2015第八屆挑戰(zhàn)賽一階段優(yōu)秀集含abcd題

第八屆“認證杯”數(shù)學中國編號專用頁參賽隊伍的參賽隊號：（請各個參賽隊提前填寫好競賽統(tǒng)一編號（由競賽送至評委團前編號競賽評閱編號（由競賽評委團評閱前進行編號數(shù)學建模網(wǎng)絡賽第一階段替換替換關鍵 替換式破譯頻率分析單字母替 要以采取的較好的策略是窮搜索。但如果密文很長，我們采用的方式是對密文中的字得到的幾張字母替換表，就可以最終確定部分的字母替換規(guī)定。以上步驟，編寫參賽隊號所選題目 英要（選填Inoccasionthatattackerisassumedtohaveaccessonlytoasetofciphertexts,theonlymodelcouldbeassumeisciphertext-onlyattack.Insituationwhereciphertextisrelativelyshort,thebetterstrategyisbrute-search.Howeverinsituationciphertextisrelativelylong,theattackmodetoadoptistomakestatisticalysisoffrequenceoflettersincypertext:collectstatisticsseparayofthetimeseachsingleletterandtwoconsecutivelettersappearintheciphertext,aswellasthetimeseachletterinalphabetholdsthefirst,second,thirdandthelastpositionofeachword,rankthemandcompareitsorderwiththeLetterFrequency,recementchartsofcorrespondentlettersshallbemadeaccordingtothat.Finally,comparetherecementchartswhichwasobtainedpreviouslyincertainrules,shalltherecementrulesoflettersbepartiallydefined.Forpreviousprocedures,wemadealgorithmofthemandcomputedthembyprogrammingwithC-.Ontheotherhand,forthoselettersleftuncertaininciphertext,artificialjudgementshallbehelpfulwiththewritingregulationofEnglishwords.Atthispoint,theentirerecementchartsisaccessible,accordingtowhich,theciphertexthasbeentransformedintointext,soastofinishtheworkofdecipherment.Intheevaluationofitonthecrackmodel,wecombinetheprincipleandtheprogramdesignoftheprogrammingandoperationsituation,identifiedthefollowingthreeevaluationcriteria:"Thenumberofletterswecandetermineinthetable".Infact,themainrulesadoptedinthemodelandthecombinationsofruleswillmakeusgetdifferentlettersubstitutiontable,sothenumberofletterswecandeterminewillbedifferent.Generally,themorerecementaprogramcando,thehigherprecision ewecanget."Timetheprogramneedtogetthelettersubstitutiontable".Thepasswordcrackingperformancetestdependsonthetimesoperationcanrunonaspecifiedtimeaswell.Therefore,soinourmodel,weaddaprogramtocalculatetherunningtimeofthemainprogram(inmilliseconds).Inasense,thelesstimeittakes,thestrongeritis."Thereliabilityofdecodedintext".Theultimategoalistodecipherthemodelandgettheintextthatweneed.Therefore,thereliabilityofdecodedintextisalsothekeypointwhatweconcernof.Consideringthelimitationsofthecomputer,inthisprocess,wewilltesttheworderrorrate,grr,andtheexpressionofsentencesbyourselves.Andthatisastandardastheassessmentofthemodel.Key:Recetypepassword,Cryptysis,Frequencyysis,Singleletter替換式法，但由于其容易被，所以在現(xiàn)代需要加密的場合已經(jīng)很少使用。如免費的COCA1等相關資料。模型的假設與符號的說模型的假設符號的說明26i字母出現(xiàn)的第i個位置上的符號（包含字第i個位置上的問題一的分析夠采取的方式是唯密文。