(8)已知n,e,d求p,q

一看这个标题你就应该有个觉悟，n一定无法直接分解得到p和q。

题目: 10-存货5

题目给出了两个文件，一个是加密脚本chall.py，一个是加密后输出的内容output.txt。

分析一下加密脚本：

from gmpy2 import invertfrom md5 import md5from secret import p, qe = 65537n = p*qphi = (p-1)*(q-1)d = invert(e, phi)print n, e, dprint "Flag: flag{%s}" %md5(str(p + q)).hexdigest()

 

加密脚本真的是很简单啊，flag就是str(p+q)进行md5运算之后的得到的字符串，从output.txt中可以得到n,e,d。

用Winhex打开output文件提取数据


 

现在的关键问题就是求出p和q来，google一把梭好像可以找到这种骚操作，当时线上比赛做这个题目的时候真的就是google找到的类似题目，百度啊，可不可以靠谱一点。

解题脚本:

已知n,e,d求p,q

#!/usr/bin/python#coding:utf-8import randomfrom md5 import md5def gcd(a, b):if a < b:a, b = b, awhile b != 0:temp = a % ba = bb = tempreturn adef getpq(n,e,d):p = 1q = 1while p==1 and q==1:k = d * e - 1g = random.randint ( 0 , n )while p==1 and q==1 and k % 2 == 0:k /= 2y = pow(g,k,n)if y!=1 and gcd(y-1,n)>1:p = gcd(y-1,n)q = n/preturn p,qdef main():n = 16352578963372306131642407541567045533766691177138375676491913897592458965544068296813122740126583082006556217616296009516413202833698268845634497478988128850373221853516973259086845725813424850548682503827191121548693288763243619033224322698075987667531863213468223654181658012754897588147027437229269098246969811226129883327598021859724836993626315476699384610680857047403431430525708390695622848315322636785398223207468754197643541958599210127261345770914514670199047435085714403641469016212958361993969304545214061560160267760786482163373784437641808292654489343487613446165542988382687729593384887516272690654309e = 65537d = 9459928379973667430138068528059438139092368625339079253289560577985304435062213121398231875832264894458314629575455553485752685643743266654630829957442008775259776311585654014858165341757547284112061885158006881475740553532826576260839430343960738520822367975528644329172668877696208741007648370045520535298040161675407779239300466681615493892692265542290255408673533853011662134953869432632554008235340864803377610352438146264524770710345273439724107080190182918285547426166561803716644089414078389475072103315432638197578186106576626728869020366214077455194554930725576023274922741115941214789600089166754476449453p,q = getpq(n,e,d)print pprint qprint "Flag: flag{%s}" %md5(str(p + q)).hexdigest()if __name__ == '__main__':main()

 (9)私钥文件修复

题目: 11-Jarvis OJ -Crypto-God Like RSA

 

呵呵，这个题我认了，别的不会的题目起码都能看个大概，这个题绝了，只是知道解题脚本中对应的变量是谁了(哈哈哈)，顺带把变量给你们注释了，反正我是写不出来。

这里面涉及到的东西太多了，我觉得绝不单单是Python脚本的问题，什么数学、什么算法的，必须给你安排的明明白白的。So，我把这题作为了一个模板，以后有类似的题目，直接掏出来用，莫非这真是"上帝之手"？

