Table of Contents. xiii

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1 Table of Contents 1 Introduction to Cryptography and Data Security Overview of Cryptology (and This Book) SymmetricCryptography Basics Simple Symmetric Encryption: The Substitution Cipher Cryptanalysis General Thoughts on Breaking Cryptosystems How Many Key Bits Are Enough? Modular Arithmetic and More Historical Ciphers Modular Arithmetic IntegerRings Shift Cipher (or Caesar Cipher) Affine Cipher Discussion and Further Reading LessonsLearned Problems Stream Ciphers Introduction Stream Ciphers vs. Block Ciphers Encryption and Decryption with Stream Ciphers Random Numbers and an Unbreakable Stream Cipher Random Number Generators TheOne-TimePad Towards Practical Stream Ciphers Shift Register-Based Stream Ciphers Linear Feedback Shift Registers (LFSR) Known-PlaintextAttackAgainstSingleLFSRs Trivium Discussion and Further Reading xiii

2 xiv Table of Contents 2.5 LessonsLearned Problems The Data Encryption Standard (DES) and Alternatives Introduction to DES ConfusionandDiffusion OverviewoftheDESAlgorithm InternalStructureofDES Initial and Final Permutation The f -Function Key Schedule Decryption Security of DES Exhaustive Key Search Analytical Attacks ImplementationinSoftwareandHardware DESAlternatives The Advanced Encryption Standard (AES) and the AES Finalist Ciphers TripleDES(3DES)andDESX Lightweight Cipher PRESENT Discussion and Further Reading LessonsLearned Problems The Advanced Encryption Standard (AES) Introduction OverviewoftheAESAlgorithm Some Mathematics: A Brief Introduction to Galois Fields Existence of Finite Fields PrimeFields Extension Fields GF(2 m ) Addition and Subtraction in GF(2 m ) Multiplication in GF(2 m ) Inversion in GF(2 m ) InternalStructureofAES Byte Substitution Layer Diffusion Layer Key Addition Layer Key Schedule Decryption ImplementationinSoftwareandHardware Discussion and Further Reading LessonsLearned Problems...118

3 Table of Contents xv 5 More About Block Ciphers Encryption with Block Ciphers: Modes of Operation Electronic Codebook Mode (ECB) Cipher Block Chaining Mode (CBC) Output Feedback Mode (OFB) Cipher Feedback Mode (CFB) Counter Mode (CTR) Galois Counter Mode (GCM) Exhaustive Key Search Revisited Increasing the Security of Block Ciphers Double Encryption and Meet-in-the-Middle Attack TripleEncryption KeyWhitening Discussion and Further Reading LessonsLearned Problems Introduction to Public-Key Cryptography Symmetricvs.AsymmetricCryptography Practical Aspects of Public-Key Cryptography Security Mechanisms TheRemainingProblem:AuthenticityofPublicKeys ImportantPublic-KeyAlgorithms Key Lengths and Security Levels Essential Number Theory for Public-Key Algorithms Euclidean Algorithm Extended Euclidean Algorithm Euler s Phi Function Fermat s Little Theorem and Euler s Theorem Discussion and Further Reading LessonsLearned Problems The RSA Cryptosystem Introduction EncryptionandDecryption Key Generation and Proof of Correctness Encryption and Decryption: Fast Exponentiation Speed-up Techniques for RSA Fast Encryption with Short Public Exponents Fast Decryption with the Chinese Remainder Theorem FindingLargePrimes HowCommonArePrimes? Primality Tests RSA in Practice: Padding

4 xvi Table of Contents 7.8 Attacks ImplementationinSoftwareandHardware Discussion and Further Reading LessonsLearned Problems Public-Key Cryptosystems Based on the Discrete Logarithm Problem Diffie Hellman Key Exchange Some Algebra Groups Cyclic Groups Subgroups TheDiscreteLogarithmProblem TheDiscreteLogarithmProbleminPrimeFields The Generalized Discrete Logarithm Problem Attacks Against the Discrete Logarithm Problem Security of the Diffie Hellman Key Exchange The Elgamal Encryption Scheme From Diffie Hellman Key Exhange to Elgamal Encryption The Elgamal Protocol Computational Aspects Security Discussion and Further Reading LessonsLearned Problems Elliptic Curve Cryptosystems How to Compute with Elliptic Curves Definition of Elliptic Curves Group Operations on Elliptic Curves Building a Discrete Logarithm Problem with Elliptic Curves Diffie Hellman Key Exchange with Elliptic Curves Security ImplementationinSoftwareandHardware Discussion and Further Reading LessonsLearned Problems Digital Signatures Introduction Odd Colors for Cars, or: Why Symmetric Cryptography Is NotSufficient Principles of Digital Signatures Security Services The RSA Signature Scheme

5 Table of Contents xvii Schoolbook RSA Digital Signature Computational Aspects Security The Elgamal Digital Signature Scheme Schoolbook Elgamal Digital Signature Computational Aspects Security The Digital Signature Algorithm (DSA) TheDSAAlgorithm Computational Aspects Security The Elliptic Curve Digital Signature Algorithm (ECDSA) TheECDSAAlgorithm Computational Aspects Security Discussion and Further Reading LessonsLearned Problems Hash Functions Motivation: Signing Long Messages Security Requirements of Hash Functions Preimage Resistance or One-Wayness Second Preimage Resistance or Weak Collision Resistance Collision Resistance and the Birthday Attack OverviewofHashAlgorithms Dedicated Hash Functions: The MD4 Family Hash Functions from Block Ciphers The Secure Hash Algorithm SHA Preprocessing HashComputation Implementation Discussion and Further Reading LessonsLearned Problems Message Authentication Codes (MACs) Principles of Message Authentication Codes MACs from Hash Functions: HMAC MACs from Block Ciphers: CBC-MAC Galois Counter Message Authentication Code (GMAC) Discussion and Further Reading LessonsLearned Problems...329

6 xviii Table of Contents 13 Key Establishment Introduction SomeTerminology Key Freshness and Key Derivation The n 2 KeyDistributionProblem Key Establishment Using Symmetric-Key Techniques KeyEstablishmentwithaKeyDistributionCenter Kerberos Remaining Problems with Symmetric-Key Distribution Key Establishment Using Asymmetric Techniques Man-in-the-MiddleAttack Certificates Public-KeyInfrastructures(PKI)andCAs Discussion and Further Reading LessonsLearned Problems References Index...367

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