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

19

Advanced Topics

Zero-Knowledge Proofs

Chapter Contents

Chapter Contents

19.1.The Schnorr identification protocol
19.2.Sigma protocols
19.3.More examples of sigma protocols
19.3.1.Proof of discrete log equality
19.3.2.Proving ANDs and ORs
19.4.Noninteractive proofs and signatures
19.4.1.The Fiat-Shamir transformation
19.4.2.Schnorr signatures
Exercises
Chapter Notes & References

Previous Chapter18. Authenticated Key Exchange
Next Chapter20. Post-Quantum Cryptography

This chapter will become available online in July 2026.

Previous Chapter18. Authenticated Key Exchange
Next Chapter20. Post-Quantum Cryptography

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 Creative Commons CC-BY-ND-NC license.

Site design by Nicholas Rougeux