from Crypto.Util.number import *\nfrom secret import flag\n\nm = bytes_to_long(flag)\np = getPrime(512)\nq = getPrime(512)\ne = 65537\nn = p*q\nc = pow(m,e,n)\nprint(f'p = {p}')\nprint(f'q = {q}')\nprint(f'c = {c}')\n'''\np = 12567387145159119014524309071236701639759988903138784984758783651292440613056150667165602473478042486784826835732833001151645545259394365039352263846276073\nq = 12716692565364681652614824033831497167911028027478195947187437474380470205859949692107216740030921664273595734808349540612759651241456765149114895216695451\nc = 108691165922055382844520116328228845767222921196922506468663428855093343772017986225285637996980678749662049989519029385165514816621011058462841314243727826941569954125384522233795629521155389745713798246071907492365062512521474965012924607857440577856404307124237116387085337087671914959900909379028727767057\n'''<\/code><\/pre>\n\n\n\n\u5f88\u660e\u663e\u5c31\u662f\u6700\u57fa\u7840\u7684rsa<\/code><\/pre>\n\n\n\nimport gmpy2\np = 12567387145159119014524309071236701639759988903138784984758783651292440613056150667165602473478042486784826835732833001151645545259394365039352263846276073\nq = 12716692565364681652614824033831497167911028027478195947187437474380470205859949692107216740030921664273595734808349540612759651241456765149114895216695451\nn = p*q\ne=65537\nprint(n)\n#159815598674904640027098331162347988922194433731964450257065506925289826150266802038662002544129457139047934452929223408615917720106891707480466247184676672373769176533991030505629330283054451556177512592574735088228984703255202745127991386941533156933557260334687275503248793438858493994669328447123309243923\nphi_n=(p-1)*(q-1) \nd= gmpy2.invert(e,phi_n)\nprint(d)\n#36112565432910612541942706962223039930860084671813808136730138579071624204026749338397326634969759536935789879204554213012391862872315780339018030342522185433437772588688970979667097963086458493604270236302678345514661708353601478921375772129292333594441864048042124579326951080450744716155318735421067840273<\/code><\/pre>\n\n\n\n\u7136\u540e\u4e00\u4e2a\u4e00\u4e2a\u4ee3\u5165\u897f\u4e8c\u98ce\u7684\u5de5\u5177\u91cc\uff0cEuler\u5c31\u662fphi_n<\/p>\n\n\n\n![\"\"](\"data:image\/svg+xml;base64,PCEtLUFyZ29uTG9hZGluZy0tPgo8c3ZnIHdpZHRoPSIxIiBoZWlnaHQ9IjEiIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8yMDAwL3N2ZyIgc3Ryb2tlPSIjZmZmZmZmMDAiPjxnPjwvZz4KPC9zdmc+\")
<\/div><\/figure>\n\n\n\n\u6216\u8005\u53ef\u4ee5\u5b8c\u5168\u5199\u811a\u672c\u505a\uff1a<\/p>\n\n\n\n
import gmpy2\nfrom Crypto.Util.number import long_to_bytes\n\ne=65537\np = 12567387145159119014524309071236701639759988903138784984758783651292440613056150667165602473478042486784826835732833001151645545259394365039352263846276073\nq = 12716692565364681652614824033831497167911028027478195947187437474380470205859949692107216740030921664273595734808349540612759651241456765149114895216695451\nc = 108691165922055382844520116328228845767222921196922506468663428855093343772017986225285637996980678749662049989519029385165514816621011058462841314243727826941569954125384522233795629521155389745713798246071907492365062512521474965012924607857440577856404307124237116387085337087671914959900909379028727767057\nn=p*q\nphi=(p-1)*(q-1)\nd=gmpy2.invert(e,phi)\nm = pow(c,d,n)\nprint(long_to_bytes(m))<\/code><\/pre>\n\n\n\nfactordb (\u4e2d\u7ea7)<\/h2>\n\n\n\ne = 65537\nn = 87924348264132406875276140514499937145050893665602592992418171647042491658461\nc = 87677652386897749300638591365341016390128692783949277305987828177045932576708<\/code><\/pre>\n\n\n\n<\/div><\/figure>\n\n\n\n\u7b97\u4e00\u4e0bd<\/p>\n\n\n\n
import gmpy2\np=275127860351348928173285174381581152299\nq=319576316814478949870590164193048041239\nn = p*q\ne=65537\nphi_n=(p-1)*(q-1) \nd= gmpy2.invert(e,phi_n)\nprint(d)\n#10866948760844599168252082612378495977388271279679231539839049698621994994673<\/code><\/pre>\n\n\n\n<\/div><\/figure>\n\n\n\nyafu (\u4e2d\u7ea7)<\/h2>\n\n\n\nfrom Crypto.Util.number import *\nfrom secret import flag\n\nm = bytes_to_long(flag)\nn = 1\nfor i in range(15):\n n *=getPrime(32)\ne = 65537\nc = pow(m,e,n)\nprint(f'n = {n}')\nprint(f'c = {c}')\n'''\nn = 15241208217768849887180010139590210767831431018204645415681695749294131435566140166245881287131522331092026252879324931622292179726764214435307\nc = 