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May 8, 2017 00:27
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RSA Algorithm in PowerShell. Just Cause
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| <# | |
| Created By Casey Smith | |
| @subTee | |
| RSA in PowerShell. | |
| Just Cause... | |
| Reference notes for the curious | |
| p = 61 <= first prime number (destroy this after computing e and d) | |
| q = 53 <= second prime number (destroy this after computing e and d) | |
| pq = 3233 <= modulus (give this to others) | |
| e = 17 <= public exponent (give this to others) | |
| d = 2753 <= private exponent (keep this secret!) | |
| Your public key is (pq,e). | |
| Your private key is d. | |
| The encryption function is: encrypt(T) = (T^e) mod pq | |
| = (t^17) mod 3233 | |
| The decryption function is: decrypt(C) = (C^d) mod pq | |
| = (C^2753) mod 3233 | |
| To encrypt the plaintext value 123, do this: | |
| encrypt(123) = (123^17) mod 3233 | |
| = 337587917446653715596592958817679803 mod 3233 | |
| = 855 | |
| To decrypt the ciphertext value 855, do this: | |
| decrypt(855) = (855^2753) mod 3233 | |
| = 50432888958416068734422899127394466631453878360035509315554967564501 | |
| 05562861208255997874424542811005438349865428933638493024645144150785 | |
| 17209179665478263530709963803538732650089668607477182974582295034295 | |
| 04079035818459409563779385865989368838083602840132509768620766977396 | |
| 67533250542826093475735137988063256482639334453092594385562429233017 | |
| 51977190016924916912809150596019178760171349725439279215696701789902 | |
| 13430714646897127961027718137839458696772898693423652403116932170892 | |
| 69617643726521315665833158712459759803042503144006837883246101784830 | |
| 71758547454725206968892599589254436670143220546954317400228550092386 | |
| 36942444855973333063051607385302863219302913503745471946757776713579 | |
| 54965202919790505781532871558392070303159585937493663283548602090830 | |
| 63550704455658896319318011934122017826923344101330116480696334024075 | |
| 04695258866987658669006224024102088466507530263953870526631933584734 | |
| 81094876156227126037327597360375237388364148088948438096157757045380 | |
| 08107946980066734877795883758289985132793070353355127509043994817897 | |
| 90548993381217329458535447413268056981087263348285463816885048824346 | |
| 58897839333466254454006619645218766694795528023088412465948239275105 | |
| 77049113329025684306505229256142730389832089007051511055250618994171 | |
| 23177795157979429711795475296301837843862913977877661298207389072796 | |
| 76720235011399271581964273076407418989190486860748124549315795374377 | |
| 12441601438765069145868196402276027766869530903951314968319097324505 | |
| 45234594477256587887692693353918692354818518542420923064996406822184 | |
| 49011913571088542442852112077371223831105455431265307394075927890822 | |
| 60604317113339575226603445164525976316184277459043201913452893299321 | |
| 61307440532227470572894812143586831978415597276496357090901215131304 | |
| 15756920979851832104115596935784883366531595132734467524394087576977 | |
| 78908490126915322842080949630792972471304422194243906590308142893930 | |
| 29158483087368745078977086921845296741146321155667865528338164806795 | |
| 45594189100695091965899085456798072392370846302553545686919235546299 | |
| 57157358790622745861957217211107882865756385970941907763205097832395 | |
| 71346411902500470208485604082175094910771655311765297473803176765820 | |
| 58767314028891032883431850884472116442719390374041315564986995913736 | |
| 51621084511374022433518599576657753969362812542539006855262454561419 | |
| 25880943740212888666974410972184534221817198089911953707545542033911 | |
| 96453936646179296816534265223463993674233097018353390462367769367038 | |
| 05342644821735823842192515904381485247388968642443703186654199615377 | |
| 91396964900303958760654915244945043600135939277133952101251928572092 | |
