基于RBF神经网络和混沌映射的哈希函数构造(IJEM-V1-N4-1)

I.J.EngineeringandManufacturing2011,4,1-9PublishedOnlineAugust2011inMECS()DOI:10.5815/ijem.2011.04.01Availableonlineat’sOfficeChongqingEducationCollegeChongqing400067,ChinabTeachingandResearchSectionofComputerChongqingEducationManagementSchoolChongqing400066,ChinacDepartmentofComputerScienceChongqingEducationCollegeChongqing400067,ChinaAbstractOne-wayHashfunctionisnotonlywidelyusedintheaspectsofthedigitalsignature,identityauthenticationandintegritychecking,etc.butalsotheresearchhotspotinthefieldofcontemporarycryptography.Inthispaper,itfirstlyutilizedneuralnetworkandpracticedthechaoticsequencesproducedbyone-dimensionalnonlinearmapping.Andthen,itconstructedHashfunctionwithcipherkeybymeansofalteringsequences.Oneoftheadvantagesofthisalgorithmisthatneuralnetworkhidesthechaoticmappingrelationsandmakeitdifficulttoobtainmappingdirectly.Simulationexperimentshowedthatthealgorithmhavegoodunidirectionalityandweakcollision,andstrongerconfidentialitythanthetradition-basedHashfunction,aswellaseasytoachieve.IndexTerms:RBFneuralnetwork;Chaoticmapping;Hashfunction©2011PublishedbyMECSPublisher.Selectionand/orpeerreviewunderresponsibilityoftheResearchAssociationofModernEducationandComputerScience.1.IntroductionHashfunctionisanaggregatetransformationfromthewholemessageaggregatetoasummaryaggregatewithfixed-lengthmessages,itcanbedividedintotwocategories[1,2]:theHashfunctionwithcipherkeyandwithoutcipherkey.TheHashfunctionwithoutcipherkeyisakeylinkindigitalsignature.Itnotonlycangreatlyshortenthesignaturetime,butalsoplaysanimportantroleininformationintegritycheckandsecurestorageofaccountsandpasswordsinoperatingsystem.TheHashfunctionwithcipherkeycanbeusedforauthentication,sharedcipherkeyandsoftwareprotection,etc[2,3].Hashfunctioncontainsthreefeatures.a)IfgivenMessagemandHashfunctionH,itisveryeasytocalculatethevalueofHash)(mHh;b)IfgivenHashvalueh,itisverydifficulttocalculateMaccordingtohmH)(,(alsocalledunidirectionality);*Correspondingauthor.E-mailaddress:[e-mail];[e-mail];[e-mail]2HashFunctionConstructionBasedonRBFNNandChaoticMappingc)Ifgivenm,itisverydifficulttofindanothermessage'mandmeet)()'(mHmH,(alsocalledcollision-resistance).Thetraditionalone-wayHashmethodshaveseveralstandards,suchasMD2,MD5andSHA,etc.ItmostlygetsHashresultsbasedonthesupplicatedmethodsofXORandEQVoperations.Ithaslowsecurityandbigcomputationalburden,anddifficulttofindrapidandreliableencryptionmethods.Indocumentsliterature[4-7],itputsforwardsomeHashfunctionconstructionoperationsbasedonchaos.However,thesealgorithmsaredesignimplementationsbasedonacertainnonlinearmappingandthelimitationtochaoticmappingparameterandstatestimulationprecision;alsomakechaoticsequencesshowtheshortcomingssuchasshortcycle,strongcorrelationandlocallinear.Therefore,thechaoticsystemimplementedinthelowerprecisionisnotsuitabletoconstructHashfunction.Justaimingatthis,thepaperputsforwardchaoticHashalgorithmbasedonneuralnetwork.Thecharacteristics,suchasneuralnetworknonlinear,associativememory,massivelyparalleldistributionandhighfaulttolerance,areavailabletocryptographiccommunication.Onlyoperateitsparallelarithmeticmethoddirectlybyintegratedcircuit.Thepaperutilizedradialbasisfunctionneuralnetwork(RBFNN)topracticetheknownchaoticsequences,theresultingnonlinearsequencesconstructedHashfunctionwithcipherkey.Throughmakingfulluseoftheflexibilityofneuralnetwork,intheunifiedsystemstructure,itcancarryoutthatdifferentchaoticsystemproduceavarietyofchaoticsequencesbymeansofalteringthenetworkconnectionweightnumbers.Meanwhile,itturnsthechaoticmappingrelationsintoimplicitform,andmakesitmoreconcealed.Thisalgorithmhashighsensitivitytoinitialvalue,goodunidirectionaliltyandweakcollision,andstrongerconfidentialitybasedonchaoticmappingHashfunction,aswellaseasytoachieve.2.TheStudyofRBFNeuralNetworkversusChaoticSequence2.1.RBFneuralnetwork(RBFNN)ThestructureofRBFradialbasisneuralnetworkisshowninFig.1.Itisakindofneuralnetworkwithsimplestructure,superiorperformanceandthecapacityoflocalapproximation.Itcontainstwolayers:hiddenlayerandoutputlayer.Assumethenumberofinputnodesisn,thehiddenlayernodeism,andtheoutputnodeis1.RBFNNNetworkinputis:TnxxxX],,,[21Then,thenetworkoutputis:hiiiinXwbXfy10n)()(SelectGaussfunctions:)2exp()(2inniCxX2.2.TheCharacteristicsofPiecewise-nonlinearChaoticMappingAsshowninFig.2,one-dimensionalnonlinearmappingwithgooddynamiccharacteristics:IIf:,),,1,0(],1,0[NiIIiiisdefinedasfollows:[12,13]HashFunctionConstructionBasedonRBFNNandChaoticMapping3)1,5.0()5.0(5.00],[)()(1)(12111kkkiikikiiiikiiikxifxFxifIIxifaxIIaaxaIIxF(1)]1,0[kx2,5.00110NIIIINiNjaj,,1,0),1,0()0,1(1010)(NiiiiaII(2)WefoundmappingF(·)hasthefollowingproperties:i)Iterativesystem)0()(1kxFxkkischaos;ii)Sequence1}{kkxisuniformlydistributedintheinterval[0,1],anddistributionfunction1)(xf;iii)Sequence1}{kkxhastheaut