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Logistic映射在数字图像加密算法中的应用 Title:TheApplicationofLogisticMappinginDigitalImageEncryptionAlgorithm Abstract: Digitalimageencryptionplaysavitalroleinsecuringsensitivevisualinformation.Oneeffectiveapproachtoachievingimageencryptionisthroughtheuseofchaostheory.Amongthevariouschaos-basedencryptionalgorithms,LogisticMappingstandsoutforitssimplicity,versatility,androbustness.ThispaperexplorestheapplicationoftheLogisticMappingalgorithmindigitalimageencryption,discussingitsunderlyingprinciples,advantages,andpotentialchallenges.Furthermore,itprovidesanoverviewofrecentadvancementsinimageencryptiontechniquesutilizingLogisticMapping,highlightingtheireffectivenessandrelevantresearchdirections. 1.Introduction: Digitalimagescontainvastamountsofinformation,makingthemhighlyvulnerabletounauthorizedaccessandmalicioustampering.Encryptiontechniquesarecrucialforprotectingimageintegrityandconfidentiality.Chaostheoryandchaos-basedalgorithmshaveproventobehighlyefficientinimageencryptionduetotheirrandomandnon-linearcharacteristics.TheLogisticMappingalgorithm,extensivelyusedinvariousfields,offersgreatpotentialforsecureimageencryption. 2.LogisticMappingAlgorithm: TheLogisticMappingalgorithmisaone-dimensionaldiscretechaoticmapthatexhibitshighlychaoticbehavior.Itisdefinedbytherecursiveequationx(n+1)=r*x(n)(1-x(n)),wherex(n)isthecurrentstate,andristhecontrolparameterthatdeterminesthechaoticrange.TheLogisticMapgeneratesasequenceofpseudo-randomnumbersthathaveexcellentrandomnessproperties. 3.Pixel-levelImageEncryption: TheLogisticMappingalgorithmcanbeemployedforpixel-levelimageencryption.BytreatingeachpixelvalueasaninputtotheLogisticMap,chaos-basedtransformationsareappliedtoscramblethepixelpositionsandalterpixelvaluesaccordingtothegeneratedpseudo-randomsequence.Thistechniqueensuresthattheencryptedimageappearsasrandomnoiseandisindistinguishablefromtheoriginalimagewithoutproperdecryption. 4.AdvantagesofLogisticMapping-basedEncryption: 4.1Robustness:LogisticMappingusesasinglecontrolparameter,makingitcomput