From 68482d5d8deb66754138c9ba67430d6d05148d83 Mon Sep 17 00:00:00 2001 From: bleichen Date: Mon, 4 Nov 2019 02:50:27 -0800 Subject: [PATCH] Moving test vectors for primality test into a JSON file. Adding more tests: - the previous test did not include any primes. Hence arithmetic errors in a primality test would likely remain undetected. - some primes have been generated so that the multiplier for a Montgomery reduction is an edge case (e.g. high or low Hamming weight). - adding negatives of primes. Different libraries disagree, whether such integers are prime or not. The corresponding test vectors have a flag and result "acceptable". The following libraries have been tested: java.math.BigInteger: primality testing is not part of JCA and hence is provider independent. sympy: Old versions of sympy used a weak set of bases and was deterministic. This is no longer the case. NOKEYCHECK=True PiperOrigin-RevId: 278337837 GitOrigin-RevId: 02debe45343e8da38b21a6e7a56a4a2b1c050bd8 --- .../wycheproof/testcases/BigIntegerTest.java | 471 +--- schemas/primality_test_schema.json | 91 + testvectors/primality_test.json | 2261 +++++++++++++++++ 3 files changed, 2398 insertions(+), 425 deletions(-) create mode 100644 schemas/primality_test_schema.json create mode 100644 testvectors/primality_test.json diff --git a/java/com/google/security/wycheproof/testcases/BigIntegerTest.java b/java/com/google/security/wycheproof/testcases/BigIntegerTest.java index 699a281..9d76424 100644 --- a/java/com/google/security/wycheproof/testcases/BigIntegerTest.java +++ b/java/com/google/security/wycheproof/testcases/BigIntegerTest.java @@ -13,8 +13,10 @@ */ package com.google.security.wycheproof; -import static org.junit.Assert.fail; +import static org.junit.Assert.assertEquals; +import com.google.gson.JsonElement; +import com.google.gson.JsonObject; import java.math.BigInteger; import org.junit.Test; import org.junit.runner.RunWith; @@ -27,433 +29,52 @@ import org.junit.runners.JUnit4; */ @RunWith(JUnit4.class) public class BigIntegerTest { - public static final BigInteger[] NONPRIMES = - new BigInteger[] { - // small non prime integers - new BigInteger("-1"), - new BigInteger("0"), - new BigInteger("1"), - // If p is prime then the Mersenne number 2^p-1 is pseudoprime for base 2. - new BigInteger("147573952589676412927"), - new BigInteger("2361183241434822606847"), - // pseudoprime squares derived from Wiefrich primes - new BigInteger("1194649"), - new BigInteger("12327121"), - // G. Jaeschke: "On strong pseudoprimes to several bases", Math o. comp. v.61, p 915-926 - new BigInteger("2152302898747"), - new BigInteger("3474749660383"), - new BigInteger("341550071728321"), - new BigInteger("41234316135705689041"), - new BigInteger("1553360566073143205541002401"), - new BigInteger("56897193526942024370326972321"), - // A list of strong pseudoprimes to 12 or more bases from - // https://arxiv.org/pdf/1509.00864v1.pdf - new BigInteger("360681321802296925566181"), - new BigInteger("164280218643672633986221"), - new BigInteger("318665857834031151167461"), - new BigInteger("7395010240794120709381"), - new BigInteger("2995741773170734841812261"), - new BigInteger("667636712015520329618581"), - new BigInteger("3317044064679887385961981"), - new BigInteger("3110269097300703345712981"), - new BigInteger("552727880697763694556181"), - new BigInteger("3404730287403079539471001"), - // Richarg G.E. Pinch, "Some primality testing algorithms" - // Some composites that passed Maple V's primality test. - new BigInteger("10710604680091"), - new BigInteger("4498414682539051"), - new BigInteger("6830509209595831"), - // Composites that passed the primality test of Mathematica 2.0 - new BigInteger("38200901201"), - new BigInteger("6646915915638769"), - // Composites that passed Axioms primality tests - new BigInteger("168790877523676911809192454171451"), - new BigInteger("68528663395046912244223605902738356719751082784386681071"), - // A composite q that was acceptied by Gnu Crypto. p = 2*q + 1 is prime and could have been - // used to break the SRP with that library. - // http://www.iacr.org/archive/pkc2005/33860010/33860010.pdf - new BigInteger( - "2338274894573145273314679073561004052325493799717332496500873981" - + "9154269566267911565762670147721173495706686483597956042863296855" - + "8985491020031718032728786934761830612407539788738389834804112831" - + "0484933712924414264511799715503596253054638290097305254378560604" - + "3457282155730383806702845548017315217454390994052035233808454053" - + "2209678251"), - // I. Damgard, P. Landrock, and C. Pomerance. "Average case error estimates for the strong - // probable prime