Encryptionalgorithm
Inellipticcurveencryption(ECC),aspecialformofellipticcurveisused,thatis,anellipticcurvedefinedinafinitefield.Theequationisasfollows:
y²=x³+ax+b(modp)
Herepisaprimenumber,andaandbaretwonon-negativeintegerslessthanp.Theysatisfy:
4a³+27b²(modp)≠0wherex,y,a,b∈Fp,thepoint(x,y)thatsatisfiestheformula(2)andaninfinitepointOformanellipseCurveE.
TheellipticcurvediscretelogarithmproblemECDLPisdefinedasfollows:GivenaprimenumberpandanellipticcurveE,forQ=kP,findapositiveintegerklessthanpwhenPandQareknown.ItcanbeprovedthatitiseasiertocalculateQwithkandP,butitismoredifficulttocalculatekfromQandP.Sofar,thereisnoeffectivemethodtosolvethisproblem.Thisistheprincipleoftheellipticcurveencryptionalgorithm.
Comparison
ComparisonbetweenellipticcurvealgorithmandRSAalgorithm
EllipticcurvepublickeysystemisastrongcompetitortoreplaceRSA.ComparedwiththeRSAmethod,theellipticcurveencryptionmethodhasthefollowingadvantages:(1)Highersecurityperformance.Forexample,160-bitECChasthesamesecuritystrengthas1024-bitRSAandDSA.
(2)Theamountofcalculationissmallandtheprocessingspeedisfast.Intermsoftheprocessingspeedofprivatekeys(decryptionandsignature),ECCismuchfasterthanRSAandDSA.
(3)SmallstoragespaceoccupiedThekeysizeandsystemparametersofECCaremuchsmallerthanRSAandDSA,sothestoragespaceoccupiedismuchsmaller.
(4)ThelowbandwidthrequirementmakesECChaveawiderangeofapplicationprospects.
ThesecharacteristicsofECCmakeitsuretoreplaceRSAandbecomeageneralpublickeyencryptionalgorithm.Forexample,thecreatorsoftheSETprotocolhaveadopteditasthedefaultpublickeycryptographicalgorithminthenext-generationSETprotocol.