The Great Factoring Challenge

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Behold, the Great Factoring Challenge! Not to be confused with the RSA Factoring Challenge, which has been ongoing now for many years (some of the challenges have now been solved and their solutions are now available) and has cash prizes involved.

I started this challenge after a discussion in #wikipedia-en about RSA and the ease of cracking RSA keys. Anyone is welcome to join, so have at it!

All moduluses (moduli?) are given in hexadecimal (preceeded by 0x) and decimal. Many thanks to w:User:Shirik for providing the decimal conversions of the moduli for 768, 1024, and 2048!

Solutions: Please send your solutions (the two prime numbers p and q used to create each modulus, see Wikipedia) to these problems to factoring [ a t ] fastlizard4 [ d o t ] org! Including your Wikipedia/IRC username will get you an accolade of some sort! Regardless, any name you list in your email will be used to provide you credit in the Correct Solutions section below. If you want to include any details on how you solved the problems, include them in your email and they will also be posted here in the solutions list!

Before attempting these problems, you may wish to familiarize yourself with the RSA algorithm. Using the symbols from the algorithm description in the linked article, the moduli below are n, and you want to factor n to find p and q while knowing only n.

The moduli below are from RSA keys generated using the openssl command line utility on a 64-bit Ubuntu Linux server. The command used was sudo openssl genrsa -out $1.key $1 where $1 is the key strength (128, 256, 512, 768, 1024, and 2048). The modulus for each key was found by running openssl rsa -modulus -in $1.key -out $1.mod and the primes were found using openssl rsa -text -in $1.key -out $1.txt. Both the text files containing the primes and the original private keys are on file.

Difficulties noted with each modulus are not necessarily what you'll experience. The difficulty of each problem depends on what algorithms you use, for example. However, the difficulties are useful for determining the relative difficulty of the problems with each other. It should be noted that the best current public cryptanalysis of RSA is up to 768-bits; that is, moduli of up to 768 bits in length have already been factored.

Testcases

This RSA moduli below are for testing implementations only. No solutions will be accepted for this; indeed, the answers are even provided below. However, you can (and should) use these testcases to ensure that any program you write or use is actually working correctly.

RSA/32 A

Difficulty: So easy a VAX could do it. Your DVD player, too.

   Private-Key: (32 bit)
   modulus n: 3934128073 (0xea7e07c9)
   publicExponent: 65537 (0x10001)
   privateExponent: 3096202993 (0xb88c4ef1)
   prime1 p: 62939 (0xf5db)
   prime2 q: 62507 (0xf42b)
   exponent1: 31021 (0x792d)
   exponent2: 30789 (0x7845)
   coefficient: 61045 (0xee75)
   -----BEGIN RSA PRIVATE KEY-----
   MC0CAQACBQDqfgfJAgMBAAECBQC4jE7xAgMA9dsCAwD0KwICeS0CAnhFAgMA7nU=
   -----END RSA PRIVATE KEY-----

RSA/32 B

Difficulty: So easy a VAX could do it. Your DVD player, too.

   Private-Key: (32 bit)
   modulus n: 3583955293 (0xd59ed15d)
   publicExponent: 65537 (0x10001)
   privateExponent: 2867418417 (0xaae95531)
   prime1 p: 60779 (0xed6b)
   prime2 q: 58967 (0xe657)
   exponent1: 33933 (0x848d)
   exponent2: 19769 (0x4d39)
   coefficient: 42230 (0xa4f6)
   -----BEGIN RSA PRIVATE KEY-----
   MC4CAQACBQDVntFdAgMBAAECBQCq6VUxAgMA7WsCAwDmVwIDAISNAgJNOQIDAKT2
   -----END RSA PRIVATE KEY-----