test." Math. of Comp. v.61 (203), pp. 177-194. - // - // This paper gives bounds for the number of bases necessary to distinguish composites from - // primes assuming that the tested integer has been chosen at random. - // - // The result is sometimes misinterpreted and used for pseudo primality tests. There the - // assumption of the paper may not be valid, especially if the integer to test has been - // chosen by a potentially malicious party. The following pseudoprimes are 1024 to 1280 bits - // long, pass the MR test for about 1/4 of all bases. They may expose pseudo primality tests - // that misinterpret the paper above. - new BigInteger( - "1730626114143993906582329178627391355248485443639984363030847275" - + "1308542667309368405802823431259718338553667079600118481458180717" - + "8685660312964257923307841168376622412972295432300191118906455596" - + "0636099366430317210651098229261736987868487865820945209431391380" - + "09108180649097618810676094425505547347369635059151651"), - new BigInteger( - "1360998858923994584770803056737393786894832450662215840614559215" - + "7078401469699701619693552331616875038702785662417391573713804038" - + "4334162971247398689854706029275431407028615888533012918610480990" - + "0223861487963796923928503972465761214360888693859314270808955367" - + "40913457414488449790876563256100025424908640036566991"), - new BigInteger( - "3166883756083864374213797577792765404121225450334428749136082272" - + "6277047033553982548405648549530365358167591776542577633638251648" - + "4708794514891794859629545011811469601460428778510574606216627610" - + "9305946545256861710197652701722202600572822026157108510694466031" - + "21873496655525294839125742517721479483987924741221051"), - new BigInteger( - "1867856940026786421328012256561867196437042470176831233408635728" - + "4012048133274069029642553787088950310027377534718962029124718226" - + "6051117402306961193255486702389001315623336948708913938663766675" - + "8226042898352219886123870222547007370332879734207273564946511954" - + "31833673259400609717994958747847898007198993092012403"), - new BigInteger( - "1796390661263009677994016718416108866609292079197277387452323006" - + "0275054640418696223480642324316099214952402651731083265854610369" - + "8224730515713772933976457906751697355710699183284927973990745341" - + "2311585789546147810071014069499060003398982340466066800822746698" - + "64309065127941774208780103317444828873858305613764441"), - new BigInteger( - "1971945240855615239359385779848543278459852521629467703761094672" - + "8118959477624582999696057042356627216821194209090396598966531204" - + "6718418693934025583647341695134065566474352554207810854787929284" - + "0150420997586371167811999782663434687606795518115913678131471778" - + "75984898571603525952885934025286780854976730638309011"), - new BigInteger( - "3150008132483461686934076250569912489352161839369648385736587811" - + "5997183822673267428826594197361084397177321281419482762875475084" - + "9549588421903702315436565970387119142993552663715551586581960248" - + "0385985798377103010348982470471826679560834315129605222126122792" - + "66245495948831504762364224662571600318327270033084451"), - new BigInteger( - "1708946102366142320715649564941267111465045510329061281476212740" - + "3257341007679575909346478379354045686824680545379443269343860874" - + "7656833753674500442989626468892341565281803639470271121897646438" - + "0297951614184327979794615696929197488480659590917557764806142256" - + "64177795195470929762281195447906351417368682849843661"), - new BigInteger( - "3440003701993474165051634746793659123122285886429390887874425798" - + "0539628797086399700050400512078053335053587477375429177907276765" - + "7299212000552180980839328379536622696237474649639004862671352175" - + "9289352494669383679530748723706821659664185661303953233767365167" - + "67872755699135674189217223109386132423577475778316621"), - new BigInteger( - "1384489093437226718803143517408309162781203263729355872818628349" - + "4469526441585078582037579393159945688413133085030944516305313234" - + "8118439725196722488178936032989162127096990828542718648126854836" - + "3215014994571003679167792328172868632219526006267874696849394364" - + "51238457213158274397103569820623680840515654121967511"), - new BigInteger( - "3164393868232068713466361644489248900506521258778648162638744470" - + "1911965299134147189251276735683301303659631352068168884603764242" - + "2058303711027020977731971469313828021385806157441077657252831199" - + "5151267291454080409585783805054468065763411635886980943812129069" - + "12979884469786023782783106107762632814558326808787771"), - new