12608550100856399369399391849907846147170257754920996952259023159548789970041433744454761458030776176806265496305629236559551086998780836655717\n'''<\/code><\/pre>\n\n\n\n<\/div><\/figure>\n\n\n\nimport gmpy2\ne = 65537\np1=2151018733\np2=2201440207\np3=2315495107\np4=2585574697\np5=2719600579\np6=2758708999\np7=2767137487\np8=2906576131\np9=2923522073\np10=3354884521\np11=3355651511\np12=3989697563\np13=4021078331\np14=4044505687\np15=4171911923\n\n\nphi = (p1 - 1) * (p2 - 1) * (p3 - 1) * (p4 - 1) * (p5 - 1) * (p6 - 1) * (p7 - 1) * (p8 - 1) * (p9 - 1) * (p10 - 1) * (p11 - 1) * (p12 - 1) * (p13 - 1) * (p14 - 1) * (p15 - 1)\nd = gmpy2.invert(e, phi)\nprint(d)\n#3936755899646600686215566512896866674683133415527864719997715318148147385203287657188495205983652573089554541753973835730576494171914667753473<\/code><\/pre>\n\n\n\n<\/div><\/figure>\n\n\n\ne\u7684\u5b66\u95ee<\/h2>\n\n\n\nfrom Crypto.Util.number import *\nm=bytes_to_long(b'xxxxxx')\np=getPrime(256)\nq=getPrime(256)\ne=74\nn=p*q\nc=pow(m,e,n)\nprint(\"p=\",p)\nprint(\"q=\",q)\nprint(\"c=\",c)\n#p= 86053582917386343422567174764040471033234388106968488834872953625339458483149\n#q= 72031998384560188060716696553519973198388628004850270102102972862328770104493\n#c= 3939634105073614197573473825268995321781553470182462454724181094897309933627076266632153551522332244941496491385911139566998817961371516587764621395810123<\/code><\/pre>\n\n\n\n\u8fd9\u91cc\u5f88\u660e\u663e\uff0ce\u548cphi\u90fd\u662f\u5076\u6570\uff0c\u4e0d\u4e92\u7d20\uff0c\u76f4\u63a5\u5957\u677f\u5b50<\/p>\n\n\n\n
import gmpy2\nfrom Crypto.Util.number import *\n\n\n# \u5f53e\u7ea6\u53bb\u516c\u7ea6\u6570\u540e\u4e0ephi\u4e92\u7d20\ndef decrypt(p, q, e, c):\n n = p * q\n phi = (p - 1) * (q - 1)\n t = gmpy2.gcd(e, phi)\n d = gmpy2.invert(e \/\/ t, phi)\n m = pow(c, d, n)\n print(m)\n msg = gmpy2.iroot(m, t)\n print(msg)\n if msg[1]:\n print(long_to_bytes(msg[0]))\n\np= 86053582917386343422567174764040471033234388106968488834872953625339458483149\nq= 72031998384560188060716696553519973198388628004850270102102972862328770104493\nc= 3939634105073614197573473825268995321781553470182462454724181094897309933627076266632153551522332244941496491385911139566998817961371516587764621395810123\ne=74\ndecrypt(p, q, e, c) \n#LitCTF{e_1s_n0t_@_Prime}<\/code><\/pre>\n\n\n\n\u6216\u8005\u76f4\u63a5\u7528\u5185\u7f6e\u7684\u529f\u80fd<\/p>\n\n\n\n<\/div><\/figure>\n\n\n\nThe same common divisor (\u9ad8\u7ea7)<\/h2>\n\n\n\nfrom Crypto.Util.number import *\nm=bytes_to_long(b'xxxxxx')\ne=65537\np=getPrime(1024)\nq1=getPrime(1024)\nq2=getPrime(1024)\nn1=p*q1\nn2=p*q2\nc1=pow(m,e,n1)\nc2=pow(m,e,n2)\nn3=n1^n2\nprint('n1=',n1)\nprint('n3=',n3)\nprint('c1=',c1)\nprint('c2=',c2)\n#n1= 9852079772293301283705208653824307027320071498525390578148444258198605733768947108049676831872672654449631852459503049139275329796717506126689710613873813880735666507857022786447784753088176997374711523987152412069255685005264853118880922539048290400078105858759506186417678959028622484823376958194324034590514104266608644398160457382895380141070373685334979803658172378382884352616985632157233900719194944197689860219335238499593658894630966428723660931647038577670614850305719449893199713589368780231046895222526070730152875112477675102652862254926169713030701937231206405968412044029177246460558028793385980934233\n#n3= 4940268030889181135441311597961813780480775970170156650560367030148383674257975796516865571557828263935532335958510269356443566533284856608454193676600884849913964971291145182724888816164723930966472329604608512023988191536173112847915884014445539739070437180314205284883149421228744714989392788108329929896637182055266508625177260492776962915873036873839946591259443753924970795669864031580632650140641456386202636466624658715315856453572441182758855085077441336516178544978457053552156714181607801760605521338788424464551796638531143900048375037218585999440622490119344971822707261432953755569507740550277088437182\n#c1= 7066425618980522033304943700150361912772559890076173881522840300333719222157667104461410726444725540513601550570478331917063911791020088865705346188662290524599499769112250751103647749860198318955619903728724860941709527724500004142950768744200491448875522031555564384426372047270359602780292587644737898593450148108629904854675417943165292922990980758572264063039172969633878015560735737699147707712154627358077477591293746136250207139049702201052305840453700782016480965369600667516646007546442708862429431724013679189842300429421340122052682391471347471758814138218632022564279296594279507382548264409296929401260\n#c2= 