1】FrequenciesofthelettersintheEnglishlanguage（最常用英文字母頻率）：ETA,O,I,N,S,H,R,D,L,C,U,MW,F,GYP,BVK,J,X,Q,Z3】Themostcommonfirstletterinawordinorderoffrequency（單詞中最常見的首T,O,A,W,B,C,D,S,F,M,R,H,I,Y,E,G,L,N,O,U,J,4】Themostcommonsecondletterinawordinorderoffrequency（單詞中最常見H,O,E,I,A,U,N,R,5】Themostcommonthirdletterinawordinorderoffrequency（單詞中最常見的E,S,A,R,N,6】Themostcommonlastletterinawordinorderoffrequency（單詞中最常見的末E,S,T,D,N,R,Y,F,L,O,G,H,A,K,M,P,U,【規(guī)則7】Themostcommondigraphsonorderoffrequency（最常用的雙連字母）：TH,HEANINER,ON,REED,ND,HAATEN,ES,OF,NTEA,TITO,IO,LE,IS,OU,AR,AS,DE,RT,VE,ON,ST,NT,NG,OR,ET,IT,AR,TE,問題二的分析個標準評估我們模型破譯能力：密文破譯后的準確性就越高。在這樣的事實下，“程序運行所得的字母替換表中確定的替換的個數(shù)的多少”作為我們評估模型破譯能力的第一條標準。1000問題一模型的建立與求解lwnsozbnwvwbaybnvbsqwvwohwdizwrb,bnpbpoouwrpawxawpbwzwmypo,bnpbbnwjpawwrzslwzqjbnwiaxawpbsalibnxwabpiryrpoiwrpqowaienbv,bnpbpusrebnwvwpawoihw,oiqwabjprzbnwfyavyibshnpffirwvv.bnpbbsvwxyawbnwvwaienbv,esdwaruwrbvpawirvbibybwzpusreuwr,zwaidirebnwiatyvbfslwavhasubnwxsrvwrbshbnwesdwarwz,bnpblnwrwdwaprjhsaushesdwaruwrbqwxsuwvzwvbayxbidwshbnwvwwrzv,ibivbnwaienbshbnwfwsfowbspobwasabspqsoivnib,przbsirvbibybwrwlesdwaruwrb,opjireibvhsurzpbisrsrvyxnfairxifowvprzsaeprikireibvfslwavirvyxnhsau,pvbsvwwuusvboicwojbswhhwxbbnwiavphwbjprznpffirwvv.fayzwrxw,irzwwz,lioozixbpbwbnpbwsdwaruwrbvosrewvbpboivnwzvnsyozrsbbwxnprewzhsaoienbprzbaprviwrbxpyvwv;przpxxsazireojpoowaiwrxwnpbnvnwlr,bnpbuprcirzpawusawzivfsvwzbsvyhhwa,lniowwdiovpawvyhhwapbow,bnprbsaienbbnwuvwodwvbjpbsoivnirebnwhsauvbslnixnbnwjpawpxxyvbsuwz.qyblnwrposrebapirshpbyvwvprzyvyafpbisrv,fyavyireirdpaipbojbnwvpuwsbtwxbwdirxwvpzwvierbsawzyxwbnwuyrzwapbvsoybwzwvfsbivu,ibivbnwiaaienb,ibivbnwiazybj,bsbnaslshhvyxnesdwaruwrb,przbsfasdizwrwleypazvhsabnwiahybyawvwxyaiby.說，單詞中e出現(xiàn)的頻率比x的頻率要大得多。在該模型中，我們首先分析密文中單個字記出現(xiàn)的頻數(shù)記為i，然后成對列出i和i。再選用由Beker和Piper統(tǒng)計得出的Beker-Piper字母頻率表（見表1），將上述統(tǒng)計出的各字母頻數(shù)iBeker-Piper字母頻率表，得出由單表 Beker-Piper字母頻率abcdefghijklmnopqrstuvwxyz下面，我們用所給密文進行第一輪演示：（程序見附件高到低的順序排列，根據(jù)Beker-Piper字母頻率表，給出單個字母替換圖（見圖1），并制成表格（見表2）。圖 單個字母頻率分析運行AB FGHNT GXUIJ NOPHB RLAQR VWXVS IEMYZCD在英文中由單個字母組成的單詞只有ai，具有很大的特殊性。由于密文中保留了單詞間的空格及標點符號，所以，我們可以根據(jù)在第i個位置上的符號（包含字母、若i1和i1均為空格或標點，則輸出i上的字母，該字母對應明文中的字母a或者字母i。下面，我們用所給密文進行第二輪演示：（程序見附件圖 單字母單詞分析運行表 單字母單詞替換密文字母 明文字母 或密文字母 明文字母 換，現(xiàn)在我們需要做的是觀察雙連字組合的頻率。這里，密文中第i個位置上的再根據(jù)【規(guī)則7】，將雙連字母ii1的頻數(shù)按由高到低的順序依次對應到雙連字母頻率表下面，我們用所給密文進行第三輪演示：（程序見附件圖 雙連字母頻率分析運行 字母多出現(xiàn)T，O，A，W等，第二位出現(xiàn)字母H，O，E，I，A的頻率計較高，以此類CF程序統(tǒng)計各個字母重復出現(xiàn)的次數(shù)，即統(tǒng)計i3】，將首下面，我們用所給密文進行第四輪演示：（程序見附件圖 首字母頻率分析運行 P SWFH O BCDSLFOMZRAHEIXYUENGQRYTCDLNOUJK圖 第二位字母頻率分析運行表 第二位字母替換AABRCDEFGHTIJKLMNOPUHQRSTUVWXEOIYZN圖6 AB FGHNIJ NOPSQR VWXREIYZA圖 末字母頻率分析運行末字母替換密文字母ABCDEFGH明文字母NSUWLO密文字母IJKLMNOP明文字母YKGAM密文字母QRSTUVWX明文字母FRHTE密文字母YZ明文字母PD根據(jù)表2至表8的對應結(jié)果，以及頻率的規(guī)則，我們先取各表頻數(shù)最高的兩位，比對的替換判斷為正確替換。由此得到7對替換。單詞結(jié)果見圖8），并制成表格（見表9）。