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1、SOLUTIONSMANUALforINTRODUCTIONTOCRYPTOGRAPHYwithCodingTheory,2ndeditionWadeTrappeWirelessInformationNetworkLaboratoryandtheElectricalandComputerEngineeringDepartmentRutgersUniversityLawrenceC.WashingtonDepartmentofMathematicsUniversityofMarylandAugust26,2005ContentsExercisesChap
2、ter2-Exercises1Chapter3-Exercises6Chapter4-Exercises14Chapter5-Exercises17Chapter6-Exercises19Chapter7-Exercises23Chapter8-Exercises25Chapter9-Exercises27Chapter10-Exercises28Chapter11-Exercises29Chapter12-Exercises31Chapter13-Exercises33Chapter14-Exercises34Chapter15-Exercises3
3、6Chapter16-Exercises40Chapter17-Exercises44Chapter18-Exercises46-2-1Chapter19-Exercises51MathematicaproblemsChapter252Chapter363Chapter666Chapter772Chapter874Chapter975Chapter1278Chapter1679Chapter1881MapleproblemsChapter284Chapter398Chapter6102Chapter7109Chapter8112Chapter9113C
4、hapter12116Chapter16118Chapter181210MATLABproblemsChapter2124Chapter3147Chapter6151Chapter7161Chapter8164Chapter9165Chapter12167Chapter16169Chapter18174Chapter2-Exercises1.AmongtheshiftsofEVIRE,therearetwowords:arenaandriver.Therefore,AnthonycannotdeterminewheretomeetCaesar.2.Th
5、einverseof9mod26is3.Therefore,thedecryptionfunctionisx=3(y−2)=3y−2(mod26).Nowsimplydecryptletterbyletterasfollows.U=20sodecryptUbycalculating3∗20−6(mod26)=2,andsoon.Thedecryptedmessageis’cat’.3.Changingtheplaintexttonumbersyields7,14,22,0,17,4,24,14,20.Applying5x+7toeachyields5·
6、7+7=42≡16(mod26),5·14+7=77≡25,etc.ChangingbacktolettersyieldsQZNHOBXZDastheciphertext.4.Letmx+nbetheencryptionfunction.Sinceh=7andN=13,wehavem·7+n≡13(mod26).Usingthesecondlettersyieldsm·0+n≡14.Thereforen=14.Thefirstcongruencenowyields7m≡−1(mod26).Thisyieldsm=11.Theencryptionfunct
7、ionistherefore11x+14.5.Letthedecryptionfunctionbex=ay+b.Thefirstletterstellusthat7≡a·2+b(mod26).Thesecondletterstellusthat0≡a·17+b.Subtractingyields7≡a·(−15)≡11a.Since11−1≡19(mod26),wehavea≡19·7≡3(mod26).Thefirstcongruencenowtellsusthat7≡3·2+b,sob=1.Thedecryptionfunctionistherefor
8、ex≡3y+1.ApplyingthistoCRWWZyieldshappyforthepla