RSA/64

Difficulty: Easy

   Private-Key: (64 bit)
   modulus n: 16748810522526493651 (0xe86fba6e65842bd3)
   publicExponent: 65537 (0x10001)
   privateExponent: 1219545047445013185 (0x10ecb1c25c8c02c1)
   prime1 p: 4265529707 (0xfe3ed16b)
   prime2 q: 3926548793 (0xea0a6139)
   exponent1: 2656477943 (0x9e56a2f7)
   exponent2: 1525396833 (0x5aebb561)
   coefficient: 2736310387 (0xa318c873)
   -----BEGIN RSA PRIVATE KEY-----
   MD8CAQACCQDob7puZYQr0wIDAQABAggQ7LHCXIwCwQIFAP4+0WsCBQDqCmE5AgUA
   nlai9wIEWuu1YQIFAKMYyHM=
   -----END RSA PRIVATE KEY-----

128-bit RSA

Difficulty: Mild

Modulus=0xE7D605E937A0B8EB0A31DD685F3C0875

Modulus=308162938443467880757692372610071660661

256-bit RSA

Difficulty: Moderate

Modulus=0xEB5549BD79CDD3CDD48C931754B7739C2D840C4847EB722782CF103FBD79A36D

Modulus=106444210353314459494776176906754614678652995403104636173578215395897147761517

512-bit RSA

Difficulty: Challenging

Modulus=0xBE85FB983073B496AB04A0CC04EE4515CE8F5EF6BA44C4F1A0F850C68C97995CA76540206CD3BC08693BFCC61EE4FDD8509EE222C9866EC9CE0E0DF37CEA6D23

Modulus=9978518573603876093789324998666265401107033139797543804288209530518842420080876075779983260396656628637896619182831476291290515146524046523028475866672419

768-bit RSA

Difficulty: Hard

Modulus=0xBBF1DFE649EB933C3A3EFF9A8E6CC48D86032F253B70EFBF033C3462841C7362CA1FD95287A7475CAA3A225AA7ADF8BEC9F5E82E5C40C4026E07B817CF7A4B7D4AF5C183B67CB356747114A708D0AD304F749FE5757F5BF57C8BD04F69C5C925

Modulus=1139795849900923923354271059604307494555491892673422185149471786568450883672003097589714327538716710633964224199683099750023992560100740676517306775986926016123550863829762039948072259344686542838208196255416863976293523073060423973

1024-bit RSA

Difficulty: Ludicrous

Modulus=0xC0EC91D232681A7DE0D66D034B5DF9E03776F5B78CBCE9F7FF4AF7CA47E06DDECCCD6C964D905F7368C76CD2F20BBDFA073E6902C311100903EF870E57D8267656DC70E442C1420FFCC0D9F10E20ECDA65AB75B1081EDF3C69E112A233BC01BC02876DEB08139AF960CDC1701AB38ED86FF4E7D18AA235A035B3F5778C934DA7

Modulus=135475910240232261321675456529140759144516177876761672134498277465708747525087233245135068420553906863774343232846114200440928785995673673713968910253432672358906220969261828602410980412274211419591048864543493240823574719554970851928938915752404867450141760790762070326006945313068083053014321461750291189159

2048-bit RSA

Difficulty: Impossible (probably cannot be cracked in the next few decades without a quantum computer)

Modulus=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

Modulus=23255858762313669680919279685825337827100217609088322030372518476734397390962668356079070127999670496811281160674542568891652392913136541900550084448190677632686809852210495159272923898610518773394325492383535106871592098618067167461497963775296393965938097636030855013819409002922794204392277182870944908547678960033091644875157649672940097036088772581783047411611122223255948015774707493382671415151993748861800550863311547940110351844731780371517066075044700828247324303524675095516141163441800577418325111582149772646051129512618745229345711814905288450942831424285753833986718938630295146077713803941905910743507

4096-bit RSA

Difficulty: The engines can't take it anymore, captain! (probably cannot be cracked in the next few decades without a quantum computer)

