Algoritmo della curva ellittica

Encryptionalgorithm

Inellipticcurveencryption(ECC),aspecialformofellipticcurveisused,thatis,anellipticcurvedefinedinafinitefield.Theequationisasfollows:

y²=x³+ax+b(modp)

Herepisaprimenumber, andbaretwonon-negativeintegerslessthanp. Theysatisfy:

4a³+27b²(modp)≠0wherex,y,a,b∈Fp, punctum (x, y) satisfacit formulae(2)andaninfinitepointOformanellipseCurveE.

TheellipticcurvediscretelogarithmproblemECDLPisdefinedasfollows:GivenaprimenumberpandanellipticcurveE,forQ=kP,findapositiveintegerklessthanpwhenPandQareknown.ItcanbeprovedthatitiseasiertocalculateQwithkandP,butitismoredifficulttocalculatekfromQandP.Sofar,thereisnoeffectivemethodtosolvethisproblem.Thisistheprincipleoftheellipticcurveencryptionalgorithm.

Comparatio

ComparatiobetweenellipticcurvealgorithmandRSAalgorithm

EllipticcurvepublickeysystemisastrongcompetitortoreplaceRSA.ComparedwiththeRSAmethod,theellipticcurveencryptionmethodhasthefollowingadvantages:(1)Highersecurityperformance.Forexample,160-bitECChasthesamesecuritystrengthas1024-bitRSAandDSA.

(2)Theamountofcalculationissmallandtheprocessingspeedisfast.Intermsoftheprocessingspeedofprivatekeys(decryptionandsignature),ECCismuchfasterthanRSAandDSA.

(3)SmallstoragespaceoccupiedThekeysizeandsystemparametersofECCaremuchsmallerthanRSAandDSA,sothestoragespaceoccupiedismuchsmaller.

(4)ThelowbandwidthrequirementmakesECChaveawiderangeofapplicationprospects.

ThesecharacteristicsofECCmakeitsuretoreplaceRSAandbecomeageneralpublickeyencryptionalgorithm.Forexample,thecreatorsoftheSETprotocolhaveadopteditasthedefaultpublickeycryptographicalgorithminthenext-generationSETprotocol.

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