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[讨论]示波器和密码芯片
卡插在哪呢? |
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[讨论]示波器和密码芯片
http://www.dpabook.org/Stefan/smangard.asc 作者主页 书里推荐也有这网站 作者主页用的PGP-------cryptoex.com ,很GNU -----BEGIN PGP PUBLIC KEY BLOCK----- Version: CryptoEx OpenPGP Engine Version 2.1 Comment: CryptoEx Client Suite - http://www.cryptoex.com mQGiBEYTnJQRBAD0iP1YTknbzSC0neSRBzZrM2w4DUUdD3yIsxx8Wy2O9vPJI8BD 8KVbGI2Ou1WMuF040zT9fBdXQ6MdGGzeMyEstSr/POGxKUAYEY18hKcKctaGxAMZ yAcpesqVDNmWn6vQClCbAkbTCD1mpLC2UeK65U5EOXyfKl4xL/bbXHWugQCg/5+c fL2JSyIZJrqrol7DVeknwrEEAO2F1MidohOozi6oKLISOzeMrv2am4CK93TIl6TP +QUTExRb7MLaEiIpkQtd1PwSUTn848jWxIdFVsF2zwmhJzcqxcHY+uKFBME7xtPT FUvFFeau3cwYFdfobO7LlJ3lZTvisLI/r1A9w4jFgSAfFzIx30VsyqY+3x0+flM3 SFKbBAChXULz16kUO4+WsKhPihNjCSic2RJP6DXZMZfnXEuLrYeXQYbIX3AjLDt5 aA8lWy/iEbr4YJcPG8noCedwtq7wDywtLSwBSXA63rAADB72KUnqTZk/y8xQWSpM dvt3uLWLX3bjRKXqd6r/BcJAmg4rggzP4/lL4SW7Gtu+iDh344kARgQfEQIAEAUC RhOclAkQHbmaymnEcDQAAPLTAKDyaTqAU2VZNqEvHo7BgAk/I8sMBQCaA5iM9tA9 cZ4sF3BoIaUaKpqopt20QE1hbmdhcmQgU3RlZmFuIChJRkFHIEFJTSBDQyBUSSBD SSkgPFN0ZWZhbi5NYW5nYXJkQGluZmluZW9uLmNvbT6JAEYEEBECABAFAkYTnJQJ EB25msppxHA0AAAPkwCfbB3nLudK2TFYHzScSTMRhTDDarcAoMyWUlF7/VZ4VXuD mSQqG7FaxFe9uQINBEYTnJQQCAD2Qle3CH8IF3KiutapQvMF6PlTETlPtvFuuUs4 INoBp1ajFOmPQFXz0AfGy0OplK33TGSGSfgMg71l6RfUodNQ+PVZX9x2Uk89PY3b zpnhV5JZzf24rnRPxfx2vIPFRzBhznzJZv8V+bv9kV7HAarTW56NoKVyOtQa8L9G AFgr5fSI/VhOSdvNILSd5JEHNmszbDgNRR0PfIizHHxbLY7288kjwEPwpVsYjY67 VYy4XTjTNP18F1dDox0YbN4zISy1Kv884bEpQBgRjXyEpwpy1obEAxnIByl6ypUM 2Zafq9AKUJsCRtMIPWakXUGfnHy9iUsiGSa6q6Jew1XpMgs7AAICCACbnLW5dz9A ab2bLNUl9PwodP9rcGR30TAMIrX6deMjStuFRDK7pNxXTrFLU+K5PpulF6f5YVT9 wcPsrEQfirbqDKbDwSDmv3wcnn2JjcP1ljGznzaZEoxi3wjpyyMQBW8pbbA1aYEd qqVB/uxcxKX/kV/5/fDgjpzpSIkvB7DJPPYlQ5BbDDVIW31vN8Ji5ZjtBiwQLpFw 2TH27lrwrGuhelY9X2Dxzy4VOPqhnFNia5cxJ7L+PuOdxHndFpLcYvFvosMW0lGV ze7v8slF1vNew4z+41u+JCnUjonKOOBB3bB5fFqY9ABZI1Hoh7WG6Lnk8jimvXsZ bc69LcWIhKikiQBGBBgRAgAQBQJGE5yUCRAduZrKacRwNAAAH9oAniC5UJdd0i55 i5Dsirq56umdgyh3AKDiz8oO+cBBTmiNk8lSyyYqB/Z/HQ== =y40j -----END PGP PUBLIC KEY BLOCK----- |
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[讨论]示波器和密码芯片
卖吗? |
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[原创]群论的一些基础知识
