2016 全国高校密码数学挑战赛-赛题三

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2025年1月10日16:40:35评论5 views字数 49916阅读166分23秒阅读模式

2016 全国高校密码数学挑战赛-赛题三

RSA 加密体制破译题目
首届（2016）全国高校密码数学挑战赛-赛题三

题意

给出了加密例子及格式
还给出了要还原的通信数据，要求尽可能多地还原参数(q, p, n, phi(n), m, d, e)

一些姿势

看这里
RSA 大礼包

解题过程

懒得再写了 直接贴报告
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三

破解随机数生成器

这块我在尝试的时候猜到了是线性同余，然而没想到它是 16bit 拼在一起的...我直接用 p 算 a b 了就肯定 gg。和答案擦肩而过
不过这种随机数为何能找到素数也是挺神奇的，参考的答案里也没具体给出那篇论文，所以我也不知道。
我的报告如下
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三
2016 全国高校密码数学挑战赛-赛题三

分解所有 N

利用上面报告中给出的方法分解

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from gmpy2 import *
import time

N = [90058705186558569935261948496132914380077312570281980020033760044382510933070450931241348678652103772768114420567119848142360867111065753301402088676701668212035175754850951897103338079978959810673297215370534716084813732883918187890434411552463739669878295417744080700424913250020348487161014643951785502867L,
 92921790800705826977497755832938592891062287903332844896046168726101016067456726822505517352409138948392871113192427210529297191908638888388136391240683157994654207338463678065440899870434887094216772312358731142317774259942199808535233769089985063860828267808621928898445383706310204223006136919334252875849L,
 #90252653600964453524559669296618135272911289775949194922543520872164147768650421038176330053599968601135821750672685664360786595430028684419411893316074286312793730822963564220564616708573764764386830123818197183233443472506106828919670406785228124876225200632055727680225997407097843708009916059133498338129L,
 92270627783020341903769877272635163757611737252302329401876135487358785338853904185572496782685853218459404423868889360808646192858060332110830962463986164014331540336037718684606223893506327126112739408023014900003600028654929488487584130630596342720833061628867179840913592694993869009133576053124769728363L,
 90058705186558569935261948496132914380077312570281980020033760044382510933070450931241348678652103772768114420567119848142360867111065753301402088676701668212035175754850951897103338079978959810673297215370534716084813732883918187890434411552463739669878295417744080700424913250020348487161014643951785502867L,
 99193711547257063160816850544214924340574358752670644615293764532335872088470223740970673347993652626497557387222167784182876395436088845281840169701654629849214222297784511349059698963212947299142320497759258889425182705042123217476724761095690092179821753840224757786599021225709340258545979566824267620959L,
 #146839643970016464813197409569004275595828791825722617066607993001682901023784267554815946189374651530288894322286859792246413142980277245909181062525398546369553995023529451396820549308690493928593324007689135648753323161394735120908960458860801743476353228970081369439513197105039143930008573928693059198131L,
 155266493936043103849855199987896813716831986416707080645036022909153373110367007140301635144950634879983289720164117794783088845393686109145443728632527874768524615377182297125716276153800765906014206797548230661764274997562670900115383324605843933035314110752560290540848152237316752573471110899212429555149L,
 102900163930497791064402577447949741195464555746599233552338455905339363524435647082637326033518083289523250670463907211548409422234391456982344516192210687545692054217151133151915216123275005464229534891629568864361154658107093228352829098251468904800809585061088484485542019575848774643260318502441084765867L,
 97767951046154372321400443371234495476461828137251939025051233003462769415459435471728054384852461870179980010660162922547425212869925648424741526671585598167502856111641944825179295197098826911226483155821197251989297102189187139234080795582529077092266799813985026581245196104843272305656744384140745492897L,
 93836514358344173762895084384953633159699750987954044414830106276642828025218933012478990865656107605541657809389659063108620208004740646099662700112782252200834393363574089818787717951026690934986964275526538236750596344542450864284576226592039259070002692883820960186403938410354082341916474419847211138467L,
 112306066601652819062206435724795595603085908011001671184332227488970057128128821831260649058569739569103298091727188365019228385820143813415009397359257831092635374404034997011441653286642458431865026213129412677064308342580757248577955071384972714557250468686599901682728173096745710849318629959223270431039L,
 90267480939368160749458049207367083180407266027531212674879245323647502822038591438536367206422215464489854541063867946215243190345476874546091188408120551902573113507876754578290674792643018845798263156849027209440979746485414654160320058352559498237296080490768064578067282805498131582552189186085941328701L,
 #94390533992358895550704225180484604016029781604622607833044135524814562613596803297695605669157378162035217814540004231075201420796787547733762265959320018107419058832819010681344133011777479722382525797938558181629835768471461434560813554411133962651212455645589624432040989600687436833459731886703583047283L,
 120008876536855131221255979370745233738591934188224528487535120483456214085493237482915446419599357910343450285858995374277365393767669569942204888383426461862651659865189178784473131914234181752055950431093341514138390898892413182538823693941124637301582389014479754627419560568004831093116617428970538503551L,
 147733349387696521015664992396355145811249793103958464053225389476050097503928022819269482555955365534137156079172704297584033078453033637103720972881068435459202133846880715879894340131656691631756162323422868846616160423755883726450486845175227682329583615739797782025647376042249605775433971714513081755709L,
 90673177193017332602781813187879442725562909473411994052511479411887936365983777106776080722300002656952655125041151156684340743907349108729774157616323863062525593382279143395837261053976652138764279456528493914961780300269591722101449703932139132398288208673556967030162666354552157189525415838326249712949L,
 #111178307033150739104608647474199786251516913698936331430121060587893564405482896814045419370401816305592149685291034839621072343496556225594365571727260237484885924615887468053644519779081871778996851601207571981072261232384577126377714005550318990486619636734701266032569413421915520143377137845245405768733L,
 93394639108667212482180458616036741615058981058942739509025631675767304945732437421192075466824789572910657586684470553691049259504106442090140927782673066834126848556317079995332229262871079799089771973100731889841015960713908117908583988637159206246729697336281050046919985463146705713899703248595045701819L,
 #94154993593274109828418786834159728190797445711539243887409583756844882924221269576486611543668906670821879426307992404721925623741478677756083992902711765865503466687919799394258306574702184666207180530598057989884729154273423032471322027993848437082723045300784582836897839491321003685598931080456249945287L,
 90916739755838083837461026375700330885001446224187511395518230504776419813625940046511904838818660297497622072999229706061698225191645268591198600955240116302461331913178712722096591257619538927050886521512453691902946234986556913039431677697816965623861908091178749411071673467596883926097177996147858865293L]

