Syllabus

The following is a list of topics that are covered. Click on each topic for links to lecture notes and suggested readings.

Aug 23: Overview of Cryptography

Topics (Lecture Notes)
- Introduction to cryptography
- The one-time pad and perfect secrecy
References
- Boneh-Shoup (Chapter 2.1-2.2)

Aug 25: Semantic Security and PRGs

Topics (Lecture Notes)
- Pseudorandom generators (PRGs)
- Cryptographic definitions and security reductions
- Semantic security
References
- Boneh-Shoup (Chapter 2.3-2.4, 3.1-3.5)

Aug 30: PRG Composition and Hybrid Arguments

Topics (Lecture Notes)
- The Blum-Micali PRG
- Hybrid arguments
- Candidate stream cipher constructions
References
- Boneh-Shoup (Chapter 3.4.2, 3.6, 3.9)

Sep 1: CPA-Security and Pseudorandom Functions

Topics (Lecture Notes)
- Chosen-plaintext security (CPA-security)
- Pseudorandom functions (PRFs) and permutations (PRPs)
- PRF switching lemma
References
- Boneh-Shoup (Chapter 4.1, 4.4, 5.1-5.3)

Sep 6: Using Block Ciphers

Topics (Lecture Notes)
- Block cipher modes of operation (CTR, CBC, ECB)
References
- Boneh-Shoup (Chapter 5.4-5.5)

Sep 8: Block Cipher Constructions

Topics (Lecture Notes)
- Feistel networks, Luby-Rackoff, and DES/3DES
- Even-Mansour cipher
- Advanced Encryption Standard (AES)
References
- Boneh-Shoup (Chapter 4.2, 4.5, 4.7)

Sep 13: Message Integrity

Topics (Lecture Notes)
- Message authentication codes (MACs)
- MACs from PRFs
- Domain extension for PRFs (rawCBC and ECBC)
References
- Boneh-Shoup (Chapter 6)

Sep 15: Collision-Resistant Hash Functions

Topics (Lecture Notes)
- Domain extension for PRFs (CMAC and PMAC)
- Collision resistant hash functions (CRHFs)
References
- Boneh-Shoup (Chapter 6, Chapter 8.1-8.2)

Sep 20: Collision-Resistant Hash Functions

Topics (Lecture Notes)
- Merkle-Damgård construction
- Davies-Meyer compression function
- Hash-based MACs
References
- Boneh-Shoup (Chapter 8.3-8.6)

Sep 22: HMAC, Authenticated Encryption, and CCA Security

Topics (Lecture Notes)
- Hash-based MACs: HMAC and HKDF
- Authenticated encryption and CCA-security
References
- Boneh-Shoup (Chapter 8.7, Chapter 9.1-9.3)

Sep 27: Authenticated Encryption

Topics (Lecture Notes)
- Authenticated encryption wtih associated data
- One-time MACs and Carter-Wegman MACs
- Examples: Poly1305 and AES-GCM
References
- Boneh-Shoup (Chapter 9.1-9.7)

Sep 29: Symmetric Cryptography through One-Way Functions

Topics (Lecture Notes)
- One-way functions (OWFs)
- Hard-core bits and Goldreich-Levin
References
- Boneh-Shoup (Chapter 3.4)

Oct 4: Secure Key Agreement and Prime-Order Groups

Topics (Lecture Notes)
- Secure key-agreement protocols
- Merkle puzzles
- Prime-order groups: definitions and properties
References
- Boneh-Shoup (Chapter 10.4-10.5, 10.8)

Oct 6: The Discrete Logarithm Problem

Topics (Lecture Notes)
- Computational problems over prime-order groups
- Discrete log, CDH, and DDH
- Concrete instantiations of discrete log groups
References
- Boneh-Shoup (Chapter 10.4-10.5)

Oct 11: Problem Session (Review of Prime-Order Groups)

Oct 13: Public-Key Encryption

Topics (Lecture Notes)
- Diffie-Hellman key exchange
- Public-key encryption
- ElGamal encryption
References
- Boneh-Shoup (Chapter 11.2-11.3, 11.5)

Oct 18: PRFs from Discrete Log

Topics (Lecture Notes)
- Random self-reducibility of discrete log and DDH
- Oblivious PRFs from DDH
- The random oracle model
References
- Boneh-Shoup (Chapter 8.10, 11.7)

Oct 20: Introduction to Composite-Order Groups

Topics (Lecture Notes)
- Digital signatures
- Composite-order groups: definitions and properties
- The RSA trapdoor permutation
References
- Boneh-Shoup (Chapter 10.2-10.3, 13.1)

Oct 25: Public-Key Cryptography from RSA

Topics (Lecture Notes)
- Security of RSA-FDH in the random oracle model
- PKCS1 signatures
- Insecurity of textbook RSA
References
- Boneh-Shoup (Chapter 11.4, 13.2-13.4)

Oct 27: PKE from RSA and TLS

Topics (Lecture Notes)
- Public-key encryption from RSA
- Certificates and the public-key infrastructure (PKI)
- Transport Layer Security (TLS)
References
- Boneh-Shoup (Chapter 12.8, 21.1, 21.10)

Nov 1: Authenticated Key Exchange

Topics (Lecture Notes)
- Authenticated key-exchange protocols: constructions and attacks
References
- Boneh-Shoup (Chapter 21.1-21.6)

Nov 3: Identification Protocols

Topics (Lecture Notes)
- Identification protocols and threat models
- Password storage and management
- One-time passwords (SecurID, TOTP, S/Key)
- Challenge-response authentication and active security
References
- Boneh-Shoup (Chapter 18.1-18.6)

Nov 8: Zero-Knowledge Proofs

Topics (Lecture Notes, Video)
- Proof systems
- Interactive proofs
- Defining zero knowledge and the simulation paradigm
References
- Boneh-Shoup (Chapter 20.1)
- The Knowledge Complexity of Interactive Proof Systems by Shafi Goldwasser, Silvio Micali, and Charles Rackoff

Nov 10: Zero-Knowledge for NP

Topics (Lecture Notes, Video)
- Zero knowledge proofs for NP
- Bit commitments from PRGs
References
- Boneh-Shoup (Chapter 19.1)

Nov 15: Proofs of Knowledge

Topics (Lecture Notes)
- Proofs of knowledge
- Schnorr's proof of knowledge of discrete log
- Proving relations in the exponent
References
- Boneh-Shoup (Chapter 19.1-19.3)

Nov 17: Non-Interactive Proofs and ECDSA

Topics (Lecture Notes)
- The Fiat-Shamir heuristic
- Schnorr signatures and (EC)DSA signatures
References
- Boneh-Shoup (Chapter 20.3)

Nov 22: Thanksgiving Holidays (No Class)

Nov 24: Thanksgiving Holidays (No Class)

Nov 29: Post-Quantum Cryptography

Topics (Lecture Notes)
- Implications of quantum computing on cryptography
- Signatures from one-way functions (Lamport signatures)
References
- Boneh-Shoup (Chapter 14.1-2)

Dec 1: Post-Quantum Key Exchange and Lattices

Topics (Lecture Notes)
- The learning with errors (LWE) assumption
- Public-key encryption from LWE
- Key agreement from LWE
References
- A Decade of Lattice Cryptography, by Chris Peikert (Chapter 4.2, 5.2)

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