感觉用工具学才好 ,就象线性代数,我们的教科书误人子弟,用MALAB/MAPLE工具才显威力。赶上潮流才行,要不总再64卦周易里转,像同态的核,理想。。。。例子都不好懂 唠骚几句: 像陶轩哲关于素数获菲尔兹奖,我国的素数家王元(60多了吧)被采访时说了,他的方法非常新,不好懂啊 庞加来猜想的那个俄国。。夫,用的也是刚在前几个月才被别人论文得出的结果 费马大定理更是几个大家互相交流得出的结果 有限单群分类定理:15000页 300页下的抽象代数教科书才仅能讲点26个散单群名称 韩国人日本人在26个散单群里有名字,日本人在代数素论更是牛 就像编译器,还没搞懂CPU微指令,可新书上又说了,GPU将和CPU抢地盘了,刚想翻翻编译器原理,可INTEL又多核了,那个高纳德都反对多核,可现谁不是多核呢 虽说不和他们比,可你只要看书,就总在吊人胃口。。 感觉是群论是一种思想,和老马有非常不一至的地方,所以国家不太提倡学的太深了,国产抽象代数教科书没厚的 |
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[求助]非相临表示问题
把书上的贴上,看有没能帮上的 |
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[讨论]关于1024位RSA的破解
[QUOTE=lilianjie;937179]证书里的RSA1024数都不同,这些1024bit数有多少个? 难道都不容易分解吗? 顶端 Posted: 2010-06-17 19:17 | [楼 主] 哪位帮算下:10^309/(in10^309)-10^308/(in10^308)=10^308*in10(10/309-...[/QUOTE] 那时水平有限,算成2048位的两素因子了,不过现在知道maple里有个PRIMEPI命令可算 |
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[讨论]关于1024位RSA的破解
SAGE ,maxma |
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[求助]模剰余类中群元素的阶能比模大吗?
看了N次了,感觉就是素数拆分到最小再组合一下排列,可那只是结构,和循环群混着用的时后就老咪糊,不只是不是还有有限交换群的2级基本定理,比基本定理高点的 |
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[求助]模剰余类中群元素的阶能比模大吗?
西罗P/西罗子P /ABELSUB/所有的子群,子孙生的真多,S7就运行不了了,S5才行 验拉格朗日定理: left:= a1 * G; left; right:=G * a1; right; quot:=a1*a3 * G; G := Sym({ 0..6 }); G; R:=Order(G); R; Factorization(R); FactoredOrder(G); a:=Random(G); a; a1:=a^10; a1; a2:=a^300; a3:=a^10000; a3; a4:=a^1000450000; a4; orda1:=Order(a1); orda1; orda2:=Order(a2); orda2; orda3:=Order(a3); orda3; orda4:=Order(a4); orda4; Gcd(R,orda1); Gcd(R,orda2); Gcd(R,orda3); Gcd(R,orda4); SylowSubgroup(G, 2); Sylow(G, 2); SylowSubgroup(G, 3); Sylow(G, 3); SylowSubgroup(G, 173); Sylow(G, 173); AbelianSubgroups(G); Symmetric group G acting on a set of cardinality 7 Order = 5040 = 2^4 * 3^2 * 5 * 7 5040 [ <2, 4>, <3, 2>, <5, 1>, <7, 1> ] [ <2, 4>, <3, 2>, <5, 1>, <7, 1> ] (0, 2, 6, 1) (0, 6)(1, 2) Id(G) Id(G) 2 1 1 1 2 1 1 1 Permutation group acting on a set of cardinality 7 Order = 16 = 2^4 (0, 1) (2, 3) (2, 4)(3, 5) Permutation group acting on a set of cardinality 7 Order = 16 = 2^4 (0, 1) (2, 3) (2, 4)(3, 5) Permutation group acting on a set of cardinality 7 Order = 9 = 3^2 (0, 1, 2) (3, 4, 5) Permutation group acting on a set of cardinality 7 Order = 9 = 3^2 (0, 1, 2) (3, 4, 5) Permutation group acting on a set of cardinality 7 Order = 1 Permutation group acting on a set of cardinality 7 Order = 1 Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 7 Order = 1 Id($) [ 2] Order 2 Length 21 Permutation group acting on a set of cardinality 7 Order = 2 (5, 6) [ 3] Order 2 Length 105 Permutation group acting on a set of cardinality 7 Order = 2 (0, 4)(1, 3) [ 