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[求助]这时间2011-04-20,23:38:31 我不在线
半夜2011-04-20,23:38:31 电脑在局域网里,可网关很严------网网罐罐很多,包括无线的,但网管水平不知道怎样, 平时都被服务器盯着 现在越来越过分了 准备让北信源的伺候这位恶作剧者,奉劝:如果你被定位了,你会被抓地---------这是国家事业部门 |
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[原创]群论的一些基础知识
真是的,我学时有种被强迫接受的感觉,可不学,其它书看不懂啊,看看ECC,说小子群攻击,说弗罗自同构,扩域下降。。。再想翻翻张量分析-----懂点才明白《时间简史》---这可时尚啊 RANK=3 E3:= EllipticCurve([0,0,0,-82,0]); E3; PointsAtInfinity(E3); TorsionSubgroup(E3); NumberOfGenerators(E3); Generators(E3) ; Rank(E3); MordellWeilShaInformation(E3); AbelianGroup(E3); P1:=E3![-8,-12]; Order(P1); P2:=E3![-1,-9]; Order(P2); P3:=E3![-9,-3]; Order(P3); P4:=E3![0,0]; Order(P4); P5:=E3![49/4,231/8]; Order(P5); P6:=E3![41/4,123/8]; Order(P6); Elliptic Curve defined by y^2 = x^3 - 82*x over Rational Field {@ (0 : 1 : 0) @} Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*$.1 = 0 4 [ (0 : 0 : 1), (-8 : 12 : 1), (-1 : -9 : 1), (-9 : -3 : 1) ] 3 Torsion Subgroup = Z/2 Analytic rank = 3 The 2-Selmer group has rank 4 Found a point of infinite order. Found 2 independent points. Found 3 independent points. After 2-descent: 3 <= Rank(E) <= 3 Sha(E)[2] is trivial (Searched up to height 100 on the 2-coverings.) [ 3, 3 ] [ (0 : 0 : 1), (49/4 : 231/8 : 1), (41/4 : 123/8 : 1), (-9 : 3 : 1) ] [ <2, [ 0, 0 ]> ] Abelian Group isomorphic to Z/2 + Z + Z + ZDefined on 4 generators Relations: 2*$.1 = 0 0 0就是无限远点,3个Z群,生成元P1/P2/P3 0 0 2 2阶点两个挠子群,生成元P4 0 还给了两能生成 Z群的点-----分数也行,只要是有理点 0 ----------- 100000*P4;挠子群Z转不出去 100001*P4; (0 : 1 : 0) (0 : 0 : 1) Z群就不同了,10倍就天文数字了,可至无穷啊 (5329/144 : 377191/1728 : 1) (-118764872/42003361 : -3937849795044/272223782641 : 1) (905925300579649/81949277077056 : 15640109412983368378849/741852714479323912704 : 1) (-2343465084196597805000/58051145063946951161569 : -25447354793050005176981463556943100/13986729827640029730757694665036753 : 1) (6302474098508073788197910531446609/651331880237428048545105511066896 : -176342732523930673371934739457017411658357216614489/16622774127029891762931364\ 252673114873466120250944 : 1) (-3813430085070199683943976557798873904463613832/228336826875138911896596598141\ 8615777603848641 : 125494893852863155426100974766561536605189928217522571232033\ 4800833324/10910984586392115360355313355505782235146810851274627664315031114256\ 1 : 1) (1880701588819492767318652030277859714069703191156088494052609/8018344141367449\ 6508774280969881993157804843783416953223424 : -237919946592218328913913464119432611871936626120863837945348807020008535118330\ 0600626847871/22705289196485300714253305436925878920371641314520424153731523057\ 840376182235816117587968 : 1) (-18815230184579826991959942950507242936389088171715617440267931518219770954888\ /2785944412729486384827083679528629259002420636194629323893461343681407696961 : 2305204200717457550192851363078188878716253530093747095851230611288478913625408\ 572457649696650868753188600387657492/147047847011317425399566847867848018869257\ 649673254707518241304784767107976145675764728694749353143581342134675041 : 1) (190909762816982266589447623951781585733423203877205763763861577911709314049308\ 99671515742264401/3759205612578986117009614770431984774241158894350139721932557\ 