BigInteger( - "3429610981008641614862240834440649965306153336087134811684334214" - + "2781784784880823158748073620472850986640780368357758806487624898" - + "6627917970721407574366482474956464008840562218539437088991213443" - + "6865812444686702307687466249240837612849694711488568460832793683" - + "75653516879275492605255161494494045951397742913942521"), - new BigInteger( - "1452625971469501984029833170297844688666257429198467445330023676" - + "9656278238192507513913993052034672663086092503841752084104847874" - + "8173408690100803386628315407260460724324957380860416531476612359" - + "3906755149555321240901275978836270398698785709389076413509994529" - + "42901485886289548101644664410043634050840333618736241"), - new BigInteger( - "1038759703926769528247935492263828939187707228977771863002037516" - + "6447956205097712397228992931571755867770661683705025240420111189" - + "2868394359927108413461144788316226799790655169187714036057483534" - + "1379449940364129845302840193911613461736295410032863048528135257" - + "04436628490382188950208123780350213139500089456366841"), - new BigInteger( - "2092626848347087607813788288260128832160456227715887480495928337" - + "8143090879636401536763351823849725734769339835456348322174433133" - + "2528919261931329808331753456631473557050588173643619875493912344" - + "2621229276297788264420214803881217267094948976676445054939538411" - + "22580436721054077839958796624587867034849970594728503"), - new BigInteger( - "2599619740922490310102276030628575944314398371981276430688469612" - + "6677200542107317525516057185980658562393307608335402672015071146" - + "4375869967746325500371685760342898099183114419807958654613613854" - + "3992594086574371567802232690430810966098771990068625112489903295" - + "89067604336669355585402887916288037943709029191674911"), - new BigInteger( - "1484944124031033226177904474729672080414277081288126930486713099" - + "2951571588154552341076434413035940622712601649739964234772603407" - + "4857469854866669198948655053082186111410005989963123962723450119" - + "6642285521712848015932226566546835102733706632115364632204156914" - + "64644614536183219912321808854090915103775109695786903"), - new BigInteger( - "1989518237873611249304118136102198299910749751063921465712157675" - + "0160983808717982713586255483659294934004326549705203383719900307" - + "1263871954417468537542759843054899935687365194283002403584007149" - + "4878371117610681917576307737065411378178051858121032451282900716" - + "73542006653340382017735899123084476453857081318545991"), - new BigInteger( - "1001516549472529960430483041632117547467775871427023066924341669" - + "8403875533009883195522874469432253701609651260735835128759135299" - + "5655554893223580483857764100115214746205606713424344869011314868" - + "3107942731565140938612794494135227597999675233998980692687287393" - + "67463341929936509718884001903262839905032784262429503"), - new BigInteger( - "9523120659259647017050060990584944204556454726505878376759616021" - + "0162649328723702952067039028722189901551617226203049071432575686" - + "9121080710327716161595367835528315683397536615084723082551568364" - + "5739952184995573677453019127607472426963971562388390300785220049" - + "6655144350028488056721467755918814393298596327869403"), - new BigInteger( - "1132692896131390459872218381686704761578367301590229517271338668" - + "7180351798454882497438382954425835621126393661367213143371283272" - + "0317909560575328664237540188143415517690966913820407105917871661" - + "6365405171372246705778112163771743546945868623307467307997875571" - + "40869529264839386342569691698111927128704157615097153"), - new BigInteger( - "1468478445343635885853097900396288249751127795088868633754583040" - + "9902362001013473990040942210829761549194134324343879441927807081" - + "4832779046634885071582835688508933384516245429006116427382617949" - + "0797131644177507421862332328509904031871287120929769029086074503" - + "38866991708762791875618755240139448209180903665732503"), - new BigInteger( - "3584128102219288461651881096063603237206550481422480899564693370" - + "6989198816192527918220789937223699304075118319904981106473056074" - + "6022073963857677172123650694187762839204698560127083582857191356" - + "7619601857134928125369766912580367127840531257344393938629885107" - + "16841734490107828355376447675347185589367615046902903"), - new BigInteger( - "1364132540730201251194341844655148002850736352953819312409033451" - + "0581806956034928961765696532883678319811153534823893271895441595" - + "1560405730847235775035340408484490592989244418679611824558459897" - + "3970103405588145228028549820125837425523682281669049087481368021" - + "33702260393866732616878693744975284760231993354960641"), - new