Nd = [
 #90252653600964453524559669296618135272911289775949194922543520872164147768650421038176330053599968601135821750672685664360786595430028684419411893316074286312793730822963564220564616708573764764386830123818197183233443472506106828919670406785228124876225200632055727680225997407097843708009916059133498338129L,
 146839643970016464813197409569004275595828791825722617066607993001682901023784267554815946189374651530288894322286859792246413142980277245909181062525398546369553995023529451396820549308690493928593324007689135648753323161394735120908960458860801743476353228970081369439513197105039143930008573928693059198131L,
 #94390533992358895550704225180484604016029781604622607833044135524814562613596803297695605669157378162035217814540004231075201420796787547733762265959320018107419058832819010681344133011777479722382525797938558181629835768471461434560813554411133962651212455645589624432040989600687436833459731886703583047283L,
 #111178307033150739104608647474199786251516913698936331430121060587893564405482896814045419370401816305592149685291034839621072343496556225594365571727260237484885924615887468053644519779081871778996851601207571981072261232384577126377714005550318990486619636734701266032569413421915520143377137845245405768733L,
 94154993593274109828418786834159728190797445711539243887409583756844882924221269576486611543668906670821879426307992404721925623741478677756083992902711765865503466687919799394258306574702184666207180530598057989884729154273423032471322027993848437082723045300784582836897839491321003685598931080456249945287L]

def BFFactor(fname,n):#细分
    s = time.clock()
    for f16bit in xrange(1, 65537):
        print '\r',f16bit,
        Xn = bin(f16bit)[2:].zfill(16)
        while len(Xn)<1000:
            Xn += bin((365 * int(Xn[-16:],2) - 1) % 2**16)[2:].zfill(16)

        while len(Xn)>980 and int(Xn,2):
            #print Xn
            if gcd(int(Xn,2),n)!=1:
                print '[+]Frame %s Factor found!' %fname
                print '  [-]Factor1:', int(Xn,2)
                print '  [-]Factor2:', n/int(Xn,2)
                print '[!]Timer:', round(time.clock()-s), 's'
                return ''
            
            Xn = Xn[:-1]

    return '[!!!]Factor not found!\n'

def FindFactors(fname,n):#小于 512bits
    s = time.clock()
    for f16bit in xrange(1, 65537):
        Xn = bin(f16bit)[2:].zfill(16)
        while len(Xn)<520:
            #Xn.append(bin((365 * Xn[-1] - 1) % 2**16)[2:])
            Xn += bin((365 * int(Xn[-16:],2) - 1) % 2**16)[2:].zfill(16)
            #xn = ''.join([bin(i)[2:] for i in Xn])
            if gcd(int(Xn,2),n)!=1:
                print '[+]Frame %s Factor found!' %fname
                print '  [-]Factor1:', int(Xn,2)
                print '  [-]Factor2:', n/int(Xn,2)
                print '[!]Timer:', round(time.clock()-s), 's'
                return ''
    return '[!!!]Factor not found!\n'

s = time.clock()
for fname,n in enumerate(N):
    print FindFactors(fname,n)

print '[!]All Timer:', round(time.clock()-s), 's'

结果如下

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[+]Frame 0
  [-]p=6812427463539231600349464320632373878259506266011361351387035583576132041989251176508636878569037408377298402530520856411137155634830256279629494046731167
  [-]q=13219767207586640795571526377541732890465157517028423385812256305169857431521906172089205698188779144534548881591815311408600403492889107894773842719465101

[+]Frame 1
  [-]p=7273268163465293471933643674908027120929096536045429682300347130226398442391418956862476173798834057392247872274441320512158525416407044516675402521694747
  [-]q=12775796067504534889308793837705093856447186276434607181291462366302734214583227473619414509043813033676998357747882057607288385639737162184366176530607467

[+]Frame 2
  [-]p=52484065122572767557293534477361686456679280880304125291106733197354892893647364164212186415880889674435558369420400890814461263958618375991691022752189839
  [-]q=1719620105458406433483340568317543019584575635895742560438771105058321655238562613083979651479555788009994557822024565226932906295208262756822275663694111

[+]Frame 3
  [-]p=7055398260479522499340383681532186847092995337600547504968011029334785849248198827261592108738030900350146800969715064939422943632175860165796992047655507
  [-]q=13078018330994845621552747855429996741129628768867676788710615773048246855802311926334525991481279783903078961691672741494174797757666145632542141818518409

[+]Frame 4
  [-]p=6812427463539231600349464320632373878259506266011361351387035583576132041989251176508636878569037408377298402530520856411137155634830256279629494046731167
  [-]q=13219767207586640795571526377541732890465157517028423385812256305169857431521906172089205698188779144534548881591815311408600403492889107894773842719465101

[+]Frame 5
  [-]p=8534204848837515931975393694743604482233978795239717717444249645500744498481212186170560396980739879301795276459915005215431744867752453542213016868639743
  [-]q=11623075998787245402346559750331455079165060117337930034889727146620333293916811257160778523014841986594526205881807563317848049715664071879977965137310113

[+]Frame 6
  [-]p=159482692259010816139523195494724350795654007589889398757383554027183924116413427533184220914037106543253535103452324841452565420868944985464229649420240708554088156331324206733727690785373464575525698274552058386560106163093965065830071277465943834308083708065429495092746028681968670036721164931
  [-]q=920724637201