| 59788751160195962961569027116431894637342650023631004555718003693586 | |
| 05526491000090724518378668956441716490727835628100970854524135469660 | |
| 84481161338780654854515176167308605108065782936524108723263667228054 | |
| 00387941086434822675009077826512101372819583165313969830908873174174 | |
| 74535988684298559807185192215970046508106068445595364808922494405427 | |
| 66329674592308898484868435865479850511542844016462352696931799377844 | |
| 30217857019197098751629654665130278009966580052178208139317232379013 | |
| 23249468260920081998103768484716787498919369499791482471634506093712 | |
| 56541225019537951668976018550875993133677977939527822273233375295802 | |
| 63122665358948205566515289466369032083287680432390611549350954590934 | |
| 06676402258670848337605369986794102620470905715674470565311124286290 | |
| 73548884929899835609996360921411284977458614696040287029670701478179 | |
| 49024828290748416008368045866685507604619225209434980471574526881813 | |
| 18508591501948527635965034581536416565493160130613304074344579651083 | |
| 80304062240278898042825189094716292266898016684480963645198090510905 | |
| 79651307570379245958074479752371266761011473878742144149154813591743 | |
| 92799496956415653866883891715446305611805369728343470219206348999531 | |
| 91764016110392490439179803398975491765395923608511807653184706473318 | |
| 01578207412764787592739087492955716853665185912666373831235945891267 | |
| 87095838000224515094244575648744840868775308453955217306366938917023 | |
| 94037184780362774643171470855830491959895146776294392143100245613061 | |
| 11429937000557751339717282549110056008940898419671319709118165542908 | |
| 76109008324997831338240786961578492341986299168008677495934077593066 | |
| 02207814943807854996798945399364063685722697422361858411425048372451 | |
| 24465580270859179795591086523099756519838277952945756996574245578688 | |
| 38354442368572236813990212613637440821314784832035636156113462870198 | |
| 51423901842909741638620232051039712184983355286308685184282634615027 | |
| 44187358639504042281512399505995983653792227285847422071677836679451 | |
| 34363807086579774219853595393166279988789721695963455346336497949221 | |
| 13017661316207477266113107012321403713882270221723233085472679533015 | |
| 07998062253835458948024820043144726191596190526034069061930939290724 | |
| 10284948700167172969517703467909979440975063764929635675558007116218 | |
| 27727603182921790350290486090976266285396627024392536890256337101471 | |
| 68327404504583060228676314215815990079164262770005461232291921929971 | |
| 69907690169025946468104141214204472402661658275680524166861473393322 | |
| 65959127006456304474160852916721870070451446497932266687321463467490 | |
| 41185886760836840306190695786990096521390675205019744076776510438851 | |
| 51941619318479919134924388152822038464729269446084915299958818598855 | |
| 19514906630731177723813226751694588259363878610724302565980914901032 | |
| 78384821401136556784934102431512482864529170314100400120163648299853 | |
| 25166349056053794585089424403855252455477792240104614890752745163425 | |
| 13992163738356814149047932037426337301987825405699619163520193896982 | |
| 54478631309773749154478427634532593998741700138163198116645377208944 | |
| 00285485000269685982644562183794116702151847721909339232185087775790 | |
| 95933267631141312961939849592613898790166971088102766386231676940572 | |
| 95932538078643444100512138025081797622723797210352196773268441946486 | |
| 16402961059899027710532570457016332613431076417700043237152474626393 | |
| 99011899727845362949303636914900881060531231630009010150839331880116 | |
| 68215163893104666659513782749892374556051100401647771682271626727078 | |
| 37012242465512648784549235041852167426383189733332434674449039780017 | |
| 84689726405462148024124125833843501704885320601475687862318094090012 | |
| 63241969092252022679880113408073012216264404133887392600523096072386 | |
| 15855496515800103474611979213076722454380367188325370860671331132581 | |
