loepp s., protecting information-- from classical error correction to quantum cryptography

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1、ThispageintentionallyleftblankPROTECTINGINFORMATIONFormanyeverydaytransmissions,itisessentialtoprotectdigitalinforma-tionfromnoiseoreavesdropping.Thisundergraduateintroductiontoerrorcorrectionandcryptographyisuniqueindevotingseveralchapterstoquan-tumcryptographyandquantumcomputing,thusprovidinga

2、contextinwhichideasfrommathematicsandphysicsmeet.BycoveringsuchtopicsasShor’squantumfactoringalgorithm,thistextinformsthereaderaboutcurrentthink-inginquantuminformationtheoryandencouragesanappreciationoftheconnectionsbetweenmathematicsandscience.Ofparticularinterestarethepotentialimpactsofquantu

3、mphysics:(i)aquantumcomputer,ifbuilt,couldcrackourcurrentlyusedpublic-keycryp-tosystems;and(ii)quantumcryptographypromisestoprovideanalternativetothesecryptosystems,basingitssecurityonthelawsofnatureratherthanoncomputationalcomplexity.Nopriorknowledgeofquantummechanicsisassumed,butstudentsshould

4、haveabasicknowledgeofcomplexnumbers,vectors,andmatrices.SusanLoeppisanAssociateProfessorofMathematicsintheDepartmentofMathematicsandStatisticsatWilliamsCollege.Herresearchisincommuta-tivealgebra,focusingoncompletionsoflocalrings.WilliamK.Wootters,aFellowoftheAmericanPhysicalSociety,istheBarclayJ

5、ermainProfessorofNaturalPhilosophyintheDepartmentofPhysicsatWilliamsCollege.Hedoesresearchonquantumentanglementandotheraspectsofquantuminformationtheory.“Theauthorshavecombinedthetwo‘hot’subjectsofcryptographyandcod-ing,lookingateachwithregardtobothclassicalandquantummodelsofcomputingandcommunic

6、ation.Theseexcitingtopicsareunifiedthroughthesteady,consistentdevelopmentofalgebraicstructuresandtechniques.Studentswhoreadthisbookwillwalkawaywithabroadexposuretoboththetheoryandtheconcreteapplicationofgroups,finitefields,andvectorspaces.”–BenLotto,VassarCollegeProtectingInformationFromClassicalEr

7、rorCorrectiontoQuantumCryptographysusanloeppWilliamsCollegewilliamk.woottersWilliamsCollegeCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,Ca