4] Order 2 Length 105 Permutation group acting on a set of cardinality 7 Order = 2 (0, 1)(3, 6)(4, 5) [ 5] Order 3 Length 35 Permutation group acting on a set of cardinality 7 Order = 3 (1, 4, 3) [ 6] Order 3 Length 140 Permutation group acting on a set of cardinality 7 Order = 3 (0, 6, 4)(1, 2, 3) [ 7] Order 5 Length 126 Permutation group acting on a set of cardinality 7 Order = 5 (0, 1, 2, 4, 3) [ 8] Order 7 Length 120 Permutation group acting on a set of cardinality 7 Order = 7 (0, 3, 6, 2, 4, 5, 1) [ 9] Order 4 Length 35 Permutation group acting on a set of cardinality 7 Order = 4 = 2^2 (0, 4)(1, 3) (0, 1)(3, 4) [10] Order 4 Length 105 Permutation group acting on a set of cardinality 7 Order = 4 = 2^2 (0, 5, 1, 6) (0, 1)(5, 6) [11] Order 4 Length 105 Permutation group acting on a set of cardinality 7 Order = 4 = 2^2 (2, 6)(3, 4) (0, 1)(2, 6) [12] Order 4 Length 105 Permutation group acting on a set of cardinality 7 Order = 4 = 2^2 (5, 6) (0, 1)(5, 6) [13] Order 4 Length 315 Permutation group acting on a set of cardinality 7 Order = 4 = 2^2 (0, 2, 6, 4)(1, 3) (0, 6)(2, 4) [14] Order 4 Length 315 Permutation group acting on a set of cardinality 7 Order = 4 = 2^2 (0, 3)(1, 4)(5, 6) (5, 6) [15] Order 4 Length 315 Permutation group acting on a set of cardinality 7 Order = 4 = 2^2 (0, 1)(3, 6)(4, 5) (3, 5)(4, 6) [16] Order 6 Length 105 Permutation group acting on a set of cardinality 7 Order = 6 = 2 * 3 (3, 4, 5) (0, 1)(2, 6) [17] Order 6 Length 210 Permutation group acting on a set of cardinality 7 Order = 6 = 2 * 3 (0, 1, 4) (5, 6) [18] Order 6 Length 420 Permutation group acting on a set of cardinality 7 Order = 6 = 2 * 3 (0, 3, 5)(1, 6, 4) (0, 1)(3, 6)(4, 5) [19] Order 9 Length 70 Permutation group acting on a set of cardinality 7 Order = 9 = 3^2 (2, 3, 4) (0, 1, 6) [20] Order 10 Length 126 Permutation group acting on a set of cardinality 7 Order = 10 = 2 * 5 (0, 2, 1, 6, 3) (4, 5) [21] Order 8 Length 105 Permutation group acting on a set of cardinality 7 Order = 8 = 2^3 (0, 3)(1, 4)(5, 6) (0, 1)(3, 4) (0, 1)(3, 4)(5, 6) [22] Order 8 Length 105 Permutation group acting on a set of cardinality 7 Order = 8 = 2^3 (3, 4)(5, 6) (0, 1)(3, 4) (0, 1)(3, 4)(5, 6) [23] Order 8 Length 315 Permutation group acting on a set of cardinality 7 Order = 8 = 2^3 (0, 4, 1, 3) (0, 1)(3, 4) (0, 1)(3, 4)(5, 6) [24] Order 12 Length 35 Permutation group acting on a set of cardinality 7 Order = 12 = 2^2 * 3 (3, 4, 5) (0, 2)(1, 6) (0, 6)(1, 2) [25] Order 12 Length 105 Permutation group acting on a set of cardinality 7 Order = 12 = 2^2 * 3 (2, 3, 6) (0, 1)(4, 5) (4, 5) [26] Order 12 Length 105 Permutation group acting on a set of cardinality 7 Order = 12 = 2^2 * 3 (0, 5, 6, 4) (1, 3, 2) (0, 6)(4, 5) 西罗P/西罗子P /ABELSUB也看看 Symmetric group G acting on a set of cardinality 5 Order = 120 = 2^3 * 3 * 5 120 [ <2, 3>, <3, 1>, <5, 1> ] [ <2, 3>, <3, 1>, <5, 1> ] (0, 2)(1, 4) Id(G) Id(G) Id(G) 1 1 1 1 1 1 1 1 Permutation group acting on a set of cardinality 5 Order = 8 = 2^3 (0, 1) (0, 2)(1, 3) Permutation group acting on a set of cardinality 5 Order = 8 = 2^3 (0, 1) (0, 2)(1, 3) Permutation group acting on a set of cardinality 5 Order = 3 (0, 2, 3) Permutation group acting on a set of cardinality 5 Order = 3 (0, 2, 3) Permutation group acting on a set of cardinality 5 Order = 1 Permutation group acting on a set of cardinality 5 Order = 1 Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 5 Order = 1 Id($) [ 2] Order 2 Length 10 Permutation group acting on a set of cardinality 5 Order = 2 (2, 3) [ 3] Order 2 Length 15 Permutation group acting on a set of cardinality 5 Order = 2 (0, 1)(2, 3) [ 4] Order 3 Length 10 Permutation group acting on a set of cardinality 5 Order = 3 (1, 2, 3) [ 5] Order 5 Length 6 Permutation group acting on a set of cardinality 5 Order = 5 (0, 3, 4, 1, 2) [ 6] Order 4 Length 5 Permutation group acting on a set of cardinality 5 Order = 4 = 2^2 (0, 1)(2, 3) (0, 3)(1, 2) [ 7] Order 4 Length 15 Permutation group acting on a set of cardinality 5 Order = 4 = 2^2 (0, 3, 4, 2) (0, 4)(2, 3) [ 8] Order 4 Length 15 Permutation group acting on a set of cardinality 5 Order = 4 = 2^2 (2, 3) (0, 4)(2, 3) [ 9] Order 6 Length 10 Permutation group acting on a set of cardinality 5 Order = 6 = 2 * 3 (0, 1, 4) (2, 3) Conjugacy classes of subgroups ------------------------------ [ 1] Order 1 Length 1 Permutation group acting on a set of cardinality 5 Order = 1 Id($) [ 2] Order 2 Length 10 Permutation group acting on a set of cardinality 5 Order = 2 (3, 4) [ 3] Order 2 Length 15 Permutation group acting on a set of cardinality 5 Order = 2 (0, 1)(3, 4) [ 4] Order 3 Length 10 Permutation group acting on a set of cardinality 5 Order = 3 (1, 4, 3) [ 5] Order 5 Length 6 Permutation group acting on a set of cardinality 5 Order = 5 (0, 3, 2, 1, 4) [ 6] Order 4 Length 5 Permutation group acting on a set