4936713501758087453032010090000 : -26373827153651235352076330133554362293020016\ 8338935545161185268632853079379474560027219993229788750399658301115811130372933\ 8142837271804656601/23048577162798624548776580990172190660088839559951272602553\ 3782892120933828081749097515442095457075887927302595340997837489878439223000000 : 1) 1000*P1;过5万位了 The output is too long and has been truncated. RANK=4 E3:= EllipticCurve([0,-1,0,- 24649,1355209]); E3; TorsionSubgroup(E3); NumberOfGenerators(E3); Generators(E3) ; NumberOfGenerators(E3); Rank(E3); AbelianGroup(E3); Elliptic Curve defined by y^2 = x^3 - x^2 - 24649*x + 1355209 over Rational Field Abelian Group isomorphic to Z/2 + Z/2 Defined on 2 generators Relations: 2*$.1 = 0 2*$.2 = 0 6 [ (67 : 0 : 1), (113 : 0 : 1), (149 : -984 : 1), (-15 : 1312 : 1), (313 : 4920 : 1), (-56 : -1599 : 1) ] 6 4 Abelian Group isomorphic to Z/2 + Z/2 + Z + Z + Z + ZDefined on 6 generators Relations: 2*$.1 = 0 2*$.2 = 0 E3:= EllipticCurve([0,-1,0,- 24649,1355209]); E3; Generators(E3) ; NumberOfGenerators(E3); Rank(E3); AbelianGroup(E3); Order(E3); P1:=E3![67,0]; Order(P1); P2:=E3![113,0]; Order(P2); P3:=E3![149,-984]; Order(P3); P4:=E3![-15,1312]; Order(P4); P5:=E3![313,4920]; Order(P5); P6:=E3![-56,-1599]; Order(P6); Elliptic Curve defined by y^2 = x^3 - x^2 - 24649*x + 1355209 over Rational Field [ (67 : 0 : 1), (113 : 0 : 1), (149 : -984 : 1), (-15 : 1312 : 1), (313 : 4920 : 1), (-56 : -1599 : 1) ] 6 4 Abelian Group isomorphic to Z/2 + Z/2 + Z + Z + Z + Z Defined on 6 generators Relations: 2*$.1 = 0 2*$.2 = 0 >> Order(E3); ^ Runtime error in 'Order': Algorithm does not work for this ring 2------2阶点两个挠子群,生成元P1/P2 2 0 0 0 0-----------0就是无限远点,四个Z群,生成元P3/P4/P5/P6 |
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[原创]群论的一些基础知识
谢,我是看韩士安的近世代数里的习题总结的,可没底,因为符合的就几道习题,所以不确定 下面你再断断: 同态其实不应叫同态映射,看英文书定义,一个叫HOM,一个叫MAP,同态根本不提MAP,可韩士安的近世代数把同态叫同态映射,从代数结构同态看就矛盾,何况群同态 可映射定义A--B就应只有是满或单,满特殊时包同构,单特殊时包同构 free:=FreeAbelianGroup(1); free; free3:=FreeAbelianGroup(3); free3; free11:=FreeAbelianGroup(11); free; free33:=FreeAbelianGroup(33); free33; Generators(free) ; Generators(free3) ; Generators(free11) ; Generators(free33) ; NumberOfGenerators(free) ; NumberOfGenerators(free3) ; NumberOfGenerators(free11) ; NumberOfGenerators(free33) ; =========== 好好翻了翻书,总算把RANK搞懂了! http://web.math.hr/~duje/tors/rankhist.html rank >= year Author(s) ________________________________________________________________________________ 3 1938 Billing 4 1945 Wiman 6 1974 Penney - Pomerance 7 1975 Penney - Pomerance 8 1977 Grunewald - Zimmert 9 1977 Brumer - Kramer 12 1982 Mestre 14 1986 Mestre 15 1992 Mestre 17 1992 Nagao 19 1992 Fermigier 20 1993 Nagao 21 1994 Nagao - Kouya 22 1997 Fermigier 23 1998 Martin - McMillen 24 2000 Martin - McMillen 28 2006 Elkies y2 + xy + y = x3 - x2 - 20067762415575526585033208209338542750930230312178956502x + 34481611795030556467032985690390720374855944359319180361266008296291939448732243429 Independent points of infinite order: P1 = [-2124150091254381073292137463, 259854492051899599030515511070780628911531] P2 = [2334509866034701756884754537, 18872004195494469180868316552803627931531] P3 = [-1671736054062369063879038663, 