BigInteger( - "1201213090774136737579735845388953400530787071160074364126728551" - + "5147303301856817241515212573079940841340044269783294804816431383" - + "8284868252529547559069691488487393115675459439240223181642866729" - + "3429931964973711015111163544551414299071832349845971998375812575" - + "43510797169400923829329952407436122292964382266031253"), - new BigInteger( - "2749611624987217008377958765718501619519235049877079452181305657" - + "4724564026272242180811435338643866876903591496649439319889570905" - + "0358277453956447636555409300854018401232502616530331143658908539" - + "1682266093367017969369633046927346949982338985082398103545735993" - + "26268702707614772584950389057955691219494031838859791"), - new BigInteger( - "2472982114742145360236684931488791833991329788857529670921519821" - + "2275589064185672494327017904494686810840150314271250166999768972" - + "5488277075239138647902134463451436706674384070937644414378922408" - + "3974240802538174272534726968041801996779685771019246098603577098" - + "48139330190576017582503777009836399771498662905893541"), - new BigInteger( - "1865347188865809981733701115448160790425846704558108501171803277" - + "4616363375301457541345495992357828826645510919897778446537615423" - + "0882378024111971510810465276396395657415178370245114122816237302" - + "3283933030997110906700611097744954222271394790237582780817507949" - + "50528224900273599212004329531461848157373189908642761"), - new BigInteger( - "2852220663043188088074403487569592065121097371561337653207919689" - + "5806125544163953214258963319594971029379263400735515369955250013" - + "4028759770788754166339078427645792536001991144766729628117371050" - + "3065276544543379585207323093069812639902415298676791716773723086" - + "01834079961869281917489638496882679996929360595283091"), - new BigInteger( - "1812266945737014247808099956042081894034544124660090203840602123" - + "8933795306490611245152382127750687774085253618514158494675518742" - + "0904863344271961110077635791220319963938065397633608138595169161" - + "4365952732191284608496816156732317034130054052863296504407952482" - + "70402413500178325587999299003705988651612697260381081"), - new BigInteger( - "3461478020849089881636057301867459968070516872602987322072552610" - + "6122696717667098851127207650635960731479969936151065921604956606" - + "9966154794154897232197433347544538725616640069913605417680979153" - + "7941663920296351630552463916932109774095427601318332413237900565" - + "33380330505490643091283956267491266793755039018149751"), - new BigInteger( - "2919979800970068658905539811038971051531482233418344434620488229" - + "7069955478191515351496193695554391114007400265274653645749899336" - + "1682279972987736655018586409178146143048864596533190807270958265" - + "8386345811616055097769189859096393752934393213978617302764485594" - + "27971296399182413971389773786687947710326691137231821"), - new BigInteger( - "4145154657949019520090421067892641813006171355169512965016842717" - + "9656056083456770700476740539321891137934371895885040718614132068" - + "7659642286859932894319946334724710913927915623235424403674960713" - + "3015105499354740364264523832014989327244648027567866644179973588" - + "6851400410006028767095438327490143741004842299878541824964849824" - + "9350463409537126165182086675091928210325509674933575383432172361" - + "1"), - new BigInteger( - "7263570684005586918409651676342477962666063384721447164820162267" - + "3637900031379949446961412145104626127789865770334124795558653625" - + "0265693033953361779942717984970881106667840356057452866357943677" - + "0299187611159071848712668510417692823114550446719084221850233353" - + "5448622581084864206413295247972240845959033925761759264503271102" - + "8711358281311325650083539770515252900036932499310037595977096965" - + "3"), - new BigInteger( - "3266663369261434628530741133725226939380890029427130078147736465" - + "2996576096098663002890375510448427552966457154556853852292297530" - + "3748877081504218804805934729044054195328441392083622877088337833" - + "3839361634881282676119589334709165541036798092721269225600972531" - + "5718770210834831734568895865334347621480511738343920340920819445" - + "8602267925535790135884214787193459118783550610652631217006506945" - + "3"), - new BigInteger( - "2714275054823322283846947242758076394288969833351667671546539844" - + "8651643040817257191932781992745878593029648459331742640462067216" - + "1697889841582474665251728415469605782526629276939159099241968231" - + "4563946417035619325266947257091436696492494177352417584114484475" - + "6610785746958696759938071286674788996869751533043564234638049802" - + "5949514917474176492949501669603402532532836245346872590582496734" - + "1"), - new