Understanding Cryptography: From Established Symmetric and Asymmetric Ciphers to Post-Quantum Algorithms

Citation

Paar, C., Pelzl, J., & Güneysu, T. (2024). Understanding Cryptography: From Established Symmetric and Asymmetric Ciphers to Post-Quantum Algorithms (2nd ed.). Springer.

Chapter Summary

The second edition has fourteen chapters and runs to about 520 pages of text before the references and index. Each chapter presents algorithms with the mathematics they need, usually followed by security and implementation sections, then "Discussion and Further Reading", "Lessons Learned" and problems. The authors' companion site describes the new edition as heavily revised; its largest addition is the 85-page chapter on post-quantum cryptography.

Chapter 1: Introduction to Cryptography and Data Security

An overview of cryptology and of the book, followed by the basics of symmetric encryption through the substitution cipher. The chapter then discusses how cryptosystems are broken and how many key bits are enough, and introduces modular arithmetic and integer rings with the shift (Caesar) and affine ciphers as examples.

Chapter 2: Stream Ciphers

Compares stream and block ciphers, then covers random number generators, the one-time pad and the step towards practical stream ciphers. Linear feedback shift registers are presented together with a known-plaintext attack on a single LFSR, and the chapter closes with three practical designs: Salsa20, ChaCha and Trivium.

Chapter 3: The Data Encryption Standard (DES) and Alternatives

Introduces confusion and diffusion, then walks through DES: its overall structure, the initial and final permutations, the f function, the key schedule and decryption. Security (exhaustive key search, analytical attacks) and implementation follow, then alternatives: AES and its fellow finalists, Triple DES and DESX, and the lightweight cipher PRESENT.

Chapter 4: The Advanced Encryption Standard (AES)

Before the cipher itself, a section introduces Galois fields: prime fields and the extension fields GF(2^m), with addition, multiplication and inversion. The chapter then describes the internal structure of AES layer by layer (byte substitution, diffusion, key addition) and its key schedule, followed by decryption and implementation.

Chapter 5: More About Block Ciphers

Covers modes of operation (ECB, CBC, OFB, CFB, counter mode and XTS-AES), revisits exhaustive key search, and explains how to strengthen block ciphers: double encryption and the meet-in-the-middle attack, triple encryption, and key whitening.

Chapter 6: Introduction to Public-Key Cryptography

Contrasts symmetric and asymmetric cryptography, then treats the practical side: security mechanisms, the problem of authenticating public keys, the main public-key algorithm families, and key lengths and security levels. The second half supplies the number theory used later: the (extended) Euclidean algorithm, Euler's phi function, and the theorems of Fermat and Euler.

Chapter 7: The RSA Cryptosystem

Encryption, decryption, key generation and a proof of correctness, followed by fast exponentiation and speed-up techniques (short public exponents, decryption with the Chinese Remainder Theorem). The chapter also covers finding large primes and primality tests, padding in practice, key encapsulation, attacks, and implementation.

Chapter 8: Cryptosystems Based on the Discrete Logarithm Problem

Opens with the Diffie–Hellman key exchange, then introduces groups, cyclic groups and subgroups. It defines the discrete logarithm problem in prime fields and in general groups, surveys attacks on it, discusses the security of Diffie–Hellman, and derives Elgamal encryption from the key exchange.

Chapter 9: Elliptic Curve Cryptosystems

Defines elliptic curves and their group operation, builds a discrete logarithm problem on them and runs Diffie–Hellman on curves, followed by security and implementation.

Chapter 10: Digital Signatures

Explains why symmetric cryptography is not sufficient, sets out the principles, security services and applications of signatures, then presents RSA, Elgamal, DSA and ECDSA signatures, each with computational aspects and security.

Chapter 11: Hash Functions

Starts from the need to sign long messages, defines preimage resistance, second preimage resistance and collision resistance (with the birthday attack), and surveys hash functions built from block ciphers and the dedicated SHA family. SHA-256 is described in detail, followed by SHA-3: its high-level structure, padding and output, the Keccak-f permutation, and other functions based on Keccak.

Chapter 12: Post-Quantum Cryptography

New in this edition and the longest chapter. After explaining what quantum computing means for cryptography, it covers lattice-based cryptography (learning with errors, a simple LWE encryption system, Ring-LWE and LWE in practice), code-based cryptography (linear codes, syndrome decoding, encryption schemes, choice of codes) and hash-based signatures (one-time and many-time signatures), ending with a section on PQC standardization.

Chapter 13: Message Authentication Codes (MACs)

Principles of MACs, HMAC built from hash functions, and MACs from block ciphers: CBC-MAC and CMAC, the authenticated-encryption modes CCM and GCM, and GMAC.

Chapter 14: Key Management

Key derivation; key establishment with symmetric techniques (key distribution centres, the Needham–Schroeder protocol and the remaining problems of symmetric key distribution); key establishment with asymmetric techniques, the man-in-the-middle attack and certificates; public-key infrastructures, certificate chains and revocation; and practical aspects of key management.