251709377261144287808506947241319126049131] P4 = [2139130260139156666492982137, 36639509171439729202421459692941297527531] P5 = [1534706764467120723885477337, 85429585346017694289021032862781072799531] P6 = [-2731079487875677033341575063, 262521815484332191641284072623902143387531] P7 = [2775726266844571649705458537, 12845755474014060248869487699082640369931] P8 = [1494385729327188957541833817, 88486605527733405986116494514049233411451] P9 = [1868438228620887358509065257, 59237403214437708712725140393059358589131] P10 = [2008945108825743774866542537, 47690677880125552882151750781541424711531] P11 = [2348360540918025169651632937, 17492930006200557857340332476448804363531] P12 = [-1472084007090481174470008663, 246643450653503714199947441549759798469131] P13 = [2924128607708061213363288937, 28350264431488878501488356474767375899531] P14 = [5374993891066061893293934537, 286188908427263386451175031916479893731531] P15 = [1709690768233354523334008557, 71898834974686089466159700529215980921631] P16 = [2450954011353593144072595187, 4445228173532634357049262550610714736531] P17 = [2969254709273559167464674937, 32766893075366270801333682543160469687531] P18 = [2711914934941692601332882937, 2068436612778381698650413981506590613531] P19 = [20078586077996854528778328937, 2779608541137806604656051725624624030091531] P20 = [2158082450240734774317810697, 34994373401964026809969662241800901254731] P21 = [2004645458247059022403224937, 48049329780704645522439866999888475467531] P22 = [2975749450947996264947091337, 33398989826075322320208934410104857869131] P23 = [-2102490467686285150147347863, 259576391459875789571677393171687203227531] P24 = [311583179915063034902194537, 168104385229980603540109472915660153473931] P25 = [2773931008341865231443771817, 12632162834649921002414116273769275813451] P26 = [2156581188143768409363461387, 35125092964022908897004150516375178087331] P27 = [3866330499872412508815659137, 121197755655944226293036926715025847322531] P28 = [2230868289773576023778678737, 28558760030597485663387020600768640028531 http://bbs.pediy.com/showthread.php?t=128083 http://www.iiidown.com/source/9139203 有限自由阿群就是有整数无限群Z的,有一个Z,RANK=1,n个,RANK=n, 有限生成阿群就是有整数群Zm间直和,叫挠子群----都是阶有限的,在ECC里没MOD P前就是画直线只能求有限个新点, 有限生成阿群也有可能加几个无限群Z的,就叫有限生成自由阿群,象ECC里的曲线现在发现最高加了28个无限群Z,在ECC里就是画直线能求无限个新点,这28个点(生成元)如上 不过ECC曲线MOD P后就没无限群Z这直和项了 有限生成阿群麻烦在初等因子---就是Zm各项的m求法 也可表为不变因子之直和 初等因子就是素数次幂(》=1)分解之和----------不变因子转换麻烦点等看懂了贴这 A1:= AbelianGroup([2,3,4,0]); A1; Subgroups(A1); A1:= AbelianGroup([6,3]); A1; Subgroups(A1); FA := FreeAbelianGroup(2); FA; Generators(A1); Generators(FA); NumberOfGenerators(A1); NumberOfGenerators(FA); Relations(A1); Relations(FA); RelationMatrix(A1); RelationMatrix(FA); Abelian Group isomorphic to Z/2 + Z/12 + Z Defined on 4 generators Relations: 2*A1.1 = 0 3*A1.2 = 0 4*A1.3 = 0 Runtime error: Argument of Subgroups must be finite Abelian Group isomorphic to Z/3 + Z/6 Defined on 2 generators Relations: 6*A1.1 = 0 3*A1.2 = 0 Conjugacy classes of subgroups ------------------------------ [ 1] Order 18 Length 1 Abelian Group isomorphic to Z/3 + Z/6 Defined on 2 generators in supergroup A1: $.1 = A1.2 $.2 = 5*A1.1 + A1.2 Relations: 3*$.1 = 0 6*$.2 = 0 [ 2] Order 