854668035897095127498890630660344701894030345838998465420605524714323454298819946231147930930739944351187708040037822108105697983018529921300277486094149269105712677374751164879455815185393395371001495146490416978221501351569800028842842393448555836910486037183218754013655794027528039329299851644787006463456162952383099752894635657833907958930587328480492546831654755627949756658554724024525108575961076341962292900510328611128404001877137799465932130220386963518903892403159969133882215092783063943679288192557384595152566356483424061922742307738886179947575613661171671781544283180451958232826666741028590085269<\/code><\/pre>\n\n\n\nimport gmpy2\nfrom Crypto.Util.number import long_to_bytes\n\ne=65537\nc1= 7066425618980522033304943700150361912772559890076173881522840300333719222157667104461410726444725540513601550570478331917063911791020088865705346188662290524599499769112250751103647749860198318955619903728724860941709527724500004142950768744200491448875522031555564384426372047270359602780292587644737898593450148108629904854675417943165292922990980758572264063039172969633878015560735737699147707712154627358077477591293746136250207139049702201052305840453700782016480965369600667516646007546442708862429431724013679189842300429421340122052682391471347471758814138218632022564279296594279507382548264409296929401260\nn3= 4940268030889181135441311597961813780480775970170156650560367030148383674257975796516865571557828263935532335958510269356443566533284856608454193676600884849913964971291145182724888816164723930966472329604608512023988191536173112847915884014445539739070437180314205284883149421228744714989392788108329929896637182055266508625177260492776962915873036873839946591259443753924970795669864031580632650140641456386202636466624658715315856453572441182758855085077441336516178544978457053552156714181607801760605521338788424464551796638531143900048375037218585999440622490119344971822707261432953755569507740550277088437182\nn1= 9852079772293301283705208653824307027320071498525390578148444258198605733768947108049676831872672654449631852459503049139275329796717506126689710613873813880735666507857022786447784753088176997374711523987152412069255685005264853118880922539048290400078105858759506186417678959028622484823376958194324034590514104266608644398160457382895380141070373685334979803658172378382884352616985632157233900719194944197689860219335238499593658894630966428723660931647038577670614850305719449893199713589368780231046895222526070730152875112477675102652862254926169713030701937231206405968412044029177246460558028793385980934233\nn2 = n3 ^ n1\np=gmpy2.gcd(n1,n2)\nq=n1\/\/p\nc=c1\nn=p*q\nphi_n=(p-1)*(q-1)\n#\u6c42\u9006\u5143\nd=gmpy2.invert(e, phi_n)\nm=pow(c, d, n)\nprint(long_to_bytes(m))<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"\u91cd\u751f\u4e4b\u6211\u662f\u5bc6\u7801\u624b\u3002 \u5bb6\u4eba\u4eec\uff01\u8c01\u61c2\u554a\uff0cRSA\u7b7e\u5230\u90fd\u4e0d\u4f1a \u7136\u540e\u4e00\u4e2a\u4e00\u4e2a\u4ee3\u5165\u897f\u4e8c\u98ce\u7684\u5de5\u5177\u91cc\uff0cEuler\u5c31\u662fphi_n […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9],"tags":[],"class_list":["post-1837","post","type-post","status-publish","format-standard","hentry","category-wp"],"_links":{"self":[{"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/posts\/1837","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/comments?post=1837"}],"version-history":[{"count":2,"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/posts\/1837\/revisions"}],"predecessor-version":[{"id":1845,"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/posts\/1837\/revisions\/1845"}],"wp:attachment":[{"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/media?parent=1837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/categories?post=1837"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/fushuling.com\/index.php\/wp-json\/wp\/v2\/tags?post=1837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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