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1、Ronwaswrong,WhitisrightArjenK.Lenstra1,JamesP.Hughes2,MaximeAugier1,JoppeW.Bos1,ThorstenKleinjung1,andChristopheWachter11EPFLICLACAL,Station14,CH-1015Lausanne,Switzerland2Self,PaloAlto,CA,USAAbstract.Weperformedasanitycheckofpublickeyscollectedontheweb.Ourmaingoalwastotestthevalidityoftheassumptiont
2、hatdi erentrandomchoicesaremadeeachtimekeysaregenerated.Wefoundthatthevastmajorityofpublickeysworkasintended.Amoredisconcerting ndingisthattwooutofeveryonethousandRSAmodulithatwecollectedo ernosecurity.Ourconclusionisthatthevalidityoftheassumptionisquestionableandthatgeneratingkeysintherealworldfor
3、multiple-secrets"cryptosystemssuchasRSAissigni cantlyriskierthanforsingle-secret"onessuchasElGamalor(EC)DSAwhicharebasedonDie-Hellman.Keywords:Sanitycheck,RSA,99.8%security,ElGamal,DSA,ECDSA,(batch)factoring,discretelogarithm,Euclideanalgorithm,seedingrandomnumbergenerators,K9.1IntroductionVarious
4、studieshavebeenconductedtoassessthestateofthecurrentpublickeyinfrastruc-ture,withafocusonX.509certi cates(cf.[4]).KeygenerationstandardsforRSA(cf.[22])havebeenanalysedandfoundtobesatisfactoryin[18].In[12]and[26](andthereferencestherein)severalproblemshavebeenidenti edthataremostlyrelatedtothewaycert
5、i catesareused.Inthispaperwecomplementpreviousstudiesbyconcentratingoncomputationalandrandomnesspropertiesofactualpublickeys,issuesthatareusuallytakenforgranted.Comparedtothecollectionofcerti catesconsideredin[12],wheresharedRSAmoduliareotveryfrequent",wefoundamuchhigherfractionofduplicates.Morewo
6、rrisomeisthatamongthe4.7milliondistinct1024-bitRSAmodulithatwehadoriginallycollected,morethan12500haveasingleprimefactorincommon.Thatthishappensmaybecrypto-folklore,butitwasnewtous,anditdoesnotseemtobeadisappearingtrend:inourcurrentcol-lection3of7.1million1024-bitRSAmoduli,almost27000arevulnerablean
7、d2048-bitRSAmoduliarea ectedaswell.Whenexploited,itcoulda ecttheexpectationofsecuritythatthepublickeyinfrastructureisintendedtoachieve.Wesummarizeour ndings,referringtolatersectionsfordetails.Wecollec