6 Length 1 Abelian Group isomorphic to Z/6 Defined on 1 generator in supergroup A1: $.1 = 5*A1.1 Relations: 6*$.1 = 0 [ 3] Order 9 Length 1 Abelian Group isomorphic to Z/3 + Z/3 Defined on 2 generators in supergroup A1: $.1 = A1.2 $.2 = 4*A1.1 + 2*A1.2 Relations: 3*$.1 = 0 3*$.2 = 0 [ 4] Order 3 Length 1 Abelian Group isomorphic to Z/3 Defined on 1 generator in supergroup A1: $.1 = 2*A1.1 Relations: 3*$.1 = 0 [ 5] Order 6 Length 1 Abelian Group isomorphic to Z/6 Defined on 1 generator in supergroup A1: $.1 = 3*A1.1 + 2*A1.2 Relations: 6*$.1 = 0 [ 6] Order 6 Length 1 Abelian Group isomorphic to Z/6 Defined on 1 generator in supergroup A1: $.1 = A1.1 + A1.2 Relations: 6*$.1 = 0 [ 7] Order 6 Length 1 Abelian Group isomorphic to Z/6 Defined on 1 generator in supergroup A1: $.1 = 5*A1.1 + A1.2 Relations: 6*$.1 = 0 [ 8] Order 2 Length 1 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup A1: $.1 = 3*A1.1 Relations: 2*$.1 = 0 [ 9] Order 3 Length 1 Abelian Group isomorphic to Z/3 Defined on 1 generator in supergroup A1: $.1 = 2*A1.2 Relations: 3*$.1 = 0 [10] Order 3 Length 1 Abelian Group isomorphic to Z/3 Defined on 1 generator in supergroup A1: $.1 = 4*A1.1 + 2*A1.2 Relations: 3*$.1 = 0 [11] Order 3 Length 1 Abelian Group isomorphic to Z/3 Defined on 1 generator in supergroup A1: $.1 = 4*A1.1 + A1.2 Relations: 3*$.1 = 0 [12] Order 1 Length 1 Abelian Group of order 1 Abelian Group isomorphic to Z + Z Defined on 2 generators (free) { A1.1, A1.2 } { FA.2, FA.1 } 2 2 [ 6*FA.1 = 0, 3*FA.2 = 0 ] [] [6 0] [0 3] Matrix with 0 rows and 2 columns A1:= AbelianGroup([3,4]); A1; A2:= AbelianGroup([3]); A2; FA := FreeAbelianGroup(200); FA; DirectSum(A1, A2); DirectSum(A1, FA); DirectSum(A2, FA); Abelian Group isomorphic to Z/12 Defined on 2 generators Relations: 3*A1.1 = 0 4*A1.2 = 0 Abelian Group isomorphic to Z/3 Defined on 1 generator Relations: 3*A2.1 = 0 Abelian Group isomorphic to Z (200 copies) Defined on 200 generators (free) Abelian Group isomorphic to Z/3 + Z/12 Defined on 2 generators Relations: 3*$.1 = 0 12*$.2 = 0 Abelian Group isomorphic to Z/12 + Z (200 copies) Defined on 201 generators Relations: 12*$.1 = 0 Abelian Group isomorphic to Z/3 + Z (200 copies) Defined on 201 generators Relations: 3*$.1 = 0 |
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[分享]GCHQ、M15/M16/英国密码管理机构
正题1 READING OXFORD SWINDON BATH BRISTOL CHELTENHAM GLOUCESTER CARDIFF EXETER PLYMOUTH 三字母一样不是OXFORD就是EXETER ,后移一位的凯撒码 EXETER 正题2 PLAYGROUND 先找出全有5个字母的 1234567890 编码 96521 ------NRGLP 对照 正题3 1x=i 2x=H 3X=a 4x=v 5x =e 6x =s 7x= e 8x=n 9x=t 10x= t 11x= h 12x=e 13x=s 14x=t 15x= a 16x=s 17x= s 18x=h 19x =t 20x=o 21x=f 22x=r 23x=a 24x=n 25x= c 26x= e 复活节easter day 和26字母有关。。。连起来: i have sent the stash 隐藏物 to france 正题4 后移一位的凯撒码 BORDEAUX 正题5 superstitious 迷信的 consecutive 连续 http://www.nongli.net/ 不含S,没0/2/3/4/6,只有1/5才行 2011年6月周5是24号能被4整除,不出门 2011年6月周1是27号 ------OK 正题6 confiscate - 没收 laptop膝上型电脑(笔记本电脑) ? S G D S G D |
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[讨论]示波器和密码芯片
谢! 学硬件要环境。。。前几天把张SHEN份证烧了,看了看RIFD环状天线,那CPU才半厘米的长方形,发现要是溶了那膜多好,可溶解液还得 买,要是能重贴上另一人的膜。。。嘿嘿, 准备备考青年政治学院 |
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[求助]帮忙看下这个是用的什么加密算法?
