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A Course in Cryptography
 
Heiko Knospe :  Technische Hochschule Köln, University of Applied Sciences, Cologne, Germany
A Course in Cryptography
Hardcover ISBN:  978-1-4704-5055-7
Product Code:  AMSTEXT/40
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-5389-3
Product Code:  AMSTEXT/40.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-5055-7
eBook: ISBN:  978-1-4704-5389-3
Product Code:  AMSTEXT/40.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Add to cart
A Course in Cryptography
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A Course in Cryptography
Heiko Knospe :  Technische Hochschule Köln, University of Applied Sciences, Cologne, Germany
Hardcover ISBN:  978-1-4704-5055-7
Product Code:  AMSTEXT/40
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
eBook ISBN:  978-1-4704-5389-3
Product Code:  AMSTEXT/40.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Hardcover ISBN:  978-1-4704-5055-7
eBook ISBN:  978-1-4704-5389-3
Product Code:  AMSTEXT/40.B
List Price: $174.00 $131.50
MAA Member Price: $156.60 $118.35
AMS Member Price: $139.20 $105.20
Add to cart
  • Book Details
     
     
    Pure and Applied Undergraduate Texts
    Volume: 40; 2019; 323 pp
    MSC: Primary 94; Secondary 68; 81; 11

    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.
  • Table of Contents
     
     
    • Cover
    • Title page
    • Contents
    • Preface
    • Getting Started with SageMath
    • 0.1. Installation
    • 0.2. SageMath Command Line
    • 0.3. Browser Notebooks
    • 0.4. Computations with SageMath
    • Chapter 1. Fundamentals
    • 1.1. Sets, Relations and Functions
    • 1.2. Combinatorics
    • 1.3. Computational Complexity
    • 1.4. Discrete Probability
    • 1.5. Random Numbers
    • 1.6. Summary
    • Exercises
    • Chapter 2. Encryption Schemes and Definitions of Security
    • 2.1. Encryption Schemes
    • 2.2. Perfect Secrecy
    • 2.3. Computational Security
    • 2.4. Indistinguishable Encryptions
    • 2.5. Eavesdropping Attacks
    • 2.6. Chosen Plaintext Attacks
    • 2.7. Chosen Ciphertext Attacks
    • 2.8. Pseudorandom Generators
    • 2.9. Pseudorandom Functions
    • 2.10. Block Ciphers and Operation Modes
    • 2.11. Summary
    • Exercises
    • Chapter 3. Elementary Number Theory
    • 3.1. Integers
    • 3.2. Congruences
    • 3.3. Modular Exponentiation
    • 3.4. Summary
    • Exercises
    • Chapter 4. Algebraic Structures
    • 4.1. Groups
    • 4.2. Rings and Fields
    • 4.3. Finite Fields
    • 4.4. Linear and Affine Maps
    • 4.5. Summary
    • Exercises
