Алгоритъм за криптиране
Inellipticcurveencryption(ECC),aspecialformofellipticcurveisused,thatis,anellipticcurvedefinedinafinitefield.Theequationisasfollows:
y²=x³+ax+b(modp)
Тук е описанопримерно число,иаидве неотрицателни цели числа,по-малки отp.Те удовлетворяват:
4a³+27b²(modp)≠0къдетоx,y,a,b∈Fp,точката(x,y),която удовлетворява формулата(2)и безкрайна точкаOformanellipseCurveE.
TheellipticcurvediscretelogarithmproblemECDLPisdefinedasfollows:GivenaprimenumberpandanellipticcurveE,forQ=kP,findapositiveintegerklessthanpwhenPandQareknown.ItcanbeprovedthatitiseasiertocalculateQwithkandP,butitismoredifficulttocalculatekfromQandP.Sofar,thereisnoeffectivemethodtosolvethisproblem.Thisistheprincipleoftheellipticcurveencryptionalgorithm.
Сравнение
СравнениеbetweenellipticcurvealgorithmandRSAalgorithm
EllipticcurvepublickeysystemisastrongcompetitortoreplaceRSA.ComparedwiththeRSAmethod,theellipticcurveencryptionmethodhasthefollowingadvantages:(1)Highersecurityperformance.Forexample,160-bitECChasthesamesecuritystrengthas1024-bitRSAandDSA.
(2)Theamountofcalculationissmallandtheprocessingspeedisfast.Intermsoftheprocessingspeedofprivatekeys(decryptionandsignature),ECCismuchfasterthanRSAandDSA.
(3)SmallstoragespaceoccupiedThekeysizeandsystemparametersofECCaremuchsmallerthanRSAandDSA,sothestoragespaceoccupiedismuchsmaller.
(4)ThelowbandwidthrequirementmakesECChaveawiderangeofapplicationprospects.
ThesecharacteristicsofECCmakeitsuretoreplaceRSAandbecomeageneralpublickeyencryptionalgorithm.Forexample,thecreatorsoftheSETprotocolhaveadopteditasthedefaultpublickeycryptographicalgorithminthenext-generationSETprotocol.