Šifrovací goritmus
Inellipticcurveencryption(ECC),aspecialformofellipticcurveisused,thatis,anellipticcurvedefinedinafinitefield.Theequationisasfollows:
y²=x³+ax+b(modp)
Zde je prvočíslo a a dvě nezáporná celá čísla menší než p. Vyhovují:
4a³+27b²(modp)≠0 kdex,y,a,b∈Fp,bod(x,y),který vyhovuje vzorci(2)anekonečnýmbodůmoformanellipsekřivkaE.
TheellipticcurvediscretelogarithmproblemECDLPisdefinedasfollows:GivenaprimenumberpandanellipticcurveE,forQ=kP,findapositiveintegerklessthanpwhenPandQareknown.ItcanbeprovedthatitiseasiertocalculateQwithkandP,butitismoredifficulttocalculatekfromQandP.Sofar,thereisnoeffectivemethodtosolvethisproblem.Thisistheprincipleoftheellipticcurveencryptionalgorithm.
Srovnání
SrovnáníbetweenellipticcurvealgorithmandRSAalgorithm
EllipticcurvepublickeysystemisastrongcompetitortoreplaceRSA.ComparedwiththeRSAmethod,theellipticcurveencryptionmethodhasthefollowingadvantages:(1)Highersecurityperformance.Forexample,160-bitECChasthesamesecuritystrengthas1024-bitRSAandDSA.
(2)Theamountofcalculationissmallandtheprocessingspeedisfast.Intermsoftheprocessingspeedofprivatekeys(decryptionandsignature),ECCismuchfasterthanRSAandDSA.
(3)SmallstoragespaceoccupiedThekeysizeandsystemparametersofECCaremuchsmallerthanRSAandDSA,sothestoragespaceoccupiedismuchsmaller.
(4)ThelowbandwidthrequirementmakesECChaveawiderangeofapplicationprospects.
ThesecharacteristicsofECCmakeitsuretoreplaceRSAandbecomeageneralpublickeyencryptionalgorithm.Forexample,thecreatorsoftheSETprotocolhaveadopteditasthedefaultpublickeycryptographicalgorithminthenext-generationSETprotocol.