[+]Frame 7
  [-]p=12406300145307944335209213373018196725715201666535385618794522686524721950743049201561939737652055430279463659191670498628785792792237461236532551241091557
  [-]q=12515132804905159708127766136325707992321377113998710477445811836263405233128780498152047439057240132542217905573440500557504942936575400253824837109325257

[+]Frame 8
  [-]p=8649620751833675845720949489383858845796447401365353800898878144845175406172676844999275150219630606359684669242320399096050331623719946048021382644892803
  [-]q=11896494295276874055593281869319334151651783133808673396575485807068776793606182148494465816391713137317129560972663854384901692609500496853548961122888889

[+]Frame 9
  [-]p=9578503710865082752572619447703250581238252879412822133271432204532787671643027893670256331928358458734493559747171810834463456086852684437858903431104943
  [-]q=10207017087152588040715048402680785398862222629910637172475793288776252558629748676497021478354292685455714591071372731030921157909006333951719151324136879

[+]Frame 10
  [-]p=9686924917554805418937638872796017160525664579857640590160320300805115443578184985934338583303180178582009591634321755204008394655858254980766008932978633
  [-]q=9686924917554805418937638872796017160525664579857640590160320300805115443578184985934338583303180178582009591634321755204008394655858254980766008932978699

[+]Frame 11
  [-]p=10567461048505039641972710268713128944634687748250712080474984695584136876402672898538333956369978635390580930966654058991315304961329166742263216335895001
  [-]q=10627535420870140157264943381237995845188613757283488311986534170673076876359166440468642831586000127005789867628311873382408383407839525066568105400526039

[+]Frame 12
  [-]p=6985860474362742689823213380101231514167124463232248283942151780607845942841460091693138693954396501918480507964569322391710334462720533595017918609916463
  [-]q=12921454883136991414340641129184178393731045365222406074761149065515779165690863384311170163255060973667442222325395407973824379536104548265452893540473427

[+]Frame 13
  [-]p=28159870572597920594563893250499572739237769660647238839011417383170724985058502301163390234256825164330439886062865686161169349465086627567328776299903327
  [-]q=3351951982485649274893506249551461531869841455148098344430890360930441007518386744200468574541725856922507964546621512713438470702986642490397676148760429

[+]Frame 14
  [-]p=10954856299233465126359914171500305822846165431085183673999109759449706415739193445885099004577509868426540084786683485568001351280541116090063034118634519
  [-]q=10954856299233465126359914171500305822846165431085183673999109759449706417636519711881707731622506407722143163847672064459333431572992021257881551867597529

[+]Frame 15
  [-]p=12129590228679741504121711843970362493049315734589299243022334854180628199056110072388206407916677887428330057500003256795368137540193144088105889375346813
  [-]q=12179582871512776468956891745877445010350618063676813770961929030122878089063984750168929497808121238411849832804023412100455762402728468432020965274841793

[+]Frame 16
  [-]p=6998204055345503454608535735199373144581147952412423572966494183179306005216278935510553634487794945379209006773628864213102839984362642462197184843259867
  [-]q=12956635227542071202375560927144520333507358619831580670377595997503810379893056493870213428580918250332435506596912071784762831942734238145246920736537647

[+]Frame 17
  [-]p=33168227830849222860094691158174263663422336899723339302414624335921937096795361698659264621281924482566876836548283550012466892022559940789243695658550143
  [-]q=3351951982485649274893506249551461531869841455148098344430890360930441007518386744200468574541725856922511753810518751644117399610974624147782234049900131

[+]Frame 18
  [-]p=7273268163465293471933643674908027120929096536045429682300347130226398442391418956862476173798834057392247872274441320512158525416407044516675402521694747
  [-]q=12840807874760119497562989864651565491645077946976950748211992253853323703532620362223764981952516328133916264333884385029280730688894521589959051436522977

[+]Frame 19
  [-]p=86725761611859895386396141031497189948984447138542215420462553101081991008304507461163078354877970282649251051457532902955009856009405853917396630017011320500357081664483071782135584899953560478866041032397335990722689211113937797406269980402604895207480485168493674422769645640726941944110986793
  [-]q=1085663496559

[+]Frame 20
  [-]p=7006433107252813175095285828299335809650512229854304253471035955787617465825842990081320535410435973346940338772266519696972554709877157476961995216696227
  [-]q=12976180370825816046330723693051565324091920359016588247467647785104809172783057319885443026117787490599861213721564637212466483142611446237049740392927759


所有参数

有了 pq，求所有参数都是轻而易举：

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import re 
from gmpy2 import *
import time
import pprint

Data = []
for i in range(21):
    with open('Frame'+str(i)) as fp:
        data = re.findall('(.{256})(.{256})(.{256})',fp.read().replace('\n',''))
        Data += data

N = [int(n,16) for n,e,c in Data if int(e,16)]
C = [int(c,16) for n,e,c in Data if int(e,16)]
E = [int(e,16) for n,e,c in Data if int(e,16)]


with open('pq.txt','r') as fp:
    data = fp.read()
    p = [int(i) for i in re.findall(r'p=([0-9]+)', data)]
    q = [int(i) for i in re.findall(r'q=([0-9]+)', data)]
    pq = zip(p,q)

cN = [i*j for i,j in pq]
if [i for i in range(21) if cN[i] != N[i]]: print '[!!!]You are wrong!!';kill
else: print '[!]Well done in pq'

print '[+]Hacking Frame...'

print '  [-]Calculating Phi...',
Phi = [(i-1)*(j-1) for i,j in pq]
print 'Done!'

print '  [-]Calculating d...',
D = [invert(E[i],Phi[i]) for i in range(21)]
print 'Done!'

print '  [-]Hacking m...',
M = [('%x' %pow(C[i],D[i],N[i])) for i in range(21)]
print 'Done!'