都22位 20 6CjkB55ASjMuZKONvjIq2A 21 6CjkB55ASjM1TjxVnQZRzg 2 都是6CjkB55ASjM 11位 19 Yv6tUzgatVq8y6V7/53Xww 21 6CjkB55ASjM1TjxVnQZRzg 都是1可在个位十位却不同 多传点数上来,看看规律 30.31 18,17之类的 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 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 S = AlphabeticStrings() E = SubstitutionCryptosystem(S) X = pt.frequency_distribution() Z = ct.frequency_distribution() Y = DiscreteRandomVariable(X,Z.function()) for j in range(26): ... K = S([ (j+k)%26 for k in range(26) ]) ... print "%s: %s" % (j, X.translation_correlation(Y,E(K))) X = pt.frequency_distribution() m = 11 r = 0.75 match = [ [] for i in range(m) ] for i in range(m): ... Z = ct[i::m].frequency_distribution() ... Y = DiscreteRandomVariable(X,Z.function()) ... for j in range(26): ... K = S([ (j+k)%26 for i in range(26) ]) ... corr = X.translation_correlation(Y,E(K)) ... if corr > r: ... match[i].append(j) Exercise F2 = FiniteField(2) PS.<x> = PowerSeriesRing(F2) f = x^2 + x g = x^3 + x + 1 f/g + O(x^16) x + x^4 + x^5 + x^6 + x^8 + x^11 + x^12 + x^13 + x^15 + O(x^16) |
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[求助]关于libtomcrypt
上这问问 http://webchat.freenode.net/?channels=libtom http://brlcad.org/xref/source/src/other/tcl/libtommath/ |
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[原创]群论的一些基础知识
Z4:=AbelianGroup(GrpPerm,[4]); Z4; Z6:=AbelianGroup(GrpPerm,[6]); Z6; Z4Z4 := hom< Z4 -> Z4 | Z4.1 -> Z4.1 >; Z4Z4; Z4Z6 := hom< Z4 -> Z6 | Z4.1 -> Z6.1 >; Z4Z6; Z6Z4 := hom< Z6 -> Z4 | Z6.1 -> Z4.1 >; Z6Z4; Z6Z6 := hom< Z6 -> Z6 | Z6.1 -> Z6.1 >; Z6Z6; Z4Z4(Z4) eq Z4; Z6Z4(Z6) eq Z4; Z6Z4(Z6) eq Z4; Image(Z6Z6); Kernel(Z4Z4); Domain(Z4Z4); Domain(Z6Z6); Domain(Z6Z4); Domain(Z4Z6); Codomain(Z4Z4); Codomain(Z6Z6); Codomain(Z4Z6); Codomain(Z6Z4); DirectProduct(Z4, Z6) ; Order(1); Order(6); sub<Z4 | 1> ; sub<Z6 | 1> ; Index(Z4, Z6); Permutation group Z4 acting on a set of cardinality 4 Order = 4 = 2^2 (1, 2, 3, 4) Permutation group Z6 acting on a set of cardinality 6 Order = 6 = 2 * 3 (1, 2, 3, 4, 5, 6) Endomorphism of GrpPerm: Z4, Degree 4, Order 2^2 induced by (1, 2, 3, 4) |--> (1, 2, 3, 4) Homomorphism of GrpPerm: Z4, Degree 4, Order 2^2 into GrpPerm: Z6, Degree 6, Order 2 * 3 induced by (1, 2, 3, 4) |--> (1, 2, 3, 4, 5, 6) Homomorphism of GrpPerm: Z6, Degree 6, Order 2 * 3 into GrpPerm: Z4, Degree 4, Order 2^2 induced by (1, 2, 3, 4, 5, 6) |--> (1, 2, 3, 4) Endomorphism of GrpPerm: Z6, Degree 6, Order 2 * 3 induced by (1, 2, 3, 4, 5, 6) |--> (1, 2, 3, 4, 5, 6) true true true Permutation group acting on a set of cardinality 6 Order = 6 = 2 * 3 (1, 2, 3, 4, 5, 6) Permutation group acting on a set of cardinality 4 Order = 1 Permutation group Z4 acting on a set of cardinality 4 Order = 4 = 2^2 (1, 2, 3, 4) Permutation group Z6 acting on a set of cardinality 6 Order = 6 = 2 * 3 (1, 2, 3, 4, 5, 6) Permutation group Z6 acting on a set of cardinality 6 Order = 6 = 2 * 3 (1, 2, 3, 4, 5, 6) Permutation group Z4 acting on a set of cardinality 4 Order = 4 = 2^2 (1, 2, 3, 4) Permutation group Z4 acting on a set of cardinality 4 Order = 4 = 2^2 (1, 2, 3, 4) Permutation group Z6 acting on a set of cardinality 6 Order = 6 = 2 * 3 (1, 2, 3, 4, 5, 6) Permutation group Z6 acting on a set of cardinality 6 Order = 6 = 2 * 3 (1, 2, 3, 4, 5, 6) Permutation group Z4 acting on a set of cardinality 4 Order = 4 = 2^2 (1, 2, 3, 4) Permutation group acting on a set of cardinality 10 Order = 24 = 2^3 * 3 (1, 2, 3, 4) (5, 6, 7, 8, 9, 10) Integer Ring Integer Ring Permutation group acting on a set of cardinality 4 Id($) Mapping from: GrpPerm: $, Degree 4 to GrpPerm: Z4 |
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[原创]群论的一些基础知识
G := AbelianGroup([1,2]); G; H:=AbelianGroup([1,2,3]); H; T1 := Hom(G, H); T1; T2:= Hom(H, H); T2; T3:= Hom(H, G); T3; Abelian Group isomorphic to Z/2 Defined on 2 generators Relations: G.1 = 0 2*G.2 = 0 Abelian Group isomorphic to Z/6 Defined on 3 generators Relations: H.1 = 0 2*H.2 = 0 3*H.3 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*T1.1 = 0 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*T2.1 = 0 Abelian Group isomorphic to Z/2 Defined on 1 generator Relations: 2*T3.1 = 0 |
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[原创]群论的一些基础知识
谢! 越看越难了! 是两 书上就一行,HOM(Z4,Z6)={φ:x---->ax,a=0,3},x上带一横------剩余类,看了这N久,没搞懂 用下面这样行不行:我是猜的,不知对不对 Z4------Z6 Lcm(4,6)/4=3;从3开始乘1,2,3。。。但最大不超6,所以就一个3*1 所以a=0,a=3 a=0是Z4 Z6------Z4 Lcm(4,6)/6=2;从2开始乘1,2,3。。。但最大不超4,所以就一个2*1 所以a=0,a=2 a=0是Z6 再找个大的 Z1050------------Z1500 Lcm(1050,1500)/1050=10,从10开始乘1,2,3。。。但最大不超1500,所以就10,2*10,3*10......149*10, 所以a=0,a=10.20,30....1480,1490 a=0是Z1050 共150个同态 Z1500------------Z1050 Lcm(1050,1500)/1500=7,从7开始乘1,2,3。。。但最大不超1050,所以就7,2*7,,3*7.。。。。。149*7, 所以a=0,a=7,14,21,。。。。。1043 a=0是Z1500 共150个同态 |
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[讨论]国产非对称公匙的悬赏了:
是啊, 中国搞--体制 --系统没啥希望,象SM2/3,全挪过来就OK了 数学要特行,电子工程学也要特行才敢搞什麽 -体制 --系统-------想想地球生态系统 前几天翻到本国产新书-------关于云安全可证安全密码系统,好像是姐弟俩写的,说ECC过时了,提了种拓扑变 换,拓扑变幻等新系统,那书上全都提-----从协议形式化到云的新名词都不漏,挺厚的,可象文学家写技术书, 企业里的工会主席妇联主任一样 |
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[分享]知道素数前或后1/4 BIT位RSA攻击例子
颜明年出的书: Quantum Attacks on Public-Key Cryptosystems http://www.springer.com/computer/security+and+cryptology/book/978-1-4419-7721-2 |
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[原创]群论的一些基础知识