of cardinality 5 Order = 4 = 2^2 (0, 1)(3, 4) (0, 3)(1, 4) [ 7] Order 4 Length 15 Permutation group acting on a set of cardinality 5 Order = 4 = 2^2 (0, 3, 2, 4) (0, 2)(3, 4) [ 8] Order 4 Length 15 Permutation group acting on a set of cardinality 5 Order = 4 = 2^2 (3, 4) (0, 2)(3, 4) [ 9] Order 6 Length 10 Permutation group acting on a set of cardinality 5 Order = 6 = 2 * 3 (1, 4)(2, 3) (0, 4, 1) [10] Order 6 Length 10 Permutation group acting on a set of cardinality 5 Order = 6 = 2 * 3 (0, 1, 2) (3, 4) [11] Order 6 Length 10 Permutation group acting on a set of cardinality 5 Order = 6 = 2 * 3 (3, 4) (2, 4, 3) [12] Order 10 Length 6 Permutation group acting on a set of cardinality 5 Order = 10 = 2 * 5 (1, 2)(3, 4) (0, 3, 2, 1, 4) [13] Order 8 Length 15 Permutation group acting on a set of cardinality 5 Order = 8 = 2^3 (3, 4) (0, 2)(3, 4) (0, 3)(2, 4) [14] Order 12 Length 5 Permutation group acting on a set of cardinality 5 Order = 12 = 2^2 * 3 (1, 4, 3) (0, 1)(3, 4) (0, 3)(1, 4) [15] Order 12 Length 10 Permutation group acting on a set of cardinality 5 Order = 12 = 2^2 * 3 (1, 2) (0, 1, 2) (3, 4) [16] Order 20 Length 6 Permutation group acting on a set of cardinality 5 Order = 20 = 2^2 * 5 (0, 3, 4, 2) (0, 4)(2, 3) (0, 3, 1, 2, 4) [17] Order 24 Length 5 Permutation group acting on a set of cardinality 5 Order = 24 = 2^3 * 3 (3, 4) (2, 4, 3) (0, 2)(3, 4) (0, 3)(2, 4) [18] Order 60 Length 1 Permutation group acting on a set of cardinality 5 Order = 60 = 2^2 * 3 * 5 (0, 1)(2, 3) (1, 4, 2) [19] Order 120 Length 1 Permutation group acting on a set of cardinality 5 Order = 120 = 2^3 * 3 * 5 (0, 1) (0, 4)(1, 2, 3) |
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[求助]模剰余类中群元素的阶能比模大吗?
G := Sym({ "a", "b", "c", "d" ,"e", "f", "g", "h" ,"i", "j", "k", "l","m" }); G; R:=Order(G); R; Factorization(R); a:=Random(G); a; a1:=a^100; a1; a2:=a^300; a3:=a^10000; a3; a4:=a^1000450000; a4; orda1:=Order(a1); orda1; orda2:=Order(a2); orda2; orda3:=Order(a3); orda3; orda4:=Order(a4); orda4; Gcd(R,orda1); Gcd(R,orda2); Gcd(R,orda3); Gcd(R,orda4); Symmetric group G acting on a set of cardinality 13 Order = 2^10 * 3^5 * 5^2 * 7 * 11 * 13 6227020800 [ <2, 10>, <3, 5>, <5, 2>, <7, 1>, <11, 1>, <13, 1> ] (f, i)(b, g, m, a, k, c, e, l, h) (b, g, m, a, k, c, e, l, h) (b, g, m, a, k, c, e, l, h) (b, g, m, a, k, c, e, l, h) 9 3 9 9 9 3 9 9 |
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[求助]模剰余类中群元素的阶能比模大吗?
