This book provides a clear and accessible introduction to practical mathematical cryptography. The presentation provides a unified and consistent treatment of the most important cryptographic topics, from the initial design and analysis of basic cryptographic schemes towards applications.

1. Symmetric Cryptography. 1.1. Definitions. 1.2. Confidentiality against Eavesdroppers. 1.3. Integrity. 1.4. Confidentiality and Integrity. 1.5. The Key Distribution Problem. 2. Key Exchange and Diffie-Hellman. 2.1. The Diffie-Hellman Protocol. 2.2. Discrete Logarithms. 2.3. Primality Testing. 2.4. Finite Fields. 2.5. Elliptic Curves. 2.6. Active Attacks. 3. Public Key Encryption. 3.1. Definitions. 3.2. Schemes Based On Diffie-Hellman. 3.3. RSA. 3.4. Factoring Integers. 3.5. Lattices. 3.6 Lattice-Based Cryptosystems. 3.7. Lattice Algorithms. 3.8. The Public Key Infrastructure Problem. 4. Digital Signatures. 4.1. Definitions. 4.2. Hash Functions. 4.3. RSA Signatures. 4.4. Schnorr Signatures. 4.5. Hash-Based Signatures. 4.6. Securing Diffie-Hellman. 4.7 The Public Key Infrastructure Problem. 5. Factoring Using Quantum Computers. 5.1. Background. 5.2. Quantum Computation. 5.3. Factoring using a Quantum Computer. 6. Computational Problems. 6.1. Definitions. 6.2. Statistical Distance. 6.3. Diffie-Hellman. 6.4 RSA. 6.5. Lattice Problems. 7. Symmetric Cryptography. 7.1. Defining Security. 7.2. Confidentiality and Underlying Primitives. 7.3. Message Authentication Codes. 7.4. Channels. 7.5. Hash Functions. 7.6. Ideal Models. 8. Public Key Encryption. 8.1 Defining. Security. 8.2. Key Encapsulation Mechanisms. 8.3. Homomorphic Encryption. 8.4. Commitment Schemes. 8.5. Cryptographic Voting. 9. Digital Signatures. 9.1. Defining Securiy. 9.2. Hash and Sign Paradigm. 9.3. Identification Schemes. 9.4. Messaging. 10. Key Exchange. 10.1. Key Exchange Protocols. 10.2. Defining Security. 10.3 Key Exchange from Key Encapsulation. 10.4. Single-Message Key Exchange. 10.5. Single-Sided Authentication. 10.6. Continuous Key Exchange. 11. Arguments. 11.1. Arguments. 11.2 Non-Interactive Arguments. 11.3. Using HVZK. 11.4. Further Useful Arguments. 12. Multi-party computation. 12.1. Secret Sharing. 12.2 Multi-Party Computation. 12.3. Distributed Decryption. 13. Messaging Protocols. 13.1 Messaging Protocols. 13.2. Defining Security. 13.3. Invasive Adversaries. 13.4. Somewhat Anonymous Messaging. 14. Cryptographic Voting. 14.1 Definitions. 14.2. How to Use a Voting Scheme. 14.3. Cast as Intended. 14.4. Coercion Resistance. Index.