Key Concepts

Chapters 1–2: Foundations and Stream Ciphers

• Modular arithmetic: arithmetic in integer rings, introduced with the shift and affine ciphers and used throughout the book.
• Linear feedback shift register: a simple key-stream generator whose linearity makes it vulnerable to known-plaintext attacks.

Chapters 3–5: Block Ciphers

• Confusion and diffusion: the two design principles behind DES and its successors.
• Galois field GF(2^m): the finite-field arithmetic underlying the AES layers.
• Modes of operation: rules such as CBC and CTR for encrypting messages longer than one block.
• Meet-in-the-middle attack: the reason double encryption gives far less security than its key length suggests.

Chapters 6–9: Public-Key Cryptography

• Extended Euclidean algorithm: the tool for computing modular inverses, needed for RSA key generation.
• Discrete logarithm problem: the hard problem behind Diffie–Hellman, Elgamal and elliptic-curve schemes, in prime fields and in general cyclic groups.

Chapters 10–14: Signatures, Hashing, Post-Quantum Schemes and Keys

• Collision resistance and the birthday attack: the strongest of the three hash-function security requirements, and the generic attack that determines how long hash outputs must be.
• Learning with errors: the lattice problem underlying the lattice-based schemes of Chapter 12.
• Authenticated encryption: modes such as CCM and GCM that provide confidentiality and integrity together.
• Certificates and PKI: the mechanism for establishing that a public key belongs to its claimed owner.

Critical Analysis

Strengths

• Accessible by design. The authors state that the necessary mathematics should be accessible with a minimum background in college-level calculus, and the contents bear this out: number theory, groups and finite fields are introduced inside the chapters that need them (Sections 4.3, 6.3 and 8.2) rather than as a prerequisite.
• Practical coverage. The book concentrates on algorithms in actual use, from ChaCha and AES to SHA-3, GCM and certificates, and most chapters include a section on implementation in software and hardware.
• Post-quantum material. The new Chapter 12 covers the three families on which the standardized post-quantum schemes are built (lattices, codes and hash-based signatures) in more than 80 pages, which keeps the edition current; Ron Rivest's foreword recommends the book for undergraduate and graduate classes alike.
• Built for teaching. Every chapter has a problem set, a further-reading discussion and a "Lessons Learned" summary. Odd-numbered solutions are free on the companion site, two one-semester curricula are published there, and Christof Paar's 25 recorded lectures on YouTube, based on the first edition, cover much of the same material.

Limitations

• Not a proof-based treatment. The authors keep the mathematics to a minimum and the contents contain no sections on formal security definitions or reductions; Rivest's foreword itself notes that the book can be augmented for students with a more theoretical orientation.
• Protocols only at the edges. Key management and PKI appear in the final chapter, but full protocols such as TLS are not given their own chapters in the contents, and systems-level security is outside its scope.
• Lighter coverage of the 2024 post-quantum standards themselves. Chapter 12 builds the underlying problems and simple schemes from scratch and has a single short section on standardization, so readers who need the exact standardized algorithms will have to go to the standards documents.
• Video lectures lag the text. The recorded lectures and slides on the companion site follow the first edition.

Where It Fits in the Course

Within this course list, Paar, Pelzl and Güneysu is the dedicated applied-cryptography text. The broad surveys, Easttom's Computer Security Fundamentals and Stallings and Brown's Computer Security: Principles and Practice, each give cryptography a part of a much wider survey of threats and defences; this book explains the algorithms underneath in far more detail, and it can be read alongside either one when a course spends several weeks on cryptography.

Katz and Lindell's Introduction to Modern Cryptography is the natural next step: it covers similar primitives through precise definitions and proofs of security. The book's second curriculum, focused on algorithms and their mathematical background, is presented on the companion site as preparation for such a theory course. For the engineering of whole systems, Ross Anderson's Security Engineering (free from the author's website) and Matt Bishop's Computer Security: Art and Science place cryptography within protocols, policy and assurance.

How to Use This Book

The book suits computer science, mathematics and electrical engineering students, from an IT-security first year to graduate level, and engineers learning on their own. The authors name only a minimum background in college-level calculus; everything else is developed in the text.

The authors teach the whole book over two semesters and publish two one-semester selections:

• Applied focus (for example a security programme): Chapter 1; Sections 2.1–2.2; Chapter 4; Section 5.1; Chapter 6; Sections 7.1–7.3, 8.1–8.3, 10.1–10.2 and 11.1–11.3; Sections 12.1 and 12.4; Section 13.1; Sections 14.1–14.3.
• Algorithms and mathematics focus (for example a mathematics programme or as preparation for theory): Chapters 1, 2, 4, 6, 7 and 9; Sections 8.1–8.4, 10.1–10.2 and 11.1–11.3; Sections 12.1, 12.2 and 12.4.

Neither published selection includes Chapter 3 on DES, so it can be skimmed. Work through the problems and check odd-numbered answers against the free solution manual; implementing a small cipher such as an affine cipher, an LFSR or textbook RSA in code is a good companion exercise. The companion site also links to CrypTool, an open-source e-learning project for experimenting with ciphers. Students who will continue to a proof-based course should pay particular attention to Chapters 6–9 and the lattice sections of Chapter 12.