]*x z6中6个都选 --------> z4中四个都选,z6中0,1 对应z4中0,1, z6中3,4对应z4中3,0 z6中2,5对应z4中2,0 0,4,5都对应0,满同态 0 1 2,3,4,5---------------->0,1,2,3 映射: [0+1 ] [3+4 ] [ 2+5 ]红=2 可交换(蓝)=2 φ(a+b) φ(a)+φ( b) MOD6 MOD4 0+1 =2 =2 0+2 =4 =0 0+3 =0 =2 0+4 =2 =0 0+5 =4 =2 1+0 =2 =2 1+2 =0 =2 1+3 =2 =0 1+4 =4 =2 1+5 =0 =0 2+0 =4 =0 2+1 =0 =2 2+3 =4 =2 2+4 =0 =0 2+5 =2 =2 3+0 =0 =2 3+1 =2 =0 3+2 =4 =2 3+4 =2 =2 3+5 =4 =0 4+0 =2 =0 4+1 =2 =4 4+2 =0 =0 4+3 2 =2 4+5 0 =2 5+0 =2 =2 5+1 =0 =0 5+2 =2 =2 5+3 =4 =0 5+4 =0 =2 z:=IntegerRing(4) ; z4:=AdditiveGroup(z); z1:=IntegerRing(6) ; z6:=AdditiveGroup(z1); H46:= hom< z4 -> z6 | z4.1 -> 0*z6.1 >; H46; H463:= hom< z4 -> z6 | z4.1 -> 3*z6.1 >; H463; H640:= hom< z6 -> z4 | z6.1 -> 0*z4.1 >; H640; H642:= hom< z6 -> z4 | z6.1 -> 2*z4.1 >; H642; Kernel(H46) ; Kernel(H463) ; Kernel(H640) ; Kernel(H642) ; Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 Abelian Group isomorphic to Z/4 Defined on 1 generator in supergroup z4: $.1 = z4.1 Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z4: $.1 = 2*z4.1 Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator in supergroup z6: $.1 = z6.1 Relations: 6*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator in supergroup z6: $.1 = 2*z6.1 Relations: 3*$.1 = 0 |
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[分享]在VC++6.0中使用NTL数论库
收藏慢慢学,Number Theory真很难,分枝都有几十个 |
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[已解决][求助]一文本的加密方法
全贴出来嘛。。。加密后连标点符号也都是简体字符集里的吗?比下GB2312,GBK GB18030,UFT-8里标点符号,简体标点和UNICODE有些符号编码不一样,形状也不一样 |
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[原创]群论的一些基础知识
求域,核 z:=IntegerRing(4) ; z4:=AdditiveGroup(z); z1:=IntegerRing(6) ; z6:=AdditiveGroup(z1); H44 := hom< z4 -> z4 | z4.1 -> z4.1 >; H44; H46:= hom< z4 -> z6 | z4.1 -> 0*z6.1 >; H46; H463:= hom< z4 -> z6 | z4.1 -> 3*z6.1 >; H463; H642:= hom< z6 -> z4 | z6.1 -> 2*z4.1 >; H642; Domain(H463) ; Codomain(H463); Domain(H642) ; Codomain(H642); Image(H463) ; Image(H642) ; Kernel(H463) ; Kernel(H642) ; Mapping from: GrpAb: z4 to GrpAb: z4 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z6 to GrpAb: z4 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*z4.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*z6.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*z6.1 = 0 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*z4.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z6: $.1 = 3*z6.1 Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z4: $.1 = 2*z4.1 Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z4: $.1 = 2*z4.1 Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator in supergroup z6: $.1 = 2*z6.1 Relations: 3*$.1 = 0 z:=IntegerRing(4) ; z4:=AdditiveGroup(z); z1:=IntegerRing(6) ; z6:=AdditiveGroup(z1); H44 := hom< z4 -> z4 | z4.1 -> z4.1 >; H44; H46:= hom< z4 -> z6 | z4.1 -> 0*z6.1 >; H46; H463:= hom< z4 -> z6 | z4.1 -> 3*z6.1 >; H463; H642:= hom< z6 -> z4 | z6.1 -> 2*z4.1 >; H642; Image(H44) ; Image(H463) ; Image(H642) ; Kernel(H44) ; Kernel(H463) ; Kernel(H642) ; Mapping from: GrpAb: z4 to GrpAb: z4 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z6 to GrpAb: z4 Abelian Group isomorphic to Z/4 Defined on 1 generator in supergroup z4: $.1 = z4.1 Relations: 4*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z6: $.1 = 3*z6.1 Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z4: $.1 = 2*z4.1 Relations: 2*$.1 = 0 Abelian Group of order 1 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z4: $.1 = 2*z4.1 Relations: 2*$.1 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator in supergroup z6: $.1 = 2*z6.1 Relations: 3*$.1 = 0 求自同构: z:=IntegerRing(4) ; z4:=AdditiveGroup(z); z1:=IntegerRing(6) ; z6:=AdditiveGroup(z1); H44 := hom< z4 -> z4 | z4.1 -> z4.1 >; H44; H46:= hom< z4 -> z6 | z4.1 -> 0*z6.1 >; H46; H463:= hom< z4 -> z6 | z4.1 -> 3*z6.1 >; H463; H642:= hom< z6 -> z4 | z6.1 -> 2*z4.1 >; H642; AutomorphismGroup(z4); AutomorphismGroup(z6); Mapping from: GrpAb: z4 to GrpAb: z4 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z6 to GrpAb: z4 A group of automorphisms of Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*z4.1 = 0 Generators: Automorphism of Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*z4.1 = 0 which maps: z4.1 |--> 3*z4.1 A group of automorphisms of Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*z6.1 = 0 Generators: Automorphism of Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*z6.1 = 0 which maps: 3*z6.1 |--> 3*z6.1 2*z6.1 |--> 4*z6.1 |
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[转帖]智能卡加密算法的微分能量分析方法研究
国标里出了磁卡IC卡识别标准,有卖的,不过没仪器就只能理论学习了 中科院出的2010密码学书上说我国学者 DPA,EMC,量子通讯3之类的论文大都是这样写出的:看到国外有论文后,把那老外用的仪器整个进口,自己 再把老外论文数据换换--------OK了----------申请中科院密码学博士后 |
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[原创]群论的一些基础知识
Z4--------Z6 Z6--------Z4 画横线的对应0x/3x 2x z:=IntegerRing(4) ; z4:=AdditiveGroup(z); z1:=IntegerRing(6) ; z6:=AdditiveGroup(z1); H44 := hom< z4 -> z4 | z4.1 -> z4.1 >; H44; H46:= hom< z4 -> z6 | z4.1 -> 0*z6.1 >;--------------------------------- H46; H46:= hom< z4 -> z6 | z4.1 -> 1*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 -> 2*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 -> 3*z6.1 >;--------------------------------- H46:= hom< z4 -> z6 | z4.1 -> 4*z6.1 >; H46:= hom< z4 -> z6 | z4.1 -> 5*z6.1 >; H46:= hom< z4 -> z6 | z4.1 -> 6*z6.1 >;--------------------------------- H46:= hom< z4 -> z6 | z4.1 ->7*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 ->3*1999*z6.1 >;------------------------------ H46; H66:= hom< z6 -> z6 | z6.1 -> z6.1 >; H66; H64:= hom< z6 -> z4 | z6.1 -> 2*z4.1 >;-------------------------------- H64:= hom< z6 -> z4 | z6.1 -> 3*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 4*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 5*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 6*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 7*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 2*199*z4.1 >;------------------------------- Mapping from: GrpAb: z4 to GrpAb: z4 Mapping from: GrpAb: z4 to GrpAb: z6 >> H46:= hom< z4 -> z6 | z4.1 -> 1*z6.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z4 to GrpAb: z6 >> H46:= hom< z4 -> z6 | z4.1 -> 2*z6.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z4 to GrpAb: z6 >> H46:= hom< z4 -> z6 | z4.1 -> 4*z6.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism >> H46:= hom< z4 -> z6 | z4.1 -> 5*z6.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism >> H46:= hom< z4 -> z6 | z4.1 ->7*z6.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z6 to GrpAb: z6 >> H64:= hom< z6 -> z4 | z6.1 -> 3*z4.