题目给出三个文件，一个是公钥文件pubkey.pem，一个是残损的私钥文件private.corrupted，还有一个是密文文件flag.enc。

首先使用openssl提取公钥信息：

──(holyeyes㉿kali2023)-[~/Misc/RSA/godlikeRSA]└─$ openssl rsa -pubin -in pubkey.pem -text -modulusPublic-Key: (4096 bit)Modulus:00:c0:97:78:53:45:64:84:7d:8c:c4:b4:20:e9:33:58:67:ec:78:3e:6c:f5:f0:5c:a0:3e:ee:dc:25:63:d0:eb:2a:9e:ba:8f:19:52:a2:67:0b:e7:6e:b2:34:b8:6d:50:76:e0:6a:d1:03:cf:77:33:d8:b1:e9:d7:3b:e5:eb:1c:65:0c:25:96:fd:96:20:b9:7a:de:1d:bf:fd:f2:b6:bf:81:3e:3e:47:44:43:98:bf:65:2f:67:7e:27:75:f9:56:47:ba:c4:f0:4e:67:2b:da:e0:1a:77:14:40:29:c1:a8:67:5a:8f:f5:2e:be:8e:82:31:3d:43:26:d4:97:86:29:15:14:a9:69:36:2c:76:ed:b5:90:eb:ec:6f:ce:d5:ca:24:1c:aa:f6:63:f8:06:a2:62:cb:26:74:d3:5b:82:4b:b6:d5:e0:49:32:7b:62:f8:05:c4:f7:0e:86:59:9b:f3:17:25:02:aa:3c:97:78:84:7b:16:fd:1a:f5:67:cf:03:17:97:d0:c6:69:85:f0:8d:fa:ce:ee:68:24:63:06:24:e1:e4:4c:f8:e9:ad:25:c7:e0:c0:15:bb:b4:67:48:90:03:9b:20:7f:0c:17:eb:9d:13:44:ab:ab:08:a5:c3:dc:c1:98:88:c5:ce:4f:5a:87:9b:0b:bf:bd:d7:0e:a9:09:59:81:fa:88:4f:59:60:6b:84:84:ad:d9:c7:25:8c:e8:c0:e8:f7:26:9e:37:95:7c:e1:48:29:0f:51:e7:bd:98:2f:f6:cc:80:e7:f0:32:0b:89:51:92:4e:c2:6d:50:53:2b:3b:77:72:d1:bd:1a:1f:92:d7:12:79:61:61:c5:a4:7e:b3:85:eb:f0:7c:6d:46:03:c5:e6:d5:81:2c:ba:7e:ea:8d:51:7d:63:55:34:2a:b6:d4:dc:31:5a:f1:99:e3:dc:8c:83:0b:a2:2a:d5:3c:41:48:41:54:1a:a9:e8:b6:70:bf:d3:fe:ed:19:17:14:94:13:b3:17:e3:8b:8e:6f:53:ed:e2:44:e8:4a:32:d6:5c:0d:a8:80:f5:fc:02:e9:46:55:d5:a4:d3:e7:c6:30:77:f9:73:e9:44:52:d8:13:9d:5d:bf:9e:fa:3a:b5:96:79:82:5b:cd:19:5c:06:a9:00:96:fd:4c:a4:73:88:1a:ec:3c:11:de:b9:3d:e0:50:00:1e:ac:21:97:a1:96:7d:6b:15:f9:6c:c9:34:7f:70:d7:9d:2d:d1:48:4a:81:71:f8:12:dd:32:ba:64:31:60:08:26:4b:09:22:03:83:90:17:7f:f3:a7:72:57:bf:89:6d:e4:d7:40:24:8b:7b:bd:df:33:c0:ff:30:2e:e8:6c:1dExponent: 65537 (0x10001)Modulus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 RSA key-----BEGIN PUBLIC KEY-----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-----END PUBLIC KEY-----┌──(holyeyes㉿kali2023)-[~/Misc/RSA/godlikeRSA]└─$

然后将提取到的公钥信息填充到"恢复私钥的脚本fix.py"中，然后运行这个脚本。

私钥文件修复

​github.com/Mr-Aur0ra/RSA/blob/master/(9)%E7%A7%81%E9%92%A5%E6%96%87%E4%BB%B6%E4%BF%AE%E5%A4%8D/godlikeRSA/fix.py