Modulus=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

Modulus=938526311360739833086461038829310111015989546988043619323285662886971235826448901380366296915545764828933281116801778692444493827116328138442449511777534552067560347078549609760810239779140450264304649109141789448063030926854801115778535670049976381983873375094619299899981387136755874006653842294137574659175266609418893570722818940252472028324086117887034130412835681842166328411590258544607774245712880103916531526460135345754804456359689082457325574735312314625407274179987017793814808901334359548803204883443753606049573689281906205857714852276229126827620046176255418618385911419260853392179459564364878130571863918298271383617149901781829049915144449393594340870311559838614828254853925913240368167632956395100293761485146300093253356223341955497990286847998101246563222723504833883428643443605472253911919371626460024106295396529427405184144405862045684999562090447261723494866259298039376775826752134202521536034602508998391927173084715169491068832471823083219871411505701801100721752463409764830391226428300704403179873541191952809518304164439454251400218206210101429639056794551393158602768959067278172189269645485107142021376849270761596906287867558867704258825820241451162605541745494326239501092685160622524564030592281

8192-bit RSA

Difficulty: Fools, they called me mad! (probably cannot be cracked in my lifetime without a quantum computer)

Modulus=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

Modulus=953727866795899932427305841410142755076432360614301123626614253952365586853661576606994082077595839432579507608006723860517687235859363354809224572211571466726352988362893060254921122544904828192922092132870365402881574500660719104900445297881176949135119878573239330637717669848619536386060219048268463638746215198704496979094949128215842962902214278652717300423131954369472143968116387858320629599547303817754381494874674048470592572102692936172862842479521833166778720207387278214646814820760175382154743709592023997331397691281518525207065235050829816785383875495598975761532370478514164180621421822865146112744046647584598898224992858611423976657958073867840092536291734233352140174863875538322000756384840737327490211187894882742567264985442135247598191865799665857412389606190799148531675047810577610506686045352164159740173312094670473351533469804180572282354774354513683212155722144878290159983626797581668531865317877701781431104499663570190311702763561626050971486467792844033695129315061172327734237880334624945146255354253723581986575497336739500291767616008311094135818159443361733415530960595667517514114146906794351634830973151685396633508811258382238074401332421063471241226469924099380078492309963416481705153644879193040513203684939725287447811899187890823267786911627907594917852859800434919849079541050639996651120640057720540168534800091467724251850638113810977323953764290376145131670109725461312457923350146775681589960148698353445020059145814193374568402180395032163944771658315986558749714150150872147490833253124116399659451511452118052861326005051140241705830243770275065587215645221056183682668943278045597049228390624718424914929917013868220401001583564192050194017937957927493443861934295325185538263767938653295760392370860827127927804920612614061493855875314275569526354908432647378407723718238441787238223345037521324998859680116571349114295554785329413694604509037363125872855557432777227493981321429441265173128206328655708680765283884613436304170338955780751510163175236628485542460793053196948412069637807319916317082425956865796096231480354590760973029690799887240997768092621572807092266011871756867620973182630098942698872006788801595255856393161365292796819622596250050883403197980861774824797840540607808215719648361508812943824908692021516780177631861963443147777980093720340500449715710127462449355211107928253098250439243737728391096151331635932735272243535583773016736221336582677365182520552281507445314106211596893107

16384-bit RSA

Difficulty: I AM BECOME RSA, THE DESTROYER OF GPUs (probably cannot be cracked in my lifetime without a quantum computer)