BigInteger( - "9266983839147571189339684823228253420616685503762301572754412275" - + "1127843293258964600702452397526178329259267484695086911638972315" - + "4961995491900251718105624646921122900256992784437600453557273835" - + "3861591882136393291951512396743267427648075154617935904316277726" - + "4493865072538820667287351636308197262473273185496543102226470825" - + "6662877019047683511136380480413028925833068997034750517865449915" - + "3"), - new BigInteger( - "6943685859962113005380005918916483733270787990846044283782171250" - + "1096851232736318325302320935157976786131666696364333532268184395" - + "8665950723719162662956110077840013184726020313880442980629145593" - + "2383952066228056762115442513166346145910224582828425403465971492" - + "7260150227126350939033438077449255619231502836209591891037493966" - + "9366963730251619187615962926310287121840421140621429191345783703" - + "1"), - new BigInteger( - "8697498751458522624235585703214358189002281420472600166267178848" - + "9809876665869248037334395420081653868096056103537493131465377226" - + "0261527380426559408040456405219848362023445401145511114936506394" - + "6240472545398288332411818055040869427951279027405975059749360297" - + "5868667379863439430711990295232153128900808256212596912819669440" - + "8461633147852596585348243485566178333170181585431955731179108942" - + "1"), - new BigInteger( - "4252141813347264797276096871298065242070358505647997888003056375" - + "0053145248543520793105289129514510723624029989029530989695904117" - + "1040883775014117200916554841688641022136017868157290925811239787" - + "3664014299809018676076741787758620956387796785085878200748397774" - + "1000982778291877557074489243525397961477916369196578483491169386" - + "2005017885694815977695115290403992818456642027646266206320076800" - + "3"), - new BigInteger( - "3356647398302910967427184201762737607743709740247537918189248572" - + "1755339542838026890625250818518527348898974773340867800840791470" - + "3182072707032492007084043715576322632015800128489921814932124611" - + "2300036417841991332124497348096579076242448857352000771247540736" - + "1254949324799638105796121388483225300620211599611028678202393567" - + "8095635541751658983704832859578366318530922805928053806070359946" - + "1"), - new BigInteger( - "3687125575229624930459923973437509789116885700012081850445193578" - + "4486423768425089350932846437401841871613673810991112360643320652" - + "0225782089986669258803208183278659152741552450801685341843048568" - + "1125008729650000322084879372381541270180139663134377177885154388" - + "9558281508372272794193460069397070875763691455289959733530070186" - + "0360525342531389354962332229432027179470095997955180502375530175" - + "3"), - new BigInteger( - "6088560764944279853795552546797623009536823218028533977947580608" - + "2015023514992395624319060987001625566234648211868300524182306472" - + "7026872385780533326083682960047644674758988927136149502626557718" - + "2561494515318563339483672950711193945073071458843901227339418284" - + "3084182493461642555372639047162641075337152622892862251731700231" - + "6672547426448574167370804559242233207791080547486632014153528258" - + "1"), - new BigInteger( - "6081766267938901970682791123502557184373300073506187731779846380" - + "4083193288475152882563422230130613717216469536080649276981712202" - + "8895707724700107471391574673087393411637415445150131834443587280" - + "4243131225731630921851260690656608624225797294197741881140769183" - + "0474230365914155543155728342161658185646742117306992051014301383" - + "8040790841165308968256142923362988225719340573836171022480960175" - + "3"), - new BigInteger( - "5000879164859908887599881582814678322611278734193303790540199067" - + "6946804876309491380295619810590406766227048051997595053442615914" - + "2677702465219525342790323338314172797422380779526016709102650201" - + "6058553529785304239405043134061167377896985489252957729348463979" - + "6066933483020351454994081895283883114206539208013308687170796286" - + "8268752695525736731805658439398227370325903928664994918343915975" - + "3"), - new BigInteger( - "5033660524073962747735388920230339629907033897027296197974576730" - + "5654422857706257645566447425553553516325935964234373316093019314" - + "9125347663842235853602126989737378697014753612431648011618832921" - + "3881347704723060451053853932258315572365588301231482715348124261" - + "9244292433503547002496906691530720882968955274299548904791181715" - + "4190217453383503386985567684902027707247767653326442247588135031" - + "1"), - new