print '[+]All data is:'
for i,m in enumerate(M):
    print '  [-]Frame%d' %i
    print '    [-]p:', '%x' %p[i]
    print '    [-]q:', '%x' %q[i]
    print '    [-]n:', '%x' %N[i]
    print '    [-]f:', '%x' %Phi[i]
    print '    [-]e:', '%x' %E[i]
    print '    [-]d:', '%x' %D[i]
    print '    [-]m:', m
    print '    [-]c:', '%x' %C[i]
    
print '[!]The Password is:',''.join([m.decode('hex')[-8:] for m in sorted(set(M))])


结果如下：

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[!]Well done in pq
[+]Hacking Frame...
  [-]Calculating Phi... Done!
  [-]Calculating d... Done!
  [-]Hacking m... Done!
[+]All data is:
  [-]Frame0
    [-]p: 821273a9e7f4b6e3c1a619ad9ba8ee87167a0bf1069c6c6b948ece755cd0548f8fe2253912440af39c76143ddaf833978e4adf81aaecb27b795e0b05b620ab9f
    [-]q: fc68e047c53a33b1b35cba2b6f4eb2351590be4f56a284f9970450b30f36affdebb815576d0a774107acf03b841e5ec51ee0055fa8722a89a554b8c36e06de8d
    [-]n: 803f734ed9e3a3fbdef8e3540b7b676fb66d15d2e5139840cb3cd06e62634c00a48ea2bf9bc3d7a709dbb47be7e27dfb2c0e5b81254e6c326691471ae6ddc4a35539018ba6305daff1c480f195118b1310c546c31fe62c7aec2a947013ac2897d00fd60e7b792dd499315341895bd1d1c9aa923e9373e1e01e2856b4fc8c6893
    [-]f: 803f734ed9e3a3fbdef8e3540b7b676fb66d15d2e5139840cb3cd06e62634c00a48ea2bf9bc3d7a709dbb47be7e27dfb2c0e5b81254e6c326691471ae6ddc4a1d6bdad99f901731a7cc1ad188a19ea56e4ba7c82c2a73b15c0977547a7a5240a54759b7dfc2aab9ff50e4ec82a453f751c7fad5d401504daff7592ebd864de68
    [-]e: 42a04a989c5800528ef687c978355e9c4afd410a9dd4b08cca7669c747cce5446d5e85022ca2a2c383c28e85ad038c37ced2e18bd88529bd2480e20191958497c61823378ca06de01c8b6fb148c9bc935e433efcd960a1bf841fd60599811941a122cb1a323a76367ee78d71870b7134881ca077518c809013ae8ec6baecd519
    [-]d: 5b3b2da24b37ced4e91817ca8a52a0ac2d870c23c65d1e7172368544192a6d48c301f947394ae86093905f7949e82247b52f043e7801ea7a3562d6e27687a5f4db1dc4959f5bed65a7b12595dc4775257e03afc86df4311dd150249cb6a74384771ca87c62114130b0d79f4815b39057c452bbdfa38b69537fe874c5a1a542f9
    [-]m: 9876543210abcdef0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004d79207365637265
    [-]c: 45446fc78ac9aa9f2e38197d44b76f0c2a7ded354615d906608016e9f884fa51e20893fa0aeaf5975e28a68fbcd9ba469ea00263f812523eec79e0cf967190317bef53ee8ff29af4411a238e7fce148ae7603c9a1dec4eeac1e41ad5fb8725fd3dce4c058db10f279b3ec1fa3ebc6584547d29501cca52851148344316073e6b
  [-]Frame1
    [-]p: 8adefe85e3a08b1f5b320649f614da838cc6b64debc82c27f39a5291b8bc640ba3ae5f1590f0a62ff1029fd9e86456936f9618dd73181937f36a0e21250cd21b
    [-]q: f3eeca557b30a36f05427f1936a4e7d387d6ac1d65587e774faa9561fb4c4b5b70bebee52c80727f3f12eca96cf457e34ea622ad70a89f87737aa4f12b9c2d6b
    [-]n: 845334ac0b3eb2239fdf0e3069750901e791cb774ad36941e30d85e5a0fed57749a30dc1f1f4cb191d9863f437c98293e8e8888b963bcf16b691f1d4eef56c6807440e5fb5ec5b95df3434deda30c60dcb4e77294be027f984d5e675aeb1cbbe57e8caf140226ead6dcd9a9636a0cff586fa434804cb09d7e8c48de34ebe9049
    [-]f: 845334ac0b3eb2239fdf0e3069750901e791cb774ad36941e30d85e5a0fed57749a30dc1f1f4cb191d9863f437c98293e8e8888b963bcf16b691f1d4eef56c6688764584571b2d077ebfaf7bad7703b6b6b114bdfabf7d5a4190fe81faa91c57437bacf682b155fe3db80e12e148217ec8be07bd210a511881dfdad0fe1590c4
    [-]e: 10001
    [-]d: 4cca3c76dacfb7711505cca62b8ccf7d5b75302e3a2e159736bc5247bff622cae6e0c8cb142e8aee384e8732e26cfe69f76f7a4e07110e4c900681e0a00bacac93e48ed30df9a75802261b201aba465d7207b191ce41f1ecbebff5f258146b6df8ab7ce45153b823a28d7d1d57bf14310f2db82ff94c9363357b42f0a582be5
    [-]m: 9876543210abcdef0000000b00000000000000000000000000000000000000000000000000000000000000000000000000000000000000002e20496d6167696e
    [-]c: 251025dc5fb84476581d0f67c640d8927da6d083627c9c29f3174c17cfe316a6218194dd4be03d30ef9eccbb4c609673d853590dd122b151dcfd6d75fd202dc2c758e897babe0a4cd842ff35d086cf4e34efbd09e8ff9fbfb4b5254ca2323a463139abd16e301c37f683579ba624efbb297b9e6d5a1c68f75eb4badf9aa198c
  [-]Frame2
    [-]p: 3ea18c437be22139df56ae544e1f2232c25b9c75532c15bbfcb087a6680914d4f355b0e779b6087ddb4aa938453329b6f98f91995780017fe3249b0a4d9d28d8f
    [-]q: 20d553f6ec8df4dd610278518babe13e0efd87744717f733836c634407d0230e467b622f9787080adde08cb349423bc93efd965375b51f301bd9d9d25c61891f
    [-]n: 808627ced38a980d765454ac5dfefc10195f6fef9b35b52b742dbce2419c34080a3ef3e9673fea4dd629ff382155031ea6dcba8372d42c1862f32b2bee47e157fa7150c544635035f366f7d68234f56fa24180eb6a00a0f85c65aaeb455b8ed28f2285376cda786f8c658cfeb3752f3504a7256ea3dbd22eef20267d156fab51
    [-]f: 808627ced38a980d765454ac5dfefc10195f6fef9b35b52b742dbce2419c34080a3ef3e9673fea4dd629ff382155031ea6dcba8372d42c1862f32b2bee47e153ef83389699b347ba9cf99a401496f1056d8a3221f0274e050df0cd40bcfa1e75134c149039f2e886f9da6cc7170057fc2cb07585b6269b00a0fc9c05df3b94a4
    [-]e: 10001
