国密SM2数字签名算法与ECDSA算法对比分析研究

60SM2ECDSA650228201012SM2SM3ECDSASM2ECDSA-SM2ECDLPECDSAECDSA-SM2SM2SM20201012(21)SM2SM11ECDSA198620RSAECCFpF2mF2mE/F2my2+xy=x3+ax2+babF2mECCECCECCElGamal(ECDSA)(DSA)ECDSAD(q,FR,S,a,b,P,n,h)d,m(r,s)(1)k[1,n-1](2)kP=(x1,y1)x1z(3)r=zmodnr=01(1968-)(1978-)(1978-)(1976-)(1976-)61(4)e=H(m)(5)s=k-1(e+dr)modns=01(6)(r,s)ECDSAD(q,FR,S,a,b,P,n,h)Q,m(r,s)(1)rs[1,n-1](2)e=H(m)(3)w=s-1modn(4)u1=ewmodnu2=rwmodn(5)X=u1P+u2Q(6)X=(“”)(7)Xxzv=zmodn(8)v=r()()2SM2SM2SM2(ECDSA-SM2)MMAA1:M=ZA||MA2:e=HV(M)eA3:k[1,n-1]A4:(x1,y1)=kGx1A5:r=(e+x1)modnr=0r+k=nA3A6:s=(1+dA)-1·(k-r·dA)modns=0A3A7:M(r,s)M(rs)BB1:r[1,n-1]B2:s[1,n-1]B3:M=ZA||MB4:e=HV(M)eB5:rst=(r+s)modnt=0B6:(x1′,y1′)=sG+tPA;B7:x1′R=(e+x1′)modnR=rECDSA-SM2:ECDSA-SM2(x1,y1)(x1′,y1′)(rs)=(r,s)(x1,y1)=(x1′,y1′)r=(e+x1)modns=(1+dA)-1·(k-r·dA)modn(x1′,y1′)=sG+tPA=sG+(r+s)·dAG=(1+dA)sG+r·dAG=(1+dA)(1+dA)1(krdA)G+rdAG=(krdA)G+rdAG=KG=(x1,y1)3ECDSASM2ECDSAECDSA-SM2()ECDSANISTSM2ECDSAECDSA-SM2(1)ECDSAMECDSA-SM2M=ZA||MZA=(ENTLA||IDA||a||b||xG||yG||xG||yG)(2)ECDLPECDSAECDSA-SM2kkdAECDSA-SM2ECDSA(3)ECDSAMD5SHA-1SHA-224SHA-256SHA-384SHA-512ECDSA-SM2SM3SM3256SM3SHA-256MD5SHA-1SHA-224(4)ECDSA-SM2ECDSAECDSA-SM2ECDSAECDSA4ECDSA-SM2ECDSA62ECDSA-SM2ECDSAECDSAECDSAECDSA-SM2SM2SM2SM2SM2[1].SM2.[2]V.S.Miller.UseofEllipticCurvesinCryptography.AdvancesinCryptology-CRYPTO'85,H.C.Williams,Ed.,LNCS218Springer-Verlag.1986.[3]DarrelHankerson,AlfredMenezes,scottVanstone.GuidetoEllipticCurveCryptography[M],.:.2005.[4].F2m[D]..2008.[5],.[J]..2008.[6],.F2m[J]..2008.[7],.NAF-2k[J]..2009.[8]Johnson,Menezes,Vanstoone.Theellipticcurvedigitalsignaturealgorithm(ECDSA).InternationalJournalofInformationSecutrity.2001.TheComparisionbetweenDigitalSignaturebasedonSM2andECDSASunRongyan,CaiChangshu,ZhouZhou,ZhaoYanjie,YangJinmine-governmentnetworkmanagementcentreofYunnanprovince,Yunnan,650228,ChinaAbstract:Itisthetrendtopublishthenationalcryptoalgorithm.SM2basedonECandSM3hashfunctionarepublishedinDecember2010,anditwillbeacceptedtheoverwhelmingtest,andownstheopportunitytoworldwidemarket.Inthepaper,ECDSAandECDSA-SM2isfirstlyintroduced,thenthecorrectnessofthemathmoduleisproved.Finally,inthetermsofmassageprocesstobesigned,ECDLP,Hashfunctionselectionandsecurityproblem,thecomparisionbetweenECDSAandECDSA-SM2isgiven.Keywords:ECDSA;TheNationalSecretAlgorithm;SM2;DigitalSignaturebasedonSM2[59]3[1],,.[M]..2008.[2].[M]..2008.[3].[J]..2008.[4].[J]..2006.[5].[J]..2010.ThenewoutlookofPublicSecurityIntelligenceconcepttransformationandvalueexplorationYuChenxiChinesePeople'sPublicSecurityUniversity,Beijing,100038,ChinaAbstract:Thedevelopmentofinformationscienceandinformationconstructionofpublicsecurityinformationtogetamoreextensivespaceforthedevelopmentofthepublicsecurityinformationwork,constantlyenrichthecontent,sotheneedforpublicsecurityintelligenceconcepttransformationandvalueexplorationre-sorted.Thepublicsecurityintelligenceconcepttransformationincludesinformation,informationnetwork,intelligenceandinformationchain,publicsecurityintelligencevalueexplorationincludingspeculativeinformationculturalinformation,informationmanagementandtheinformationscience.Keywords:Publicsecurityinformation;Philosophy;Value