| 99227975522771848648475326124302804177943090938992370938053652046462 | |
| 55147267884961527773274119265709116613580084145421487687310394441054 | |
| 79639308530896880365608504772144592172500126500717068969428154627563 | |
| 70458838904219177398190648731908014828739058159462227867277418610111 | |
| 02763247972904122211994117388204526335701759090678628159281519982214 | |
| 57652796853892517218720090070389138562840007332258507590485348046564 | |
| 54349837073287625935891427854318266587294608072389652291599021738887 | |
| 95773647738726574610400822551124182720096168188828493894678810468847 | |
| 31265541726209789056784581096517975300873063154649030211213352818084 | |
| 76122990409576427857316364124880930949770739567588422963171158464569 | |
| 84202455109029882398517953684125891446352791897307683834073696131409 | |
| 74522985638668272691043357517677128894527881368623965066654089894394 | |
| 95161912002160777898876864736481837825324846699168307281220310791935 | |
| 64666840159148582699993374427677252275403853322196852298590851548110 | |
| 40229657916338257385513314823459591633281445819843614596306024993617 | |
| 53097925561238039014690665163673718859582772525683119989984646027216 | |
| 46279764077057074816406450769779869955106180046471937808223250148934 | |
| 07851137833251073753823403466269553292608813843895784099804170410417 | |
| 77608463062862610614059615207066695243018438575031762939543026312673 | |
| 77406936404705896083462601885911184367532529845888040849710922999195 | |
| 65539701911191919188327308603766775339607722455632113506572191067587 | |
| 51186812786344197572392195263333856538388240057190102564949233944519 | |
| 65959203992392217400247234147190970964562108299547746193228981181286 | |
| 05556588093851898811812905614274085809168765711911224763288658712755 | |
| 38928438126611991937924624112632990739867854558756652453056197509891 | |
| 14578114735771283607554001774268660965093305172102723066635739462334 | |
| 13638045914237759965220309418558880039496755829711258361621890140359 | |
| 54234930424749053693992776114261796407100127643280428706083531594582 | |
| 305946326827861270203356980346143245697021484375 mod 3233 | |
| = 123 | |
| #> | |
| function invmod([System.Numerics.BigInteger] $a,[System.Numerics.BigInteger] $n){ | |
| $exp = $t = $nt = $r = $nr = New-Object System.Numerics.BigInteger | |
| $exp = [System.Numerics.BigInteger]1 | |
| $t = [System.Numerics.BigInteger]0 | |
| $nt = [System.Numerics.BigInteger]1 | |
| $r = $n | |
| $nr = $a | |
| while ($nr -ne [System.Numerics.BigInteger]0) { | |
| $q = [System.Numerics.BigInteger]::Divide($r,$nr) | |
| $tmp = $nt | |
| $nt = [System.Numerics.BigInteger]::Subtract($t,[System.Numerics.BigInteger]::Multiply($q,$nt)) | |
| $t = $tmp | |
| $tmp = $nr | |
| $nr = [System.Numerics.BigInteger]::Subtract($r, [System.Numerics.BigInteger]::Multiply($q,$nr)) | |
| $r = $tmp | |
| } | |
| if ($r -gt 1) {return -1} | |
| if ($t -lt 0) {$t = [System.Numerics.BigInteger]::Add($t,$n)} | |
| return $t | |
| } | |
| $p = $q = $n = $phi = $e = $d = New-Object System.Numerics.BigInteger | |
| $p = [System.Numerics.BigInteger]53 | |
| $q = [System.Numerics.BigInteger]61 | |
| $r = [System.Numerics.BigInteger]::Multiply($p, $q) | |
| $phi = [System.Numerics.BigInteger]::Multiply([System.Numerics.BigInteger]::Subtract($p,1),[System.Numerics.BigInteger]::Subtract($q,1)) | |
| #Public Key | |
| $e = [System.Numerics.BigInteger]17 | |
| #Private Key | |
| $d = invmod $e $phi | |
| Write-Host "Modulus: $r" -fore Cyan | |
| Write-Host "Public Key: $e" -fore Green | |
| Write-Host "Private Key: $d" -fore Yellow | |
| $m = 123 | |
| Write-Host "Secret Message is $m" -fore Magenta | |
| $c = [System.Numerics.BigInteger]::ModPow($m, $e, $r) | |
| Write-Host "Encrypted Message is $c" -Fore Red | |
| $d = [System.Numerics.BigInteger]::ModPow($c, $d, $r) | |
| Write-Host "Decrypted Message is $d" -Fore Magenta |
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