    [-]d: 759c4e6951e38de923d35ff8abbb5e664d11ac9912eb3ef298ca1202ea0f4afde0826329bf3619ef487ffdf11b6f73ff64aab073016d6f3c91affc5da31b5bf33746594e57305bff450e943cf79a78cc82c4e7c36ec448fd0f18c07af173e0d339e97117da2f92e1915a74186bd000b3df214b2a24d98716383b717b5e206391
    [-]m: 9876543210abcdef0000000600000000000000000000000000000000000000000000000000000000000000000000000000000000000000002054686174206973
    [-]c: 38702ef6fd51ca1ca834ef495618da956c8f8ad222b99e256ed5e3dd9089e194de67fd427f6132715709830a73b1a1cb582e56d06af8f31bba2851dba1a1c2985b7fc233018e42554c2aabd69a225f9283a164c3aa5479363f89260219f9964738b7c78c5d08618009f3904eb55a6a570e8d4b1701f4bf1b2c99c7887ccff2c9
  [-]Frame3
    [-]p: 86b6117def3812d7dc8a70c1c32c45bb6b9e7045126032df87f2d40950d43e43c586a00d32880be7f85a1851ab7c7fcb346ec0d5efb0bdefcdc25d9973242a53
    [-]q: f9b405a30966666d096869471a3a64b1905cd32b144ef335c290674f4ba2d5f9140489b3543610fd38b8de57020ae84124ac493b691edfc50be0ee5fdd72bb89
    [-]n: 8365d1ff23709faaef6330aeca9c848b292e0872c5c41e8cbe9d0780f32ebfc5fcc7947bd666f06aa619f952afb8d7c08b9211960d1916235d8ab3a60dec45b1ef5cc21848e56d5235717186ead51ae22a5661bdfdc42e31f9181f6ab1d070fdebb078a9980d7a0571b587130a1d3056cba40cbba287cd5031838bab893b476b
    [-]f: 8365d1ff23709faaef6330aeca9c848b292e0872c5c41e8cbe9d0780f32ebfc5fcc7947bd666f06aa619f952afb8d7c08b9211960d1916235d8ab3a60dec45b06ef2aaf75046f40d4f7e977e0d6e70752e5b1e4dd715081cae94e41215595cc112254ee9114f5d2040a2906a5c95c84a728902aa49b82f9b57e03fb238a46190
    [-]e: 5
    [-]d: 4ed6b132aedd2c99c2d51d35acc44f86b24ed1de76a8df213f2b048091e8d976cade25e3e70a903ffd42c8cb363bb4a6ba2470f3a17573aed1b99efd3b8dc369dc2b3361302a926e62e58e186e7576acb569defb810c9e779bf2ef3e0ccf37a70ae32f58a3fc6b1359fb23730459de93118567ffc5d4e95d34b9bfd1552f6dbd
    [-]m: 9876543210abcdef0000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000007420697320612066
    [-]c: 76cbcaf659936784799208c3ee2420b7bbfdbb9aa8d7c89874c11314df5decd3aa97f3da89851a043af16e6570e7d03a4f3225d49e552faa2fb9f6a19ae95ba73ecd6e7cc05cd9c03e03e06f829042dba4c1a91f39ac0cad516c8de7fb45939a2038c24c13f7f62a20040473d8f3d8339a4b30a65715f98a43cc3293e51190d5
  [-]Frame4
    [-]p: 821273a9e7f4b6e3c1a619ad9ba8ee87167a0bf1069c6c6b948ece755cd0548f8fe2253912440af39c76143ddaf833978e4adf81aaecb27b795e0b05b620ab9f
    [-]q: fc68e047c53a33b1b35cba2b6f4eb2351590be4f56a284f9970450b30f36affdebb815576d0a774107acf03b841e5ec51ee0055fa8722a89a554b8c36e06de8d
    [-]n: 803f734ed9e3a3fbdef8e3540b7b676fb66d15d2e5139840cb3cd06e62634c00a48ea2bf9bc3d7a709dbb47be7e27dfb2c0e5b81254e6c326691471ae6ddc4a35539018ba6305daff1c480f195118b1310c546c31fe62c7aec2a947013ac2897d00fd60e7b792dd499315341895bd1d1c9aa923e9373e1e01e2856b4fc8c6893
    [-]f: 803f734ed9e3a3fbdef8e3540b7b676fb66d15d2e5139840cb3cd06e62634c00a48ea2bf9bc3d7a709dbb47be7e27dfb2c0e5b81254e6c326691471ae6ddc4a1d6bdad99f901731a7cc1ad188a19ea56e4ba7c82c2a73b15c0977547a7a5240a54759b7dfc2aab9ff50e4ec82a453f751c7fad5d401504daff7592ebd864de68
    [-]e: d8bffcdd82504c05a241e26742f0a867b162e5ecbf185e66f0a5fca1801a2c3a2a562549d433c600e3a4085c123535aa7ad14d55c0b3765c55c5b78b946517c14438ad876ec0f7ac22792988bb6cd7837aa64334eb5f7c668d570cbf8134b7f7e87eefa95179ca11bedcdf420eb6df9178c0a3b489a07b86ebca6adf96982d0d
    [-]d: 7d71af7541f1b1ba8a810def794f3662ee73b7e81ead2b89313e969ff5cd12b40cfed55ea2b5f1572ebf14532b17062a206371be56c78799fd20cf61113cd677537090516953f0aa64afda84c60d8a863d1639446bd3f21d24c60b406308f458640fe0bb8f3fe9ce0bf13060219b9c5da80df8594f32349831863dceaf98293d
    [-]m: 9876543210abcdef0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004d79207365637265
    [-]c: 1bdaf2dbcec34d6602c949e9b53876a4d8b62fa69dd960063b342e5101f92a0f5d88a445d7bdf36f3816aebd5a98a8f06ab2cd708e363a657665cf05cb1f289eb758e09d11351816df1edf4575f01f95efce164d62eee92bce562b94b451fd9b566e4f8625e0428ad93bc6f8342c089af2842ea6deb9ed22d450f062cc7b18a8
  [-]Frame5
    [-]p: a2f2530963d4554390860f0d758892e7735a77511e7c76cb5f6e0fd592b024efa8c29c9946240153e356219decd8aff7e32ae2e17acc14dbbc3e6465240053ff
    [-]q: ddec697b645e1a051920d29f4cb259c903941a031646c1cd5148e3a7951a9611f63c138bdd2e5a952670cdaf4282d35955e476135916045d3898b0b7f4ea31a1
    [-]n: 8d41ac379635a2c8ffa55f609be3eb6219c7ad0d3c335ac1f7ae27c3c0510e9acde319a6e00b891bddb05c6b53f62e9321340bc0f19727c0526ac811cc02c7229241045a3d125978c1181264fde49d8a148aad8a8796c12c2ab5e8d7b0f98edac907c092b70d8b36e5bdc47c5801e4225bb508b1f081f5331c9b1324875ea25f
    [-]f: 8d41ac379635a2c8ffa55f609be3eb6219c7ad0d3c335ac1f7ae27c3c0510e9acde319a6e00b891bddb05c6b53f62e9321340bc0f19727c0526ac811cc02c721116247d574dfea30177130b83ba9b0d99d9c1c3652d3889379fef55a892ed3d92a09106d93bb2f4ddbf6d52f28a660d122a5afbd1c9fdbfa27c3fe076e741cc0
    [-]e: 10001
