The Joy of Cryptography

Contents
1. Unconditional Cryptography
  
  One-Time Pad & the Provable Security Mindset
  
  Rudiments of Provable Security
  
  ☆ Secret Sharing
2. Pseudorandomness
  
  Modern Computational Cryptography
  
  Pseudorandom Generators
  
  Pseudorandom Functions
  
  Pseudorandom Permutations
3. Symmetric-Key Encryption
  
  Chosen-Plaintext Attacks Against Encryption
  
  Chosen-Ciphertext Attacks Against Encryption
4. Hashing
  
  Collision-Resistant Hash Functions
  
  ☆ Universal Hash Functions
  
  Random Oracles and Other Idealized Models
5. Asymmetric-Key Cryptography
  
  Key Exchange
  
  Public-Key Encryption
  
  RSA
  
  Digital Signatures
6. Advanced Topics
  
  Encrypted Messaging & Ratcheting
  
  Authenticated Key Exchange
  
  Zero-Knowledge Proofs
  
  Post-Quantum Cryptography
7. Appendix
  
  Math Review
  
  Binary Finite Fields
  
  Bibliography
About

11

Hashing

☆ Universal Hash Functions

Chapter Contents

Chapter Contents

11.1.Defining universal hash functions
11.2.Universal hash paradigm for PRFs
11.2.1.Handling non-block-aligned data
11.3.CBC-MAC is a UHF
11.3.1.Variable-input PRFs using CBC-MAC as a UHF
11.4.Poly-UHF: An unconditionally secure UHF
11.4.1.GHASH and GCM encryption
Exercises
Chapter Notes & References

Previous Chapter10. Collision-Resistant Hash Functions
Next Chapter12. Random Oracles and Other Idealized Models

This chapter will become available online in July 2026.

Previous Chapter10. Collision-Resistant Hash Functions
Next Chapter12. Random Oracles and Other Idealized Models

The Joy of Cryptography

An undergraduate-level textbook that introduces students to the fundamentals of provable security.

About this Book

Acknowledgements

This book is possible with support from the National Science Foundation and the Open Textbook Initiative at Oregon State University.

Unconditional Cryptography
Pseudorandomness
Symmetric-Key Encryption
1. Chosen-Plaintext Attacks Against Encryption
2. Chosen-Ciphertext Attacks Against Encryption
Hashing
Asymmetric-Key Cryptography
Advanced Topics
Appendix

The Joy of Cryptography is by Mike Rosulek and made available under the Creative Commons BY-NC-SA 4.0 license.

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