圖 單詞匹配分析運行AB FGHRT FIJ NOPIYWHLAQR VWXBN SECYZUD根據(jù)表2至表8，我們能大致確定一些字母的替換（見表9），由此我們可以知道密文中還F、G、K、M、T5個字母沒有確定，明文中則剩下J、P、Q、X、Z5個字母?，F(xiàn)在，借助英文單詞書寫規(guī)律進行人工確定。happinessFP替換。以此類推，我們可以推出ABCDEFGHRTKVGPXFIJKLMNOPIYZWQHLAQRSTUVWXBNOJMSECYZUD問題二模型的建立與求解破譯率替換出的字母個數(shù)字母總80.77%。此后，我們也用該程序試驗過幾篇密文，其破譯率維持在80%左右，可見，此程序的破譯能力較高。9weholdthesetruthstobeself-evident,thatallmenarecreatedequal,thattheyareendowedbytheircreatorwithcertainunalienablerights,thatamongthesearelife,libertyandthepursuitofhappiness.thattosecuretheserights, ernmentsareinstitutedamongmen,derivingtheirjustpowersfromtheconsentoftheerned,thatwheneveranyformof esdestructiveoftheseends,itistherightofthepeopletoalterortoabolishit,andtoinstitutenewernment,layingitsfoundationonsuchprinciplesandorganizingitspowersinsuchform,astothemshallseemmostlikelytoeffecttheirsafetyandhappiness.prudence,indeed,willdictatethaternmentslongestablishedshouldnotbechangedforlightandtransientcauses;andaccordinglyallexperiencehathshewn,thatmankindaremoredisposedtosuffer,whileevilsaresufferable,thantorightthemselvesbyabolishingtheformstowhichtheyareaccustomed.butwhenalongtrainofabusesandusurpations,pursuinginvariablythesameobjectevincesadesigntoreducethemunderabsolutedespotism,itistheirright,itistheirduty,tothrowoffsuchernment,andtoprovidenewfortheirfuture e，用此類的文章作為明文的密不適用本模型。參考文吳干華.基于頻率分析的代替破譯方法及其程序?qū)崿F(xiàn)[J].福建電腦王彩霞 分析中幾種方法的研究及其設計與實現(xiàn)[D].西學吳俊杰.的編制與破譯:破譯時間的研究[J].中國教育,2014,19:78-#include<stringh>constintmax_L=1000;voidmain(){inttext_a[26];charinti,j,k,max;}for(i=0;i<26;i++)text_a[i]=0;//初始intlen=strlen(text1);{}}{printf("%c的個數(shù)為}{if(text_a[i]>text_a[max])}}%c} }}{}}}#include<stringh>charchar*{returnNULL;inti=0;{}char*p;return}void{char*p;}}#include<stringh>constintletter_num=26;constintmax_L=1000;intmain(){charchartext_b[letter_num*letter_num][3]={"TH","HE","AN","IN","ER","ON","RE","ED","ND","AT","EN","ES","OF","NT","EA","TI","TO","IO","LE","IS","OU","AR","AS","DE","VE","ON","ST","NT","NG","OR","ET","IT","AR","TE",inti,j,k,l,max1,max2; for(inti=1;i<max_L;i++)intlen=strlen(text1);{if(text1[i]>='a'&&text1[i]<='z'&&}}{//printf("%c的個數(shù)}for(i=0;i<len-{{{{}}} text_a[max1][max2]=-}} } }for(j=0;j<38-{}if(j==38-{}{}}

return0;}【首字母頻率分析】（第二位、第三位字母頻率分析程序中改變代碼中 的值intflag=1;intflag2=0;charchar*{char*p;inti=0;{}return}int{charinput[100];inttext_a[26],i,j;char*p; intmax;intk=p[flag-1]-'a';} printf("%c\個數(shù)為}{printf("%c的個數(shù)為}{} {}{}}

printf("%c-->%c\n",text_falg2[i],text_flag[flag-printf("%c-->#include<stringh>intflag=1;intflag2=-1;charchar*{char*p;inti=0;{}returnp;}int{charinput[100];inttext_a[26],i,j;char*p; intmax;intk=p[flag-1]-'a';} }{printf("%c的個數(shù)為}{} {}{}}

printf("%c-->%c\n",text_falg2[i],text_flag[flag-printf("%c-->#in