    [-]d: 34302045853c99c0f31a912b6b4d00c904c74dfb46d39e636d73ad8358095a80fd323b66f8fdaa115e8d6b07c8447b1ea6b4c8e6e71b36778abba2e158636a58a048944b9bdba2755423e0a12081e831ee561fe23e25a31f01829df96e179bf36ee15c6d6f9847b8d75cd19493cb2c97f7da091cb077ab5937d9e47fb0623bc1
    [-]m: 9876543210abcdef0000000c00000000000000000000000000000000000000000000000000000000000000000000000000000000000000006174696f6e207769
    [-]c: 251a6449a3e9a4a444238910ed757d0dcf8d825007a94ad9e171d4caf3799b07bb5fc050aab3762ee10e234dfff101d7e551de4f61c824f55c6a4c0e895d48ab46c67a66fdac65f2f60d5a2150fca740940293ff5b2aedae129fabf3840d879ad25f9393ff9a664ffcfa0b2fe484d01994dad68c0d340246c7b63515a96dd034
  [-]Frame6
    [-]p: f9b6087d1a3861d77f8ad7c19e2c84bb3e9e47459d6061df8af21b098bd45d43f886570d1d881ae75b5a3f51467c7ecbc76e57d53ab0acef90c264996e2409534b56699d94d837f7cb2aaae1a2cc1cdb243eac65cc00dbffaa9232298474d963f226402d8028b907cefa1a71b31c5eeb550e44f55150ef0fd86283
    [-]q: d65f770611
    [-]n: d11b49bf43234d6595219ab7c21730de0a13a7a01e63831a4d4f8dc5a7e68fca0e9768ef0dabcad036e08e17e4b27c1151df364556d8f93d19565d9f40f095a49c6185f2630671eb5ec1eaa514bec32d93a0f0459b52f1e34d4b9113413403f66619262ef1d3cbb025648c997cd1438de21cfe4bea0c6e00c72ffde587929cb3
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  [-]Frame9
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  [-]Frame10
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  [-]Frame11
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  [-]Frame12
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  [-]Frame13
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  [-]Frame14
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  [-]Frame15
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    [-]c: 4a6972b03f96cc30de3f60da66c71842e600320964a69ec818047b219506a12f3e4d522b40b10eb3f630a068c908186f29bf782360e35262a4ceccad554f57d1721db61b260ac6c5fbcb020ac326562048b0fc9270afe51c63f5f27a9a3cfd78b5971d5cbf7fbf20e23ca7b429121bd0bb9ae0552d6907c659e2b450b01675d7
  [-]Frame16
    [-]p: 859e8245bc6094df41f206099ad4c0431f86f20d1c88ade7f25a8a51357c41cbce6e52d519b09fef07c20f993d242c533256c49d53d88af7222ab5e151cc9fdb
    [-]q: f762b6b985c4b873fbf63dbd0678391765ca21010e6c8ffb48dee485d1a0e11ff9324c49c41490830ac65c4d99c84227519a589146bcda0be1aec515fef07c2f
    [-]n: 811f75bead6f0c3ea1560cfa4bfd4762f1da3a30e22644ab16b1bea5a6a1af14f0c3c2e63865fd29241246c1473892232dab6224af1600f73340cbca7bf5af01ea1fa007e46064ce2f8dd92a9e7fa9f16cfeee5a6cf67683bcd97f1e7e1ba73a9f86a8e4d7496393ac9727d10530a76b03b3a23321e8bdd756fce265494f6d35
    [-]f: 811f75bead6f0c3ea1560cfa4bfd4762f1da3a30e22644ab16b1bea5a6a1af14f0c3c2e63865fd29241246c1473892232dab6224af1600f73340cbca7bf5af006d1e6708a23b177af1a59563fd32b096e7addb4c420138a081a0104776fe844ed7e609c5f98433219a0ebbea2e4438f07fc28504875358d45323676df892512c
    [-]e: 5
    [-]d: 674c5e322458d6988111a3fb6ffdd2b58e482e8d81b836ef455afeeaebb48c10c09c9beb605197541cdb6bcdd293a81c24891b508c119a5f5c33d63b965e2599f0e51f3a1b62792f27b7aab664288d458624af7034cdc6e6ce19a69f926536a57984d49e61368f4e14d89654f1d02d8d330204039f75e0a9dc1c52be60750dbd
    [-]m: 9876543210abcdef0000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000007420697320612066
    [-]c: 224cd570eaf4d650aa24d51127e1657d201c8483aa690d48d58ca56ae86ea517df43f9f130cc7ca75c8868623ba145189e2d16326a82a437516530d130161552d016adb2d8746dc92d30f2a4d90a50a63af038b0449cf2a3442ba6696b6485a46d47545591aadb1c68e901745d4f9231627c9e0c0a52cc7439cc45b21ae51aee
  [-]Frame17
    [-]p: 2794aeba5f8d3c08d879a53b557a1ef1deaebecc4937236aff339c6d47c41273cf08af1e6e21050cf32db7df694e2435e0a287b0764b28eedc67bf9162181c37f
    [-]q: 400000000000000000000000000000000000000000000000000000000000000000000000000000000000000297bc784272b16f7b8edff759502b21342f286e63
    [-]n: 9e52bae97e34f02361e694ed55e87bc77abafb3124dc8dabfcce71b51f1049cf3c22bc79b8841433ccb6df840f2bd5a6e75a1ce52f54048ff4930e7b103c6a3433a2663bd9cba0e38a35695f927eb2ff7a51939869a113d8a6cb03228c0e5d1466b1ff491129a988efdbc636ab2610caa50925554be758321178f9eb94072c1d
    [-]f: 9e52bae97e34f02361e694ed55e87bc77abafb3124dc8dabfcce71b51f1049cf3c22bc79b8841433ccb6df840f2bd5a6e75a1ce52f54048ff4930e7b103c6a317a577a95e0f7e056029b15aa3adcc3e18f65a6d3d62edd28b3913c4e0fcd35d776270d622f1958b9bd00483d7e87552a282f3ad25854d1eafad1dfa1435cfa3c
    [-]e: 10001
    [-]d: 6f02930c24f1f96ed5b657b6120670c3edca2d56c801dd543a6e864bf8fbf2c4dbe57f41d99ec28b8f7eaa3a6e68cde5b951f5f0bcbeac744388d91e70c3ebb1c59690dd8660476c0767b64925fca55c02afc3c9c4e4172df2ba630e59060a3a891dd8c47f41c67475913d15e12203150c1811a66b490de734f6f3569f65121
    [-]m: 9876543210abcdef0000000f00000000000000000000000000000000000000000000000000000000000000000000000000000000000000007977686572652e22
    [-]c: 1fca302be54fd4b4f8da498ede013bf551c714e321b17465cf55b9980ec12fdf92f4f408c15239fe5eed408248d598510c0e77618eba67321938d487d7286bd9ef539cb2b068fe02617be2954109b3b3da0c76ecf00957894d556acbce10e1ff68a536b82ef0befa92e9fd96264786fab50a3162d2564d8634338e5a6eef5e0
