Circuits and Systems for Security and Privacy

400 Pages·2016·15.748 MB·English

by  Farhana Sheikh, Leonel Sousa

Circuits Systems
and
Security Privacy
for and
© 2016 by Taylor & Francis Group, LLC
Devices, Circuits, and Systems
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Krzysztof Iniewski
Emerging Technologies CMOS Inc.
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© 2016 by Taylor & Francis Group, LLC
Circuits Systems
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a, Edited by
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es Farhana Sheikh
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f Portland, Oregon, USA
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sit Leonel Sousa
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[ INESC-ID, Instituto Superior Técnico
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b Universidade de Lisboa, Portugal
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Do MANAGING EDITOR
Emerging Technologies CMOS Inc.
Vancouver, British Columbia, Canada
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
© 2016 by Taylor & Francis Group, LLC
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Contents
Preface xix
6
1
0 Editors xxi
2
y
Jul Contributors xxiii
6
2
4 1 Introduction 1
3
1: FarhanaSheikhandLeonelSousa
1
at 1.1 MathematicsandCryptography . . . . . . . . . . . . . . . . . 2
h] 1.2 SymmetricKeyCryptographyandBlockCiphers . . . . . . . 3
ulut 1.3 SecureHashing . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
D 1.4 PublicKeyCryptography . . . . . . . . . . . . . . . . . . . . . 5
ota, 1.5 PhysicallyUnclonableFunctions . . . . . . . . . . . . . . . . . 6
es 1.6 RandomNumberGenerators . . . . . . . . . . . . . . . . . . . 6
n
n 1.7 SideChannelAttacks . . . . . . . . . . . . . . . . . . . . . . . 6
Mi
1.8 FinalRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
f
o
y
sit 2 MathematicsandCryptography 9
r
e DavidO.Novick
v
ni 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
U
[ 2.1.1 Mathematics:TheToolchestofModernCryptography 11
y
b 2.1.1.1 History:Fromoldtoolstonew . . . . . . . . . 11
d
e 2.1.1.2 Atreasuretroveoftechniques . . . . . . . . . 11
d
a
o 2.1.1.3 Purposeofthischapter . . . . . . . . . . . . . 12
nl
w 2.1.2 NotationSummary . . . . . . . . . . . . . . . . . . . . . 12
Do 2.2 ProbabilityTheory . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 BasicConcepts . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.3 TheBirthdayProblem . . . . . . . . . . . . . . . . . . . 15
2.3 Combinatorics . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.2 Permutations . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3.2.1 Representations . . . . . . . . . . . . . . . . . 17
2.3.2.2 Operationsonpermutations . . . . . . . . . . 18
2.3.2.3 Propertiesofpermutations . . . . . . . . . . . 19
2.3.2.4 Subsetpermutations. . . . . . . . . . . . . . . 20
ix
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x Contents
2.3.3 BinomialCoefficients . . . . . . . . . . . . . . . . . . . . 20
2.3.4 RecurrenceRelations . . . . . . . . . . . . . . . . . . . . 21
2.4 NumberTheory . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.2 GreatestCommonDivisor . . . . . . . . . . . . . . . . . 23
2.4.2.1 Euclid’salgorithm . . . . . . . . . . . . . . . . 23
2.4.3 ModularArithmetic . . . . . . . . . . . . . . . . . . . . 23
2.4.4 TheChineseRemainderTheorem . . . . . . . . . . . . 24
2.4.5 QuadraticResiduesandQuadraticReciprocity . . . . . 26
2.4.6 ThePrimeNumbers . . . . . . . . . . . . . . . . . . . . 27
6 2.4.6.1 Distributionoftheprimes . . . . . . . . . . . 28
1
20 2.4.6.2 Primalitytesting . . . . . . . . . . . . . . . . . 29
uly 2.4.7 Euler’sTotientFunction . . . . . . . . . . . . . . . . . . 30
6 J 2.4.8 Fermat’sLittleTheorem . . . . . . . . . . . . . . . . . . 31
2 2.4.9 Euler’sTheorem . . . . . . . . . . . . . . . . . . . . . . 31
4
3 2.5 EfficientIntegerArithmetic . . . . . . . . . . . . . . . . . . . . 32
1:
1 2.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 32
] at 2.5.2 MontgomeryMultiplication . . . . . . . . . . . . . . . . 32
h
ut 2.5.3 BarrettReduction . . . . . . . . . . . . . . . . . . . . . . 33
ul 2.5.4 KaratsubaMultiplication . . . . . . . . . . . . . . . . . 33
D
a, 2.6 AbstractAlgebra . . . . . . . . . . . . . . . . . . . . . . . . . . 34
ot 2.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 34
s
ne 2.6.2 AlgebraicStructures:AnOverview . . . . . . . . . . . 35
n
Mi 2.6.3 Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
f 2.6.3.1 Groupstructureandoperations . . . . . . . . 35
o
y 2.6.3.2 Commonpropertiesofgroups . . . . . . . . . 36
sit 2.6.3.3 Examplesofgroups . . . . . . . . . . . . . . . 37
r
e
v 2.6.3.4 Thediscretelogarithmproblem . . . . . . . . 39
ni
U 2.6.4 Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
[
y 2.6.4.1 Ringstructureandoperations . . . . . . . . . 40
b
d 2.6.4.2 Examplesofrings . . . . . . . . . . . . . . . . 40
e
d 2.6.4.3 Ideals . . . . . . . . . . . . . . . . . . . . . . . 41
a
o
nl 2.6.5 VectorSpaces . . . . . . . . . . . . . . . . . . . . . . . . 41
w 2.6.5.1 Vectorspacestructureandoperations. . . . . 41
o
D 2.6.5.2 Examplesofvectorspaces . . . . . . . . . . . 42
2.6.6 Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.6.6.1 Fieldstructureandoperations . . . . . . . . . 43
2.6.6.2 Examplesoffields . . . . . . . . . . . . . . . . 43
2.6.6.3 Finite(Galois)fields . . . . . . . . . . . . . . . 44
2.6.6.4 Finitefieldelementswhendegreed>1 . . . 44
2.6.6.5 FinitefielduseinAES . . . . . . . . . . . . . . 45
2.7 EllipticCurves . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.7.2 EllipticCurves . . . . . . . . . . . . . . . . . . . . . . . 47
2.7.3 PointRepresentation . . . . . . . . . . . . . . . . . . . . 48
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