BigInteger( - "7656692474335471169217545128846872228367812415627865759181393395" - + "8241618825828371173259648247363305034462523584509943049089351382" - + "5433879053475325827330864407124355159557574919864955631956757119" - + "9044097578241324151657090338112756973390540016908863938814598847" - + "5396824620980380695503598397306050849284639259137342875066075738" - + "4060141031090753207116787791385102134328808638802350088507846845" - + "1"), - new BigInteger( - "6916552449605114038869281931877716049700938960849845402874660241" - + "3416574115770967736955518993475194932835724065347138687353620520" - + "8331524408574865319265572656228099650675609929009824224767253657" - + "5459382651810818256784829505942965567114371502731619372511210627" - + "1610362520274480185346478545007812850057950851029848830710521787" - + "8356932374617076535457900683468313279449103472700012568700849319" - + "1"), - // F. Arnault, "Rabin-Miller primality test: composite numbers which pass it", Math. comp. - // v.64, n.209, p 355-361. - // - // A strong pseudoprime for the first 46 primes - new BigInteger( - "8038374574536394912570796143419421081388376882875581458374889175" - + "2229742737653336521865023361639600454579150420236032087665699667" - + "6098728404396540823292873879185086916685732826776177102938969773" - + "9470167082304286871099974399765441448453411558724506334092790222" - + "7529622941498423068816854043264575340183297861112989606448452161" - + "91652872597534901"), - // Richard G.E. Pinch, Absolute quadratic pseudorprimes - // http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.210.6783&rep=rep1&type=pdf - // Lucas-Charmichael-(-) numbers - new BigInteger("28295303263921"), - new BigInteger("443372888629441"), - new BigInteger("582920080863121"), - new BigInteger("894221105778001"), - new BigInteger("2013745337604001"), - // Lucas-Charmichael-(+) numbers - new BigInteger("6479"), - new BigInteger("84419"), - new BigInteger("1930499"), - new BigInteger("7110179"), - new BigInteger("15857855"), - new BigInteger("63278892599"), - new BigInteger("79397009999"), - }; - /** - * Tests BigInteger.isProbablePrime with a list of composite integers. The integers have been - * chosen to check for weak pseudoprimality tests. E.g., they are counterexamples to weak - * implementations. The implementation in jdk uses a combination of a Miller-Rabin test and a - * Lucas test. This is similar to the Baillie-PSW test - * https://en.wikipedia.org/wiki/Baillie%E2%80%93PSW_primality_test - */ + /** Convenience method to get a BigInteger from a JsonObject */ + protected static BigInteger getBigInteger(JsonObject object, String name) throws Exception { + return JsonUtil.asBigInteger(object.get(name)); + } + + /** Convenience method to get a byte array from a JsonObject */ + protected static byte[] getBytes(JsonObject object, String name) throws Exception { + return JsonUtil.asByteArray(object.get(name)); + } + @Test - public void testIsProbablePrime() throws Exception { - // The probability that a non-prime passes should be at most 1-2^{-certainty}. - int certainty = 80; - for (BigInteger n : NONPRIMES) { - if (n.isProbablePrime(certainty)) { - fail("Composite number " + n.toString() + " passed as probable prime test"); + public void testIsProbablePrimeVectors() throws Exception { + String filename = "primality_test.json"; + JsonObject test = JsonUtil.getTestVectors(filename); + int errors = 0; + int passedTests = 0; + for (JsonElement g : test.getAsJsonArray("testGroups")) { + JsonObject group = g.getAsJsonObject(); + for (JsonElement t : group.getAsJsonArray("tests")) { + JsonObject testcase = t.getAsJsonObject(); + int tcid = testcase.get("tcId").getAsInt(); + String tc = "tcId: " + tcid + " " + testcase.get("comment").getAsString(); + BigInteger value = getBigInteger(testcase, "value"); + // result is "valid" if the tested integer is prime, "invalid" if it is + // composite or -1, 0, 1 and it is "acceptable" if it is the negative of + // prime. BigInteger.isProbablyPrime() accepts the later as prime (as do + // a number of other primality tests). Such a behaviour may be a pitfall + // for cryptographic protocols. However, it can not be flagged as error. + String result = testcase.get("result").getAsString(); + + // The probability that a non-prime passes should be at most 1-2^{-certainty}. + int certainty = 80; + boolean isProbablePrime = value.isProbablePrime(certainty); + if (result.equals("invalid") && isProbablePrime) { + System.out.println("Composite number passed as prime:" + tc); + errors++; + } else if (result.equals("valid") && !isProbablePrime) { + System.out.println("Prime failed primality test:" + tc); + errors++; + } else { + passedTests++; + } } } + assertEquals(0, errors); + System.out.println("Passed primality tests:" + passedTests); } } diff --git a/schemas/primality_test_schema.json b/schemas/primality_test_schema.json new file mode 100644 index 0000000..05dce5f --- /dev/null +++ b/schemas/primality_test_schema.json @@ -0,0 +1,91 @@ +{ + "type": "object", + "definitions": { + "PrimalityTestGroup": { + "type": "object", + "properties": { + "type": { + "enum": [ + "PrimalityTest" + ] + }, + "tests": { + "type": "array", + "items": { + "$ref": "#/definitions/PrimalityTestVector" + } + } + } + }, + "PrimalityTestVector": { + "type": "object", + "properties": { + "tcId": { + "type": "integer", + "description": "Identifier of the test case" + }, + "comment": { + "type": "string", + "description": "A brief description of the test case" + }, + "value": { + "type": "string", + "format": "BigInt", + "description": "the integer to test" + }, + "result": { + "type": "string", + "description": "Test result", + "enum": [ + "valid", + "invalid", + "acceptable" + ] + }, + "flags": { + "type": "array", + "items": { + "type": "string" + }, + "description": "A list of flags" + } + } + } + }, + "properties": { + "algorithm": { + "type": "string", + "description": "the primitive tested in the test file" + }, + "generatorVersion": { + "type": "string", + "description": "the version of the test vectors." + }, + "header": { + "type": "array", + "items": { + "type": "string" + }, + "description": "additional documentation" + }, + "notes": { + "type": "object", + "description": "a description of the labels used in the test vectors" + }, + "numberOfTests": { + "type": "integer", + "description": "the number of test vectors in this test" + }, + "schema": { + "enum": [ + "primality_test_schema.json" + ] + }, + "testGroups": { + "type": "array", + "items": { + "$ref": "#/definitions/PrimalityTestGroup" + } + } + } +} diff --git a/testvectors/primality_test.json b/testvectors/primality_test.json new file mode 100644 index 0000000..4cdb5f2 --- /dev/null +++ b/testvectors/primality_test.json @@ -0,0 +1,2261 @@ +{ + "algorithm" : "PrimalityTest", + "generatorVersion" : "0.8rc17", + "numberOfTests" : 280, + "header" : [ + "Test vector of type PrimalityTest are intended for testing primality tests." + ], + "notes" : { + "CarmichaelNumber" : "Carmichael numbers are composite numbers that are pseudoprime to all bases. Carmichael numbers (especially those with a small nubmer of factors) have a high probability of passing a Miller-Rabin test.", + "NegativeOfPrime" : "Some libraries accept the negative of a prime number as prime. For crypto libraries this just adds another potential pitfall.", + "WorstCaseMillerRabin" : "This is a composite number that passes the Miller-Rabin for about 1/4 of all bases. Such composite number pass primality tests, because the author of the primality test misinterprets the paper \"Average case error estimates for the strong probable prime test.\" Math. of Comp. v.61 (203), pp. 177-194 by I. Damgard, P. Landrock, and C. Pomerance. This paper gives bounds for the number of bases necessary to distinguish composites from primes assuming that the tested integer has been chosen at random." + }, + "schema" : "primality_test_schema.json", + "testGroups" : [ + { + "type" : "PrimalityTest", + "tests" : [ + { + "tcId" : 1, + "comment" : "small non prime integer", + "value" : "ff", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 2, + "comment" : "small non prime integer", + "value" : "00", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 3, + "comment" : "small non prime integer", + "value" : "01", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 4, + "comment" : "Non-prime Mersenne number that is pseudoprime to base 2", + "value" : "07ffffffffffffffff", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 5, + "comment" : "Non-prime Mersenne number that is pseudoprime to base 2", + "value" : "7fffffffffffffffff", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 6, + "comment" : "Non-prime Fermat number", + "value" : "0100000000000000000000000000000001", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 7, + "comment" : "Non-prime Fermat number", + "value" : "010000000000000000000000000000000000000000000000000000000000000001", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 8, + "comment" : "Non-prime Fermat number", + "value" : "0100000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 9, + "comment" : "pseudoprime square derived from Wiefrich prime", + "value" : "123a99", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 10, + "comment" : "pseudoprime square derived