  [-]Frame18
    [-]p: 8adefe85e3a08b1f5b320649f614da838cc6b64debc82c27f39a5291b8bc640ba3ae5f1590f0a62ff1029fd9e86456936f9618dd73181937f36a0e21250cd21b
    [-]q: f52c8fbbed9eca4564601cdf29f2ce09c2d4c84387863a0dc48835e7da5a52515d7c49cb366e9ad5c1b027efefc2d799652434539a560c9dfbd812f70a2a7de1
    [-]n: 84ff95e263d30fad83684cc08b11dab54f5a0f3d24a8763c47b57750ed2e342022652836e2ebb30a765dc7364f417e4555d1fd72d140efb72e283007028cc2a4fe97e4fe3b5d272c917e734f8715a0c5bff2900640d8097425afa965f9b1566f339f155aceb59ede241327813c920a6fb98a6bb9209379f1bbebcc955949d8bb
    [-]f: 84ff95e263d30fad83684cc08b11dab54f5a0f3d24a8763c47b57750ed2e342022652836e2ebb30a765dc7364f417e4555d1fd72d140efb72e283007028cc2a37e8c56bc6a1dd1c7d1ec5026670df83870571174cd89a33e6d8d20ec669aa01232746c7a07565dd871605fb7646adc42e4d01e881325541bcca9ab7d2a1288c0
    [-]e: 10001
    [-]d: 41f02573746273e766bb133272c08b5a50d929acfabbbac2f01a7be9576e0cd1d1bbad5068f8ca6f6977dd08840ac87bbfacb8a7702f6da9b7ec9cc31cf4849b626659aa5842287b950c404089df572d442526b66e20cb1a6c5e07f0ac7e04d680c54ff2c02885a685af6e45123818b3e1957d4da190643ed41d5ab457639101
    [-]m: 9876543210abcdef0000000a00000000000000000000000000000000000000000000000000000000000000000000000000000000000000006d204120746f2042
    [-]c: 45d8bd62bbf9966c81722d6d4ad5e6e91fd5258c8b0747ca166237d167d5c881b100d83d73352f18a60914963ca8f7df9b9211273c8d7edac87132aadac33def0bda6c9ea91750818d869990521c6ba0a10bc1ac2273282fa4ac47efbeee99b2d35ebda2019d1ef8bf24b5017fa8481b372362aae138043a00d8761bcdca80bc
  [-]Frame19
    [-]p: 87ca9b01006c99fb8adefe85e3a08b1f5b320649f614da838cc6b64debc82c27f39a5291b8bc640ba3ae5f1590f0a62ff1029fd9e86456936f9618dd73181937f36a0e21250cd21b907e03a53240a53f9ad2bd690eb4f6a3a6663f6d6e686a47873acdb1455ce42b514eec35c790884f58a25ef96904bab3313629
    [-]q: fcc696496f
    [-]n: 8614c70089aade50e5a14de1fb8fcf0880046e9494eead3bf600ebe451e335b4c9e21de984912bca15914711a9c359056a2ad0543035e971a2faa387ea53aad48a7016735e2bb60716626cad6cf4f9cc41a59cf31ef07473a1de08a018cab7c6b95bf7ac9f501bd42fcc4c7cd834b6a7723b6abcc9a98146a750a9222cce2cc7
    [-]f: 8614c700892313b5e4a0e1480004f009fa20ce0975937b35ac0ad709ce566efe7bf655bd5c9d917783d88aad9e1faaa65499dfae0044e6d1c9123f3156e414bbacfcfe5a26384bf8f53d5fdb51647bc89c735c4ddf55a1b638cf53a9752451874bed8f4257c8e1067e86ef98ace367bb3c73da347a50dee7ade7a36ab306ad30
    [-]e: 10001
    [-]d: 444aa8e158f808be0868f8d5974cec85e864750cd459fdd3648150eda9aed471c1e9c1d9e5264c45375e3fa41679c28d5d61d24fe9cb2e5583b84b7f71e651b9156ef68e2c115880c148355e9ba2367a0355ae99eb3ace56e5b093c827e60bb081b7c9d3dcaa7012c2b72fa9efc513bc8619ebf5f6a6e221d6adb8ca4bcd06c1
    [-]m: 9876543210abcdef000000050000000000000000000000000000000000000000000000000000000000000000000000000000000000000000696e737465696e2e
    [-]c: 4b6a6a6ce0cd9d8e0df4fbd2a23af3fb45fa587406a3e052231519c4b6b0b606d64dc531a29c0a7510928d4487e7bc3d45cdbadb595ae7d53fbdee70371debcb9a938b94dc0f266326a9df6191e04f82a9cdc067d366926b58a9092f55db22f8d4bcd9777a99f14ed95083d091da69f80f448eff48a21f998bbdc97daea135c1
  [-]Frame20
    [-]p: 85c6bb4d0cc839277c9aa791e9bc410bbcae0415d1f0532f9a0294d93964d393a8965dddd4186637bc6aa321960cef1be97ee8a5b340923f83d2f2699fb4b3a3
    [-]q: f7c23f99ad24dc532256f49dc3d83af7122ae5e1c1cc4fdbdb3e9765db003effd192cd2983746c6389268b2d6f287c07d5fa1571921c51ebcc0eeff52050120f
    [-]n: 8178408d7e1155b9f5b0665a3edfe279189567aac333ca33a7304ae1bb9c9a921735888fb7bc9b41550817b1c0d42b2ab0304546709648f45147180ad5fc839fb8f90b2d30772718a7b45e6204ce7886122874759f93c198ce61d10555f03c13fd83e639a637d849c846d5589029533e567e12fd992d690ec5ef38569327fc8d
    [-]f: 8178408d7e1155b9f5b0665a3edfe279189567aac333ca33a7304ae1bb9c9a921735888fb7bc9b41550817b1c0d42b2ab0304546709648f45147180ad5fc839e3b701046768a119e08c2c2325739fc83434f8a7e0bd71e8d5920a4c6418b2980835abb324eab05ae82b5a7098af3e81a970514e653d084e3760d55f7d32336dc
    [-]e: 5
    [-]d: 4dae8d21b20a66a2c69d0a3625b987e241f33e3341ebdfb8978360210a2ac324745351efd4a45d273304db04407f4d199ce9c32a438d5ef8fd910e6ce6cab55ef076702a471fa42b9edb41516789311b8ec953186d811254cf1396108db9e5b382033d1e2f3369cf1b39ca9f535f24dcc1030c8a3249e95546d4cd2e4b7b8751
    [-]m: 9876543210abcdef0000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000007420697320612066
    [-]c: 210b2c8ca031259d2ef22a2561b23b794b3740382bd0a89ef7db9e62463c8649ef5983eb94cff6f0d6a1881a0d4e190ef8a1acc20da5da71ae31705a5501b6856c151449dfc76b7026a9fab74aa4b41c7f58eccdc35777866c117d3be1e37a4576e34c90df7b8146f1bdf841d1362287a4922cb9a80221ec165e48f0bffd4ede
[!]The Password is: My secret is a famous saying of Albert Einstein. That is "Logic will get you from A to B. Imagination will take you everywhere."