拉格朗日定理的推论给了结果,只要是有限群:对任意的a∈G,ord(a)是|G|的因子 试试看: G := Sym({0.. 100}); G; R:=Order(G); R; Factorization(R); a:=Random(G); a; a1:=a^100; a1; a2:=a^300; a3:=a^10000; a3; orda1:=Order(a1); orda1; orda2:=Order(a2); orda2; orda3:=Order(a3); orda3; Gcd(R,orda1); Gcd(R,orda2); Gcd(R,orda3); Symmetric group G acting on a set of cardinality 101 9425947759838359420851623124482936749562312794702543768327889353416977599316221\ 4765030878615918083469116234900035495995833697063026032640000000000000000000000\ 00 [ <2, 97>, <3, 48>, <5, 24>, <7, 16>, <11, 9>, <13, 7>, <17, 5>, <19, 5>, <23, 4>, <29, 3>, <31, 3>, <37, 2>, <41, 2>, <43, 2>, <47, 2>, <53, 1>, <59, 1>, <61, 1>, <67, 1>, <71, 1>, <73, 1>, <79, 1>, <83, 1>, <89, 1>, <97, 1>, <101, 1> ] (0, 89, 46, 93, 28, 5, 3, 58, 69, 83, 34, 68, 51, 37, 39, 95, 2, 42, 64, 43, 50, 81, 61, 53, 33, 70, 87, 24, 1, 36, 17, 16, 38, 57, 74, 100, 52, 35, 56, 63, 65, 23, 44, 71, 96, 85, 26, 6)(4, 14, 59, 66)(7, 82, 55, 10, 15, 62, 29, 86, 13, 30, 45, 78, 32, 8, 79, 67, 99, 48, 25, 11, 94, 60, 80, 12, 27, 54, 9, 19, 92, 77, 49, 73, 40, 90)(18, 84, 41, 97, 88, 21, 75, 20, 47, 31, 72, 98, 76, 22) (0, 28, 69, 51, 2, 50, 33, 1, 38, 52, 65, 96)(3, 34, 39, 64, 61, 87, 17, 74, 56, 44, 26, 46)(5, 83, 37, 42, 81, 70, 36, 57, 35, 23, 85, 89)(6, 93, 58, 68, 95, 43, 53, 24, 16, 100, 63, 71)(7, 40, 49, 92, 9, 27, 80, 94, 25, 99, 79, 32, 45, 13, 29, 15, 55)(8, 78, 30, 86, 62, 10, 82, 90, 73, 77, 19, 54, 12, 60, 11, 48, 67)(18, 41, 88, 75, 47, 72, 76)(20, 31, 98, 22, 84, 97, 21) (0, 2, 38)(1, 96, 51)(3, 61, 56)(5, 81, 35)(6, 95, 16)(7, 15, 13, 32, 99, 94, 27, 92, 40, 55, 29, 45, 79, 25, 80, 9, 49)(8, 48, 60, 54, 77, 90, 10, 86, 78, 67, 11, 12, 19, 73, 82, 62, 30)(17, 26, 39)(18, 88, 47, 76, 41, 75, 72)(20, 98, 84, 21, 31, 22, 97)(23, 83, 70)(24, 71, 68)(28, 50, 52)(33, 65, 69)(34, 87, 44)(36, 85, 37)(42, 57, 89)(43, 100, 93)(46, 64, 74)(53, 63, 58) 1428 476 357 1428 476 357 |
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[求助]模剰余类中群元素的阶能比模大吗?
谢! 完全剩余系Zm, 既约剩余系U(m), 完全剩余系中,交换加群,所以,每个元素自加或理解成分别用1,2,3,4。。。相乘等于e,如果是Zm群,e=0 Zm中每个元素阶,只须最大乘m就能成保正模后= e=0,虽然不一定是阶(最小正整数) 既约剩余系U(m), e=1 群的阶 欧拉函数 =4 U(10), ( 1-,3-,7-9-)MOD 10 ,e=1-,这四个系都有阶1,4,4,2 要是m大了,既约剩余系U(10000) 能保正= e=-1吗? 还有多项式剩余系能保正吗? |
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关于DES算法的一些想法,希望大家讨论讨论
P盒S盒看斯廷森的书,冯登国译了两遍的,SPN ,不过硬件的图论没环境太难了。。。 书上说DES P盒有的就不用,那是分析它,可工程上硬件的接口,密匙注入,不用就不正规,麻烦多了 DES也有很多变种。。。。 |
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