**Pure and Applied Undergraduate Texts**

Volume: 40;
2019;
323 pp;
Hardcover

MSC: Primary 94;
Secondary 68; 81; 11

**Print ISBN: 978-1-4704-5055-7
Product Code: AMSTEXT/40**

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

**Electronic ISBN: 978-1-4704-5389-3
Product Code: AMSTEXT/40.E**

List Price: $89.00

AMS Member Price: $71.20

MAA Member Price: $80.10

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#### Supplemental Materials

# A Course in Cryptography

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*Heiko Knospe*

This book provides a compact course in modern cryptography. The
mathematical foundations in algebra, number theory and probability are
presented with a focus on their cryptographic applications. The text
provides rigorous definitions and follows the provable security
approach. The most relevant cryptographic schemes are covered,
including block ciphers, stream ciphers, hash functions, message
authentication codes, public-key encryption, key establishment,
digital signatures and elliptic curves. The current developments in
post-quantum cryptography are also explored, with separate chapters on
quantum computing, lattice-based and code-based cryptosystems.

Many examples, figures and exercises, as well as SageMath (Python)
computer code, help the reader to understand the concepts and
applications of modern cryptography. A special focus is on algebraic
structures, which are used in many cryptographic constructions and
also in post-quantum systems. The essential mathematics and the modern
approach to cryptography and security prepare the reader for more
advanced studies.

The text requires only a first-year course in mathematics (calculus
and linear algebra) and is also accessible to computer scientists and
engineers. This book is suitable as a textbook for undergraduate and
graduate courses in cryptography as well as for self-study.

#### Readership

Undergraduate students interested in cryptography.

#### Reviews & Endorsements

This book does an excellent job of introducing modern cryptographic schemes and assessing their security. The book is replete with over 100 references to the cryptographic literature and takes its readers to the forefront of the topics discussed. I think that it is especially well-suited to be a textbook in departments where there are a large number of mathematics/computer science double majors.

-- Benjamin Linowitz, Oberlin College

#### Table of Contents

# Table of Contents

## A Course in Cryptography

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface xiii14
- Getting Started with SageMath 120
- Chapter 1. Fundamentals 726
- Chapter 2. Encryption Schemes and Definitions of Security 3150
- 2.1. Encryption Schemes 3251
- 2.2. Perfect Secrecy 3554
- 2.3. Computational Security 3655
- 2.4. Indistinguishable Encryptions 3756
- 2.5. Eavesdropping Attacks 3958
- 2.6. Chosen Plaintext Attacks 4160
- 2.7. Chosen Ciphertext Attacks 4362
- 2.8. Pseudorandom Generators 4564
- 2.9. Pseudorandom Functions 4867
- 2.10. Block Ciphers and Operation Modes 5271
- 2.11. Summary 5877
- Exercises 5877

- Chapter 3. Elementary Number Theory 6180
- Chapter 4. Algebraic Structures 7392
- Chapter 5. Block Ciphers 101120
- Chapter 6. Stream Ciphers 115134
- Chapter 7. Hash Functions 137156
- Chapter 8. Message Authentication Codes 151170
- Chapter 9. Public-Key Encryption and the RSA Cryptosystem 163182
- Chapter 10. Key Establishment 185204
- Chapter 11. Digital Signatures 203222
- Chapter 12. Elliptic Curve Cryptography 213232
- Chapter 13. Quantum Computing 229248
- Chapter 14. Lattice-based Cryptography 253272
- Chapter 15. Code-based Cryptography 285304
- Bibliography 313332
- Index 319338
- Back cover Back cover1344