The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption

391 Pages·2017·3.26 MB·English

by  Joshua Holden

THE MATHEMATICS OF SECRETS

THE MATHEMATICS OF
SECRETS
CRYPTOGRAPHY FROM
CAESAR CIPHERS TO
DIGITAL ENCRYPTION
JOSHUA HOLDEN
PRINCETONUNIVERSITYPRESS
PRINCETONANDOXFORD
Copyright(cid:2)c 2017byPrincetonUniversityPress
PublishedbyPrincetonUniversityPress,41WilliamStreet,
Princeton,NewJersey08540
IntheUnitedKingdom:PrincetonUniversityPress,6Oxford
Street,Woodstock,OxfordshireOX201TR
press.princeton.edu
JacketimagecourtesyofShutterstock;designbyLorraineBetzDoneker
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LibraryofCongressCataloging-in-PublicationData
Names:Holden,Joshua,1970–author.
Title:Themathematicsofsecrets:cryptographyfromCaesar
cipherstodigitalencryption/JoshuaHolden.
Description:Princeton:PrincetonUniversityPress,[2017]|
Includesbibliographicalreferencesandindex.
Identifiers:LCCN2016014840|ISBN9780691141756
(hardcover:alk.paper)
Subjects:LCSH:Cryptography—Mathematics.|Ciphers.|
Computersecurity.
Classification:LCCZ103.H6642017|DDC005.8/2—dc23LC
recordavailableathttps://lccn.loc.gov/2016014840
BritishLibraryCataloging-in-PublicationDataisavailable
ThisbookhasbeencomposedinLinuxLibertine
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CONTENTS
Preface xi
Acknowledgments xiii
IntroductiontoCiphersandSubstitution 1
1.1 AliceandBobandCarlandJulius:TerminologyandCaesar
Cipher 1
1.2 TheKeytotheMatter:GeneralizingtheCaesarCipher 4
1.3 MultiplicativeCiphers 6
1.4 AffineCiphers 15
1.5 AttackatDawn:CryptanalysisofSampleSubstitution
Ciphers 18
1.6 JusttoGetUpThatHill:PolygraphicSubstitutionCiphers 20
1.7 Known-PlaintextAttacks 25
1.8 LookingForward 26
PolyalphabeticSubstitutionCiphers 29
2.1 HomophonicCiphers 29
2.2 CoincidenceorConspiracy? 31
2.3 AlbertiCiphers 36
2.4 It’sHiptoBeSquare:TabulaRectaorVigenèreSquare
Ciphers 39
2.5 HowManyIsMany?DeterminingtheNumberof
Alphabets 43
2.6 SupermanIsStayingforDinner:Superimpositionand
Reduction 52
2.7 ProductsofPolyalphabeticCiphers 55
2.8 PinwheelMachinesandRotorMachines 58
2.9 LookingForward 73
viii • Contents
TranspositionCiphers 75
3.1 ThisIsSparta!TheScytale 75
3.2 RailsandRoutes:GeometricTranspositionCiphers 78
3.3 PermutationsandPermutationCiphers 81
3.4 PermutationProducts 86
3.5 KeyedColumnarTranspositionCiphers 91
Sidebar3.1 FunctionalNihilism 94
3.6 DeterminingtheWidthoftheRectangle 97
3.7 Anagramming 101
Sidebar3.2 ButWhenYouTalkaboutDisruption 104
3.8 LookingForward 106
CiphersandComputers 109
4.1 BringingHometheBacon:PolyliteralCiphersandBinary
Numerals 109
4.2 FractionatingCiphers 115
4.3 HowtoDesignaDigitalCipher:SP-NetworksandFeistel
Networks 119
Sidebar4.1 DigitizingPlaintext 125
4.4 TheDataEncryptionStandard 130
4.5 TheAdvancedEncryptionStandard 135
4.6 LookingForward 143
StreamCiphers 145
5.1 Running-KeyCiphers 145
Sidebar5.1 WeHaveAllBeenHereBefore 150
5.2 One-TimePads 153
5.3 BabyYouCanDriveMyCar:AutokeyCiphers 157
5.4 LinearFeedbackShiftRegisters 167
5.5 AddingNonlinearitytoLFSRs 174
5.6 LookingForward 178
CiphersInvolvingExponentiation 182
6.1 EncryptingUsingExponentiation 182
6.2 Fermat’sLittleTheorem 183
6.3 DecryptingUsingExponentiation 186
6.4 TheDiscreteLogarithmProblem 188
Contents • ix
6.5 CompositeModuli 190
6.6 TheEulerPhiFunction 192
6.7 DecryptionwithCompositeModuli 195
Sidebar6.1 Fee-fi-fo-fum 197
6.8 LookingForward 199
Public-KeyCiphers 201
7.1 RightoutinPublic:TheIdeaofPublic-KeyCiphers 201
7.2 Diffie-HellmanKeyAgreement 207
7.3 Asymmetric-KeyCryptography 213
7.4 RSA 216
7.5 PrimingthePump:PrimalityTesting 222
7.6 WhyisRSAa(Good)Public-KeySystem? 226
7.7 CryptanalysisofRSA 229
7.8 LookingForward 233
AppendixA TheSecretHistoryofPublic-KeyCryptography 235
OtherPublic-KeySystems 241
8.1 TheThree-PassProtocol 241
8.2 ElGamal 247
8.3 EllipticCurveCryptography 251
8.4 DigitalSignatures 265
8.5 LookingForward 271
TheFutureofCryptography 276
9.1 QuantumComputing 276
9.2 PostquantumCryptography 281
9.3 QuantumCryptography 292
9.4 LookingForward 301
ListofSymbols 303
Notes 305
SuggestionsforFurtherReading 345
Bibliography 349
Index 367