┌──(holyeyes㉿kali2023)-[~/Misc/RSA/godlikeRSA]└─$ python3 exp1.py                              checking 100checking 200checking 300checking 400checking 500checking 600checking 700checking 800checking 900checking 1000checking 1100checking 1200checking 1300checking 1400checking 1500checking 1600checking 1700checking 1800checking 1900checking 2000checking 2100checking 2200checking 2300checking 2400checking 2500checking 2600checking 2700checking 2800checking 2900checking 3000checking 3100checking 3200checking 3300checking 3400checking 3500checking 3600checking 3700checking 3800checking 3900checking 4000checking 4100checking 4200checking 4300checking 4400checking 4500checking 4600checking 4700checking 4800checking 4900checking 5000checking 5100checking 5200checking 5300checking 5400checking 5500checking 5600checking 5700checking 5800checking 5900checking 6000checking 6100checking 6200checking 6300checking 6400checking 6500checking 6600checking 6700checking 6800checking 6900checking 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14300checking 14400checking 14500checking 14600checking 14700checking 14800checking 14900checking 15000checking 15100checking 15200checking 15300checking 15400checking 15500checking 15600checking 15700K = 15791checking 1000checking 2000checking 3000checking 4000checking 5000checking 6000checking 7000checking 8000checking 9000checking 10000checking 11000checking 12000checking 13000checking 14000checking 15000checking 16000checking 17000checking 18000checking 19000checking 20000checking 21000checking 22000checking 23000checking 24000checking 25000checking 26000checking 27000checking 28000checking 29000checking 30000checking 31000checking 32000checking 33000checking 34000checking 35000checking 36000checking 37000checking 38000checking 39000checking 40000checking 41000checking 42000checking 43000checking 44000checking 45000checking 46000checking 47000checking 48000checking 49000checking 50000checking 51000checking 52000checking 53000Kp = 53712checking 100checking 200checking 300checking 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22400checking 22500checking 22600checking 22700checking 22800checking 22900checking 23000checking 23100checking 23200checking 23300checking 23400checking 23500checking 23600checking 23700checking 23800checking 23900checking 24000checking 24100checking 24200checking 24300checking 24400checking 24500checking 24600checking 24700checking 24800checking 24900checking 25000checking 25100checking 25200checking 25300checking 25400checking 25500checking 25600checking 25700checking 25800checking 25900checking 26000checking 26100checking 26200checking 26300checking 26400checking 26500checking 26600checking 26700checking 26800checking 26900Kq = 26920pwnedp = 30061432003658510087798871614869318011389940352798147030129806359975911392091235344042288409629143229311060231549478211871643725394470760528211801310601767727834886942210718412087541234398453046895030858579989874035849439867334906873642352112428914855967993998732685221108379784833027771293275558876952608462050146340591449046825135890871650866799299533696175818103240024841274114925018619060818213433528894936128306780366785977567327073724428211445259983614467640785163297734447975723664659822673456683284394386723716344090232882990461174301609971805075768328757325956784604364401827152431260896927633163074694121679q = 26136662545551829820746942051638228325025130519175536694008242208616774469870765684858288042819063837180243501117310278632509413217676559484513481677689042623348188876598901642459170232360966754692434316796014314498263800234390539118817050074978421973817764644287745302885861277447227180288605200894138168586207384484170481511828680117688324729381172912436910052489279406590356734739774635376711681212908417321705094537960645308009611045658947359297373154395500467689532455017647450616447445444254910371922944620114234547655209970657063715028350418518417105772707885648587233103869340985670430269862943630137067052883d = 189314060947745787654498165274830331174557121266906779862419555225211185530603428281572732893609400752227106390673469015633513601478376007980907685218789784684913841408741295031489754782076172169319157484287361680256043362028296440972189429040371100663239858141284465980874067131885490419967590348201189710575833318886977656522342412509705514383478694693754208398422979228753024497378460051423550810294749332024347106310964901579178253736977778221603016185935642494136204931234524722205937195008837883867578968312663507844825332250280433460469722801545785384920549610305670512211052257540691951435317870875619595628937534523394133353929222521584160841354771534449084153424347188585906251861248309552253930838373561942975707303028732726506301413434343525650181088504211290391497726019689042160550200171411457613452966587499555164618905387343295621486012988196484264365061465147262989915838838473704337695423465093089724153892389725410085609729143077814394217461295117827225090618358013844801017475143005461542391824369921894127873221707688828770261365746173721607819236320716542560206858465665216449930570401369383789211423678295673603341013341777685726223028517376052521329317581752900566710098686429294852358239672182937051082392901-----BEGIN RSA PRIVATE KEY-----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-----END RSA PRIVATE KEY-----┌──(holyeyes㉿kali2023)-[~/Misc/RSA/godlikeRSA]└─$

接着，将私钥文件修复脚本fix.py恢复出私钥来，存放到文件private.pem中。

这就结束了吗，没有，god不是白叫的。你会发现你根据私钥使用openssl直接解密密文文件解不开，而且直接根据p，q，d，c也无法直接求出m。这里又涉及到了RSA加密的填充模式。

这里使用的是PKCS1_OAEP填充模式，参考链接:

RSA加密填充模式

​www.cnblogs.com/lzl-sml/p/3501447.html

然后，接着运行下面的脚本即可得到flag。

┌──(holyeyes㉿kali2023)-[~/Misc/RSA/godlikeRSA]└─$ openssl rsautl -decrypt -inkey private.pem -keyform PEM -in flag.enc -oaepThe command rsautl was deprecated in version 3.0. Use 'pkeyutl' instead.PCTF{0h_U_r_ju5t_lik3_g0d}