## 最终明文
My secret is a famous saying of Albert Einstein. That is "Logic will get you from A to B. Imagination will take you everywhere."


这个题覆盖了很多的 RSA 使用不当(各种参数)造成的不安全现象，很有意思
不过我通过数论知识只解开了 17 个包，还剩 Frame 5,9,13,17 这些没有直接解出
破解随机数生成器没搞出来，参考去年一等奖的论文才弄出来。还是太菜啦

- By:tr0y.wang

免责声明:文章中涉及的程序(方法)可能带有攻击性，仅供安全研究与教学之用，读者将其信息做其他用途，由读者承担全部法律及连带责任，本站不承担任何法律及连带责任；如有问题可邮件联系(建议使用企业邮箱或有效邮箱,避免邮件被拦截，联系方式见首页)，望知悉。
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  • 本文由 发表于 2025年1月10日16:40:35
  • 转载请保留本文链接(CN-SEC中文网:感谢原作者辛苦付出)：
                   2016 全国高校密码数学挑战赛-赛题三https://cn-sec.com/archives/3616196.html
                  免责声明:文章中涉及的程序(方法)可能带有攻击性，仅供安全研究与教学之用，读者将其信息做其他用途，由读者承担全部法律及连带责任，本站不承担任何法律及连带责任；如有问题可邮件联系(建议使用企业邮箱或有效邮箱,避免邮件被拦截，联系方式见首页)，望知悉.

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