    • Chapter 5. Block Ciphers
    • 5.1. Constructions of Block Ciphers
    • 5.2. Advanced Encryption Standard
    • 5.3. Summary
    • Exercises
    • Chapter 6. Stream Ciphers
    • 6.1. Definition of Stream Ciphers
    • 6.2. Linear Feedback Shift Registers
    • 6.3. RC4
    • 6.4. Salsa20 and ChaCha20
    • 6.5. Summary
    • Exercises
    • Chapter 7. Hash Functions
    • 7.1. Definitions and Security Requirements
    • 7.2. Applications of Hash Functions
    • 7.3. Merkle-Damgård Construction
    • 7.4. SHA-1
    • 7.5. SHA-2
    • 7.6. SHA-3
    • 7.7. Summary
    • Exercises
    • Chapter 8. Message Authentication Codes
    • 8.1. Definitions and Security Requirements
    • 8.2. CBC MAC
    • 8.3. HMAC
    • 8.4. Authenticated Encryption
    • 8.5. Summary
    • Exercises
    • Chapter 9. Public-Key Encryption and the RSA Cryptosystem
    • 9.1. Public-Key Cryptosystems
    • 9.2. Plain RSA
    • 9.3. RSA Security
    • 9.4. Generation of Primes
    • 9.5. Efficiency of RSA
    • 9.6. Padded RSA
    • 9.7. Factoring
    • 9.8. Summary
    • Exercises
    • Chapter 10. Key Establishment
    • 10.1. Key Distribution
    • 10.2. Key Exchange Protocols
    • 10.3. Diffie-Hellman Key Exchange
    • 10.4. Diffie-Hellman using Subgroups of zz _{𝑝}*
    • 10.5. Discrete Logarithm
    • 10.6. Key Encapsulation
    • 10.7. Hybrid Encryption
    • 10.8. Summary
    • Exercises
    • Chapter 11. Digital Signatures
    • 11.1. Definitions and Security Requirements
    • 11.2. Plain RSA Signature
    • 11.3. Probabilistic Signature Scheme
    • 11.4. Summary
    • Exercises
    • Chapter 12. Elliptic Curve Cryptography
    • 12.1. Weierstrass Equations and Elliptic Curves
    • 12.2. Elliptic Curve Diffie-Hellman
    • 12.3. Efficiency and Security of Elliptic Curve Cryptography
    • 12.4. Elliptic Curve Factoring Method
    • 12.5. Summary
    • Exercises
    • Chapter 13. Quantum Computing
    • 13.1. Quantum Bits
    • 13.2. Multiple Qubit Systems
    • 13.3. Quantum Algorithms
    • 13.4. Quantum Fourier Transform
    • 13.5. Shor’s Factoring Algorithm
    • 13.6. Quantum Key Distribution
    • 13.7. Summary
    • Exercises
    • Chapter 14. Lattice-based Cryptography
    • 14.1. Lattices
    • 14.2. Lattice Algorithms
    • 14.3. GGH Cryptosystem
    • 14.4. NTRU
    • 14.5. Learning with Errors
    • 14.6. Summary
    • Exercises
    • Chapter 15. Code-based Cryptography
    • 15.1. Linear Codes
    • 15.2. Bounds on Codes
    • 15.3. Goppa Codes
    • 15.4. McEliece Cryptosystem
    • 15.5. Summary
    • Exercises
    • Bibliography
    • Index
    • Back cover
  • Additional Material
     
