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

16

Public-Key Cryptography

Digital Signatures

Chapter Contents

Chapter Contents

16.1.Security definitions for digital signatures
16.2.Signatures from RSA
16.2.1.Textbook RSA signatures
16.2.2.RSA-PSS
16.2.3.Self-reducibility
16.2.4.Security proof for RSA-PSS
16.2.5.A rant
16.2.6.Looking Ahead
16.3.Common signature idioms
16.3.1.Hash-then-sign
16.3.2.Certificates and chains
Exercises
Chapter Notes & References

Previous Chapter15. RSA
Next Chapter17. Encrypted Messaging and Ratcheting

This chapter will become available online in July 2026.

Previous Chapter15. RSA
Next Chapter17. Encrypted Messaging and Ratcheting

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.

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