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 >> H64:= hom< z6 -> z4 | z6.1 -> 5*z4.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 >> H64:= hom< z6 -> z4 | z6.1 -> 7*z4.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z6 to GrpAb: z4 ============ 顺便连Z4--------Z*6 的也看了:都同态 Z*6 ----------z4 只有1x,3x,5x,不同态,2x,4x,6x都同态 Z*6 和Z6不同: Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*(z*6).1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*z6.1 = 0 z:=IntegerRing(4) ; z4:=AdditiveGroup(z); z1:=IntegerRing(6) ; z6:=MultiplicativeGroup(z1); H44 := hom< z4 -> z4 | z4.1 -> z4.1 >; H44; H46:= hom< z4 -> z6 | z4.1 -> 0*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 -> 1*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 -> 2*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 -> 3*z6.1 >; H46:= hom< z4 -> z6 | z4.1 -> 4*z6.1 >; H46:= hom< z4 -> z6 | z4.1 -> 5*z6.1 >; H46:= hom< z4 -> z6 | z4.1 -> 6*z6.1 >; H46:= hom< z4 -> z6 | z4.1 ->7*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 ->3*1999*z6.1 >; H46; H66:= hom< z6 -> z6 | z6.1 -> z6.1 >; H66; H64:= hom< z6 -> z4 | z6.1 -> 2*z4.1 >; H64:= hom< z6 -> z4 | z6.1 -> 3*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 4*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 5*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 6*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 7*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 2*199*z4.1 >; Mapping from: GrpAb: z4 to GrpAb: z4 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z6 to GrpAb: z6 >> H64:= hom< z6 -> z4 | z6.1 -> 3*z4.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 >> H64:= hom< z6 -> z4 | z6.1 -> 5*z4.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 >> H64:= hom< z6 -> z4 | z6.1 -> 7*z4.1 >; ^ Runtime error in hom< ... >: Images given do not define a homomorphism Mapping from: GrpAb: z6 to GrpAb: z4 ============== 顺便连Z*4--------Z*6 的也看了:都同态 有1x,3x,5x,,2x,4x,6x都同态 Z*6 ----------z4 有1x,3x,5x,,2x,4x,6x都同态 Z*6 和Z*4同构: NumberOfGenerators(z4) ; z1:=IntegerRing(6) ; z6:=MultiplicativeGroup(z1); z6; NumberOfGenerators(z4) ; IsIsomorphic(z4, z6); Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*z4.1 = 0 1 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*z6.1 = 0 1 true z:=IntegerRing(4) ; z4:=MultiplicativeGroup(z); z4; z1:=IntegerRing(6) ; z6:=MultiplicativeGroup(z1); z6; H44 := hom< z4 -> z4 | z4.1 -> z4.1 >; H44; H46:= hom< z4 -> z6 | z4.1 -> 0*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 -> 1*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 -> 2*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 -> 3*z6.1 >; H46:= hom< z4 -> z6 | z4.1 -> 4*z6.1 >; H46:= hom< z4 -> z6 | z4.1 -> 5*z6.1 >; H46:= hom< z4 -> z6 | z4.1 -> 6*z6.1 >; H46:= hom< z4 -> z6 | z4.1 ->7*z6.1 >; H46; H46:= hom< z4 -> z6 | z4.1 ->3*1999*z6.1 >; H46; H66:= hom< z6 -> z6 | z6.1 -> z6.1 >; H66; H64:= hom< z6 -> z4 | z6.1 -> 2*z4.1 >; H64:= hom< z6 -> z4 | z6.1 -> 3*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 4*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 5*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 6*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 7*z4.1 >; H64; H64:= hom< z6 -> z4 | z6.1 -> 2*199*z4.1 >; Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*z4.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*z6.1 = 0 Mapping from: GrpAb: z4 to GrpAb: z4 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z4 to GrpAb: z6 Mapping from: GrpAb: z6 to GrpAb: z6 Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 Mapping from: GrpAb: z6 to GrpAb: z4 |