     
  • Reviews
     
     

    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Desk Copy – for instructors who have adopted an AMS textbook for a course
    Examination Copy – for faculty considering an AMS textbook for a course
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Pure and Applied Undergraduate Texts
Volume: 40; 2019; 323 pp
MSC: Primary 94; Secondary 68; 81; 11

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.
  • Cover
  • Title page
  • Contents
  • Preface
  • Getting Started with SageMath
  • 0.1. Installation
  • 0.2. SageMath Command Line
  • 0.3. Browser Notebooks
  • 0.4. Computations with SageMath
  • Chapter 1. Fundamentals
  • 1.1. Sets, Relations and Functions
  • 1.2. Combinatorics
  • 1.3. Computational Complexity
  • 1.4. Discrete Probability
  • 1.5. Random Numbers
  • 1.6. Summary
  • Exercises
  • Chapter 2. Encryption Schemes and Definitions of Security
  • 2.1. Encryption Schemes
  • 2.2. Perfect Secrecy
  • 2.3. Computational Security
  • 2.4. Indistinguishable Encryptions
  • 2.5. Eavesdropping Attacks
  • 2.6. Chosen Plaintext Attacks
  • 2.7. Chosen Ciphertext Attacks
  • 2.8. Pseudorandom Generators
  • 2.9. Pseudorandom Functions
  • 2.10. Block Ciphers and Operation Modes
  • 2.11. Summary
  • Exercises
  • Chapter 3. Elementary Number Theory
  • 3.1. Integers
  • 3.2. Congruences
  • 3.3. Modular Exponentiation
  • 3.4. Summary
  • Exercises
  • Chapter 4. Algebraic Structures
  • 4.1. Groups
  • 4.2. Rings and Fields
  • 4.3. Finite Fields
  • 4.4. Linear and Affine Maps
  • 4.5. Summary
  • Exercises
  • Chapter 5. Block Ciphers
  • 5.1. Constructions of Block Ciphers
  • 5.2. Advanced Encryption Standard
  • 5.3. Summary
  • Exercises
  • Chapter 6. Stream Ciphers
  • 6.1. Definition of Stream Ciphers
  • 6.2. Linear Feedback Shift Registers
  • 6.3. RC4
  • 6.4. Salsa20 and ChaCha20
  • 6.5. Summary
  • Exercises
  • Chapter 7. Hash Functions
  • 7.1. Definitions and Security Requirements
  • 7.2. Applications of Hash Functions
  • 7.3. Merkle-Damgård Construction
  • 7.4. SHA-1
  • 7.5. SHA-2
  • 7.6. SHA-3
  • 7.7. Summary
  • Exercises
  • Chapter 8. Message Authentication Codes
  • 8.1. Definitions and Security Requirements
  • 8.2. CBC MAC
  • 8.3. HMAC
  • 8.4. Authenticated Encryption
  • 8.5. Summary
  • Exercises
  • Chapter 9. Public-Key Encryption and the RSA Cryptosystem
  • 9.1. Public-Key Cryptosystems
  • 9.2. Plain RSA
  • 9.3. RSA Security
  • 9.4. Generation of Primes
  • 9.5. Efficiency of RSA
  • 9.6. Padded RSA
  • 9.7. Factoring
  • 9.8. Summary
  • Exercises
  • Chapter 10. Key Establishment
  • 10.1. Key Distribution
  • 10.2. Key Exchange Protocols
  • 10.3. Diffie-Hellman Key Exchange
  • 10.4. Diffie-Hellman using Subgroups of zz _{𝑝}*
  • 10.5. Discrete Logarithm
  • 10.6. Key Encapsulation
  • 10.7. Hybrid Encryption
  • 10.8. Summary
  • Exercises
  • Chapter 11. Digital Signatures
  • 11.1. Definitions and Security Requirements
  • 11.2. Plain RSA Signature
  • 11.3. Probabilistic Signature Scheme
  • 11.4. Summary
  • Exercises
  • Chapter 12. Elliptic Curve Cryptography
  • 12.1. Weierstrass Equations and Elliptic Curves
  • 12.2. Elliptic Curve Diffie-Hellman
  • 12.3. Efficiency and Security of Elliptic Curve Cryptography
  • 12.4. Elliptic Curve Factoring Method
  • 12.5. Summary
  • Exercises
  • Chapter 13. Quantum Computing
  • 13.1. Quantum Bits
  • 13.2. Multiple Qubit Systems
  • 13.3. Quantum Algorithms
  • 13.4. Quantum Fourier Transform
  • 13.5. Shor’s Factoring Algorithm
  • 13.6. Quantum Key Distribution
  • 13.7. Summary
  • Exercises
  • Chapter 14. Lattice-based Cryptography
  • 14.1. Lattices
  • 14.2. Lattice Algorithms
  • 14.3. GGH Cryptosystem
  • 14.4. NTRU
  • 14.5. Learning with Errors
  • 14.6. Summary
  • Exercises
  • Chapter 15. Code-based Cryptography
  • 15.1. Linear Codes
  • 15.2. Bounds on Codes
  • 15.3. Goppa Codes
  • 15.4. McEliece Cryptosystem
  • 15.5. Summary
  • Exercises
  • Bibliography
  • Index
  • Back cover

  • 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
Review Copy – for publishers of book reviews
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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