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1、Commenton“NovelPublicKeyEncryptionTechniqueBasedonMultipleChaoticSystems”[Phys.Rew.Lett.95,2005]WangKai,PeiWen-jiang,ZouLiu-hua,HeZhen-ya(DepartmentofRadioEngineering,SoutheastUniversity,Nanjing210096,China)Recently,anovelpublickeyencryptiontechniquebasedonmultiplechaoticsystemshasbeenproposed[Phys.
2、Rew.Lett.,95(9):098702,2005].Thisschemeemploysm-chaoticsystemsandasetoflinearfunctionsforkeymexchangeoveraninsecurechannel.Thesecurityoftheproposedalgorithmgrowsas(NP),whereN,Parethesizeofthekeyandthecomputationalcomplexityofthelinearfunctionsrespectively.Inthispaper,thefundamentalweaknessofthecrypt
3、osystemispointedoutandasuccessfulattackisdescribed.Giventhepublickeysandtheinitialvector,onecancalculatethesecretkeybasedonParsevala’stheorem.Boththeoreticalandexperimentalresultsshowthattheattackercanaccesstothesecretkeywithoutdifficulty.Thelackofsecuritydiscouragestheuseofsuchalgorithmforpractical
4、applications.PACSnumbers:05.45.Vx,89.70.+cChaoticsystemsarecharacterizedbyergodicity,sensitivedependenceoninitialconditionsandrandom-likebehaviors,propertieswhichseemprettymuchthesamerequiredbyseveralcryptographicprimitivecharacterssuchas“diffusion”and“confusion”.Sofar,theconstructingofsecret-keycry
5、ptosystems,whicharemostlybasedonbothchaoticsynchronizationandchaos-basedpseudorandombitgenerator,hasattractedagreatdealofattention,andplentyofchaos-basedstreamciphersandblockciphershadbeenpresentedinthepast[2,3].Whileallthecurrentlyusedpublic-keycryptosystemsbasedonnumbertheoryworkwellforbothencrypt
6、ionanddigitalsignatures,itisofmuchimportancetoconstructpublic-keycryptosystemsbychaoticdynamicsandtherehavebeensomeattemptsalongthisline.InRef.[4,5],apublickeycryptosystemsandmodification,whicharebasedondistributeddynamicsencryption,hadbeenproposed.Inthoseschemes,ahigh-dimensionaldissipativedynamica
7、lsystemisseparatedintotwoparts.Thebinarymessageischaracterizebydifferentattractors,whicharenamedasthe0-attractorandthe1-attractor,inthewholesystem.Anauthorizedreceiverknowsthefulldynamicsandcansimulat