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[求助]这时间2011-04-20,23:38:31 我不在线
应该通过输入法攻的,天天都来,好奇心害死人地 |
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[原创]雨过天晴管理员密码算法
雨过天晴K365.NET上过,不限大小,可关了啊,现在用UPLOADING.COM |
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[求助]这时间2011-04-20,23:38:31 我不在线
中国人一直有人----一群人盯,大街上盯就算了,为了首都安全---1:8比例---------其实60万射像头盯就OK了,网上盯就更自然的事了,证据居然让我发现了,哈哈 |
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[原创]群论的一些基础知识
两门新技术:GOOGLE API +LATEX都会。。。难学吗? 网上有在线公式站点,也方便 准备把下面三阿群初等因子不变因子搞清 s1:=Sym({ 0..8 }); A0:= AbelianGroup([2^7,3^4,5,7]); A0; s2:=Sym({ 0..12 }); s2; A1:= AbelianGroup([2^10,3^5,5^2,7^11,13]); A1; A2:= AbelianGroup([30,140,250]); A2; Symmetric group s1 acting on a set of cardinality 9 Order = 362880 = 2^7 * 3^4 * 5 * 7 Abelian Group isomorphic to Z/362880 Defined on 4 generators Relations: 128*A0.1 = 0 81*A0.2 = 0 5*A0.3 = 0 7*A0.4 = 0 Symmetric group s2 acting on a set of cardinality 13 Order = 2^10 * 3^5 * 5^2 * 7 * 11 * 13 Abelian Group isomorphic to Z/159907204637107200 Defined on 5 generators Relations: 1024*A1.1 = 0 243*A1.2 = 0 25*A1.3 = 0 1977326743*A1.4 = 0 13*A1.5 = 0 Abelian Group isomorphic to Z/10 + Z/10 + Z/10500 Defined on 3 generators Relations: 30*A2.1 = 0 140*A2.2 = 0 250*A2.3 = 0 A2:= AbelianGroup([30,140,250]); A2; FactoredOrder(A2); Abelian Group isomorphic to Z/10 + Z/10 + Z/10500 Defined on 3 generators Relations: 30*A2.1 = 0 140*A2.2 = 0 250*A2.3 = 0 [ <2, 4>, <3, 1>, <5, 5>, <7, 1> ] 阶为1050000的群有:初等因子: 1:Z2+Z2+Z2+Z2+ Z3 +Z5+Z5+Z5+Z5+Z5 +Z7 初等群 2:Z4+Z2+Z2+ Z3 +Z5+Z5+Z5+Z5+Z5 +Z7 3:Z8+Z2+ Z3 +Z5+Z5+Z5+Z5+Z5 +Z7 4:Z16+ Z3 +Z5+Z5+Z5+Z5+Z5 +Z7 5:Z2+Z2+Z2+Z2+ Z3 +Z25+Z5+Z5+Z5 +Z7 6:Z2+Z2+Z2+Z2+ Z3 +Z75+Z5+Z5 +Z7 7:Z2+Z2+Z2+Z2+ Z3 +Z375+Z5 +Z7 8:Z2+Z2+Z2+Z2+ Z3 +Z375*5 +Z7 9:Z4+Z2+Z2+ Z3 +Z25+Z5+Z5+Z5 +Z7 ............. 共有4*5=20种 1:转不变因子: 12222 11113 55555 11117=Z5+Z/10+Z/10+Z/10+Z210 9:转不变因子: 1 2 2 4 1 1 1 3 5 5 5 25 1 1 1 7=Z5+Z/10+Z/10+Z/2100 验:对!同构可关系不同,1和9中一个是11/5生成元、一个11/4生成元 A22:= AbelianGroup([2,2,2,2,3,5,5,5,5,5,7]); A22; A22:= AbelianGroup([4,2,2,2,3,25,5,5,5,7]); A22; A2:= AbelianGroup([5,10,10,10,210]); A2; A22:= AbelianGroup([5,10,10,10,210]); A22; Abelian Group isomorphic to Z/5 + Z/10 + Z/10 + Z/10 + Z/210 Defined on 11 generators Relations: 2*A22.1 = 0 2*A22.2 = 0 2*A22.3 = 0 2*A22.4 = 0 3*A22.5 = 0 5*A22.6 = 0 5*A22.7 = 0 5*A22.8 = 0 5*A22.9 = 0 5*A22.10 = 0 7*A22.11 = 0 Abelian Group isomorphic to Z/10 + Z/10 + Z/10 + Z/2100 Defined on 10 generators Relations: 4*A22.1 = 0 2*A22.2 = 0 2*A22.3 = 0 2*A22.4 = 0 3*A22.5 = 0 25*A22.6 = 0 5*A22.7 = 0 5*A22.8 = 0 5*A22.9 = 0 7*A22.10 = 0 Abelian Group isomorphic to Z/5 + Z/10 + Z/10 + Z/10 + Z/210 Defined on 5 generators Relations: 5*A2.1 = 0 10*A2.2 = 0 10*A2.3 = 0 10*A2.4 = 0 210*A2.5 = 0 |
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[求助]这时间2011-04-20,23:38:31 我不在线
干啥别被盯住了,被政府部门盯着后,您老的公安库金融库底子里有什麽知道吗?如果你愿出点银子,让私人侦探看看也行 看看解密的西德档案俄罗斯档案 |
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