谢! 看到书上有求Z4------->Z6的同态,也有求Z6-------->Z4同态,可没细说,搞不懂,能不能给列列有哪些? z:=Integers(4) ; z4:=AdditiveGroup(z); z4; Generators(z4); NumberOfGenerators(z4) ; Centre(z4); Subgroups(z4); AutomorphismGroup(z4); Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*z4.1 = 0 { z4.1 } 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*z4.1 = 0 Conjugacy classes of subgroups ------------------------------ [1] Order 4 Length 1 Abelian Group isomorphic to Z/4 Defined on 1 generator Relations: 4*z4.1 = 0 [2] Order 2 Length 1 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z4: $.1 = 2*z4.1 Relations: 2*$.1 = 0 [3] Order 1 Length 1 Abelian Group of order 1 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 z:=Integers(6) ; z6:=AdditiveGroup(z); z6; Generators(z6); NumberOfGenerators(z6) ; Centre(z6); Subgroups(z6); AutomorphismGroup(z6); Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*z6.1 = 0 { z6.1 } 1 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*z6.1 = 0 Conjugacy classes of subgroups ------------------------------ [1] Order 6 Length 1 Abelian Group isomorphic to Z/6 Defined on 1 generator Relations: 6*z6.1 = 0 [2] Order 3 Length 1 Abelian Group isomorphic to Z/3 Defined on 1 generator in supergroup z6: $.1 = 2*z6.1 Relations: 3*$.1 = 0 [3] Order 2 Length 1 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z6: $.1 = 3*z6.1 Relations: 2*$.1 = 0 [4] Order 1 Length 1 Abelian Group of order 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 z:=Integers(10) ; z10:=AdditiveGroup(z); z10; Generators(z10); NumberOfGenerators(z10) ; Centre(z10); Subgroups(z10); AutomorphismGroup(z10); Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*z10.1 = 0 { z10.1 } 1 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*z10.1 = 0 Conjugacy classes of subgroups ------------------------------ [1] Order 10 Length 1 Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*z10.1 = 0 [2] Order 5 Length 1 Abelian Group isomorphic to Z/5 Defined on 1 generator in supergroup z10: $.1 = 2*z10.1 Relations: 5*$.1 = 0 [3] Order 2 Length 1 Abelian Group isomorphic to Z/2 Defined on 1 generator in supergroup z10: $.1 = 5*z10.1 Relations: 2*$.1 = 0 [4] Order 1 Length 1 Abelian Group of order 1 A group of automorphisms of Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*z10.1 = 0 Generators: Automorphism of Abelian Group isomorphic to Z/10 Defined on 1 generator Relations: 10*z10.1 = 0 which maps: 5*z10.1 |--> 5*z10.1 |
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[分享]知道素数前或后1/4 BIT位RSA攻击例子
