Securityisnottheonlyattractivefeatureofellipticcurvecryptography.Ellipticcurvecryptosystemsalsoaremorecomputationallyefficientthanthefirstgenerationpublickeysystems,RSAandDiffie-Hellman.AlthoughellipticcurvearithmeticisslightlymorecomplexperbitthaneitherRSAorDHarithmetic,theaddedstrengthperbitmorethanmakesupforanyextracomputetime.ThefollowingtableshowstheratioofDHcomputationversusECcomputationforeachofthekeysizes.
TABLE2:RELATIVECOMPUTATIONCOSTSOFDIFFIE-HELLMANANDELLIPTICCURVES
Optimizedpointmultiplicationiscarriedoverellipticcurvewho’sequationisbeinggivenanditprovidestheresultonthecurveitselfduetothespecialpropertyoftheellipticcurvesthatanyalgebraicoperationperformedonpointslyingonthecurvegivetheresultonthecurveitself.
TABLE3:DIFFERENCEBETWEENECCANDOTHERCRYPTOGRAPHICSCHEMES
VI.PROPOSEDSCHEME:FLOWDIAGRAM
Inourscheme“ECCforCRTbasedSecretSharingusingHierarchicalWSN’s”weuseCRTforkeygenerationusingahierarchicalWSNstructure.ThenusingpointadditioninEllipticCurveCryptography,encryptionisdone.TheprocessofDecryptionisjustthereverseofit.AflowdiagramofEncryptionandDecryptionSchemeisgivenasfollows: