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GF(2~n)域上基于ONB的ECC芯片设计与实现 Introduction Inrecentyears,theuseofEllipticCurveCryptography(ECC)hasbeenincreasinginarangeofapplications,includingsecurecommunications,electronicpaymentsystems,andsmartcards.Asaresult,therehasbeenagrowinginterestindevelopingspecializedhardwaretoaccelerateECCoperations.Inthispaper,wediscussthedesignandimplementationofanECChardwareacceleratorbasedonanOrthogonalBasis(ONB)overaGaloisField(GF)(2^n). Background EllipticCurveCryptography(ECC)isasetofmathematicalalgorithmsusedtosecuredatacommunications.ECCusesellipticcurvesoverfinitefieldstogenerateandsharesecurecryptographickeys.ThesecurityofECCisbasedonthedifficultyofsolvingtheellipticcurvediscretelogarithmproblem(ECDLP).ECCoffersthesamelevelofsecurityasthetraditionalRSAencryptionwithsmallerkeysizes. GaloisField(GF)isamathematicalfieldthatconsistsofafinitenumberofelementsandtwooperations:additionandmultiplication.GFiswidelyusedincryptography,codingtheory,andalgebraicgeometry.GF(2^n)isthefinitefieldconsistingof2^nelements,wherenisapositiveinteger. OrthogonalBasis(ONB)isasetofbasisvectorsinwhicheachvectorisorthogonaltoallothervectorsintheset.ONBiswidelyusedinsignalprocessing,linearalgebra,andcryptography. DesignandImplementation ThehardwareacceleratorforECCbasedonONBoverGF(2^n)consistsofseveralmodulesincludingkeygenerator,pointmultiplication,andpointaddition.ThekeygeneratormodulegeneratesthepublicandprivatekeysfortheECCalgorithm.Thepointmultiplicationmoduleperformsthescalarmultiplicationoperationonanellipticcurvepointandgeneratesanewpointonthecurve.Thepointadditionmoduleaddstwopointsonthecurveandgeneratesanotherpointonthecurve. ThedesignofthehardwareacceleratorisbasedontheONBoverGF(2^n).TheONBisusedtorepresenttheelementsofGF(2^n)asvectorsinavectorspaceofdimensionnoverthebinaryfieldGF(2).ThebinaryfieldGF(2)consistsofthetwoelements0and1.TheONBischosentobeasetofnbinaryvectors,whereeachvectorhasexactlyonenon-zeroelement. TheONBrepresentationoftheelementsofGF(2^n)isusedtoperformarithmeticoperationsonthe

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