1 P:=NextPrime(2^21+1113); P; Q:=NextPrime(2^19+1501003); Q; n:=P *Q; n; Ilog(2,P); e:=IntegerToString(P,2); e; e:=IntegerToString(P,2); d0:=IntegerToString(0b100101,10); d0; EulerPhi(P*Q); 4249650972456 2098277 2025307 4249655096039 21 1000000000010001100101 4249650972456 37 77636249 P*d0=77636249==1+k(4249655096039-s+1)mod (2^6) 77636248==24==k(4249655096038-s)mod64 , s=P+Q 令k=1 ?,24==(38-s)mod64 s==14mod 64; 2 P^2-sP+n==0mod64 P^2-14P+4249655096038==0mod64; P^2-14P+38==0mod64 P非整数 令k=2 ?,24==2(38-s)mod64 24==(12-2s)mod64 s==6mod 64; ...... P非整数 令k=3 ?,24==3(38-s)mod64 24==(50-3s) mod64 s非整数 k=4 24==4(38-s)mod64 ==24-4s s=0mod64 s=P+Q ? =============== x^e^k==x mod n求k-------------不动点x的阶k 2^2098277^k==2mod4249655096039 ============== 变求离散对数了。。。。也不说明那k, r都怎麽来的,突然就在方程蹦里出来了。。。 |
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[分享]GCHQ、M15/M16/英国密码管理机构
1 a Cipher: SEGAP ELZZUP RUO OT EMOCLEW Plain: b Cipher: EHT YPS WSI RAE GNI LBA CEU TAO Plain: c Cipher: YKOEUDHTAHVIESCCROADCE Plain: d Cipher: WEZWI LLJAT TAXCK ATQSU NSKET Plain: e Cipher: SSA PSE TJX SME CRE STO THI GEI Plain: f Cipher: NWOY OCUA NAMK EPUY ORUO WCNO DSEZ Plain: a 倒着念 WELCOME TO OUR PUZZLE PAGES b 三字母倒着念 THE SPY IS WEARING A BLUE COAT". c 分 YKOEUDHTAHVIESCCROADCE 再连没下划线的 ----》YOU HAVE CRACKED THIS CODE". - - - - - - - - - - - d 每四字母加哑元混 WE Z WI LL J ATTA X CKAT Q SUNS K ET e SSA PSE TJX SME CRE STO THI GEI 两哑元 S SA P SE T JX S ME C RE S TO T HI G EI 两哑元 群置换 12345678 > 36827514 S SA P SE T JX S ME C RE S TO T HI G EI 1 2 3 4 5 6 7 8 T S G P T C S P 剩下的双字母7418625分别插入: -->THIS MESSAGE IS TOP SECRET f: NWOY OCUA NAMK EPUY ORUO WCNO DSEZ N WO Y O CU A N AM KE PU YO RU OW CN OD SE Z---哑元 互换 互换 互换 互换 互换 互换 互换 -->NOW YOU CAN MAKE UP YOUR OWN CODES 2 Puzzle 2: Caesar cipher MXOLX VFDHV DUXVH GWKLV FLSKH U ABCDEFGHIJKLMNOPQRSTUVWXYZ XYZABCDEFGHIJKLMNOPQRSTUVW MXOLX VFDHV DUXVH GWKLV FLSKH U------->JULIU SCAES ARUSE DTHIS CIPHE R JULIUS CAESAR USED THIS CIPHER 3 THIS CIPHER WAS ONCE USED BY FREEMASONS" freemasons什么意思 也称美生会,成立于1717年的伦敦,其起源可溯及中世纪的石匠和教堂建筑工匠的分会,共济会成立后逐渐向欧美各国扩张,成为世界上最大的国际秘密组织。它的主旨是传授执行其互助纲领,后受启蒙主义影响,以“自由、平等、友爱”为理想,成为世界市民主义的友爱组织,认为“世事盈亏,惟赖人类智慧与美德可加以弥补”,因此吸引了当代众多知识分子的加入。莫扎特、海顿、歌德、伏尔泰、加里波的、华盛顿、杰弗逊、富兰克林都是共济会成员。 但这个强调守法、慈善和互助的团体,因参与意大利统一战争与法国大革命,遭到当时君权国家政府的镇压,从而成为秘密组织。——一个由巴伐利亚某些富有的石匠艺人组成的兄弟会所收容。 ”4 单字频率: A B C D E F G H I J K L M 8.2 1.4 2.8 3.8 13.1 2.9 2.0 5.3 6.3 0.1 0.4 3.4 2.3 N O P Q R S T U V W X Y Z 7.1 8.0 2.0 0.1 6.8 6.1 10.5 2.5 0.9 1.5 0.2 2.0 0.1 ZBDDH QWBPQ KHBTM ALBKM WOCLM ESBEE JOBXE MWOPK BIXBW TUJWJ DUEME ZBLQA BUQXL JNBPQ XWHQX KTQHB YKBJV MWOAJ OBEMW PQKSJ CMNBJ WHLJN BYBBW JYDBC QZQKV CLKQX OLCLB AXRRD BEAKQ NMHBH CLJWV UQXPQ KNMEM CMWOQ XKZBY EMCB S最多为------E 用华盛顿书后代码可算 A B C D E F G H I J K L M P E T L S J X D Q A R H I N O P Q R S T U V W X Y Z V G F O Z M C Y K N U B W |
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[分享]GCHQ、M15/M16/英国密码管理机构
这是正的,上面是求职的。。。。。 http://www.gchq.gov.uk/ 还有挑战赛----------6关,7 - 12 June 2011之前,有奖啊 http://www.gchq.gov.uk/challenges/index.html |
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