Modulus=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

Modulus=1048117575583393609126303335323246650908998529810125140419371083575658662046668968178842491542842307902759041038929757449605737281293864427963015234700520715233814026239436655965033081174768840086159713624911988855898254819637588725597553334553847573432098810876828404913357819267039613555545476744501456222592520033678131122546514121367841508569829682773014369887724306761366392595205054046245138340280824829313344161869506256889060785304061029760690753106110313305440716343858831460524708256090223872316642386738636948890432998230788104023678177126849315158311355595949017719286807363934943489184546333548953447750734620620770173948836792118982014316197707204522184949890188330913105516183865975163646761266197483694014165330925752671381786586281799886176785138846952775371593462217645393761370581164860309662022410959877685881631907316573851782948702295603069827171793957876374399637130438036704052226963482045472881877933953342835735854592130183660747783327657861257238614614956073679589707875511442354077059437575126744393598100497819991222965344435319244913473691212057302965626183432671997700687410468056033828983703581315038205360830354592091947197733721238342889218050517080882181340671116809184248764408041785467386528511516738750224195402221145517882220454799578489415316046666715578131055355937629540866074299205482989605590215323764911549589129216207519585586995607959037554946660362839337064411166142199355089170219058315136093193966863399137985922316788992377058857609326302159843336838266956944261549247719234435970908318135309072169801537692076256440258998472548717897250073507435749581556164280360756049167806025877704905425039906451475472116588680439574035543115143049240602238418106892646213177571993006708536173077607471341297014794230852954423799105821418299801194123785335429016722534491407381042913427834730792536667493617422478383058703885297124571991106407952068257659195738225712955716668681184936752034804191008712842221736092691493456730053023727410168680546224379029551463107094155566029849959392872712218486365274775580616767807466748488606533684998179428323194460800697711955170430004295485428480149701014876097856255682264122358848900807732288348789942167538479753074548477858952370282700807516753900903410512832595375870237965869402685582509893492726043580725682503352285885594948406249206717377744254224931878004760632148444647595425348603342682867950734414885496673238511364862027830730154266775901179114944464387597363298433190113705720568172238578640443831984130094118865757651513971383660181175594189669998533995140862528088036986309735573831387529692992347697595551649185175240426027638157274351982506530295899066237758538351837096581793752578471507974673669010273384946880161048560945263700720960365902269525653272163361720338339690785896506285328946180838471491593683647232474894289322813097649228482348009706344953961073629432216123706116304248029306129649884265831752411203932152079534978321208282699032362890070452996032051563561539056516318261762156794288574310396171892150188563846617791743349763339080546965955102288704039573121307858591001655393827072391779324300386473843202061569927093412762462685592626021754809704068696016216513979175310139637908971722616135785673434937892247552036224749955688434727877717317870068169960239152452903158981965512496250964194495182293150942458055354481622579114512219003541404245516430312443396849285105651563147294377834012940621120953938727139132161288120244201369293209011121004990853997747332853900119279478792356924784134603449826861605714579918978536468748051713789102685582948358984395809557820653214847411734053558141988704617478727705523666693285986337823774331518260706882205237741404941923421787932944287373521899273310259147049773215536435534227806862581513178566980888047482614790186913299094307016493047788803023941016285359766403231219219962299666120758732965667397097862961286799368858096767850407621844805538751512372656685295229156899562007059521466328627222760283516173853543027726090836854259891217043064646566914322444207714234501209724471351210784600747597696118788568977116594986360164567426296935830856276955935819361067216299747187899081121886708257781973036388734664800920834450911897818308224731141972387982903188785281802660130756124899120200441444201688125763853128052628138869226114534469184078842460815950383536513625646665924938269621976575438543458442239045149597025538835592412645206728777826374834472286400433948671466418677555537711264833519538997793953115639617703703868946616985509352387344213623626400918250690538250629830847222445311599190707942015605601804995506472399798854916235368115779874369018628441131772334062623259494056678397692269380444538412489548662896151000507697899946293981184089580222802526046268735396753569214153903851680887287107720714455797293238579924484380144906879691393362201874879455958471959197566123833978610674898094308535977442146402658669152109683499289241114050572159187605899

32768-bit RSA

Difficulty: Sado-masochist (probably cannot be cracked in my lifetime without a quantum computer)

Modulus=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Correct Solutions

128-bit RSA

256-bit RSA

512-bit RSA

768-bit RSA

None yet....

1024-bit RSA

None yet....

2048-bit RSA

None yet....

4096-bit RSA

None yet...

8192-bit RSA

None yet...

16384-bit RSA

None yet...

32768-bit RSA

None yet...