from Wiefrich prime", + "value" : "00bc18d1", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 11, + "comment" : "square", + "value" : "04", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 12, + "comment" : "square", + "value" : "09", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 13, + "comment" : "square", + "value" : "010201", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 14, + "comment" : "square", + "value" : "0f2ad9", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 15, + "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926", + "value" : "01f51f3fee3b", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 16, + "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926", + "value" : "032907381cdf", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 17, + "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926", + "value" : "0136a352b2c8c1", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 18, + "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926", + "value" : "023c3db80e80e53bd1", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 19, + "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926", + "value" : "0504e8e504fd585e79193ca1", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 20, + "comment" : "G. Jaeschke: \"On strong pseudoprimes to several bases\", Math o. comp. v.61, p 915-926", + "value" : "00b7d84161830e3f6f2231a7a1", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 21, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "4c6092d9a7a5462b34e5", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 22, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "22c9a603ee84bb9c4cad", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 23, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "437ae92817f9fc85b7e5", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 24, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "0190e262098f0d746505", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 25, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "027a5f7ca7b29ee74d5525", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 26, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "008d60a89f3f36cb1fd495", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 27, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "02be6951adc5b22410a5fd", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 28, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "0292a0068ebb0ed3251f55", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 29, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "750b703e68cb957ab415", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 30, + "comment" : "A strong pseudoprimes to 12 or more bases from https://arxiv.org/pdf/1509.00864v1.pdf", + "value" : "02d0facc78aeeb89f5b299", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 31, + "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Maple", + "value" : "09bdc1c98b9b", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 32, + "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Maple", + "value" : "0ffb48c934842b", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 33, + "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Maple", + "value" : "18444fdb12afb7", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 34, + "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Mathematica 2.0", + "value" : "08e4f37e51", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 35, + "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Mathematica 2.0", + "value" : "179d55b600e7f1", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 36, + "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Axioms primality test", + "value" : "085270bd76a142abc3037d1aab3b", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 37, + "comment" : "Richard G.E. Pinch, \"Some primality testing algorithms\" a counter example for Axioms primality test", + "value" : "02cb78fe3f36c4f5f05dbe92b82798d5fc18f2bfaaa388ef", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 38, + "comment" : "A composite q that was acceptied by Gnu Crypto. http://www.iacr.org/archive/pkc2005/33860010/33860010.pdf", + "value" : "4682f52f0b54308d315b2fbec25065506c77be95912b137bc6eecffad8a299b631c55ce068702b1b3e4ce50958994c289b148fb298a8c603a0959cb0ba5ad4bcba278cf4c87e0ff85a62a25c40849662c53d0f81cf9e4431d8c391586629260e558db473997db20108278b1ae374089140d93bc2c5a808ad3aaf212f60bfc93cc0c788149dcd82f7ab", + "result" : "invalid", + "flags" : [] + }, + { + "tcId" : 39, + "comment" : "Worst case for Miller-Rabin test", + "value" : 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