Syllabus

The following is a tentative list of topics that will be covered. Adjustments may be made during the course of the semester. Lecture notes will be available within a few days following each lecture.

Jan 13: Overview of Cryptography

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

Jan 15: 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)

Jan 20: Martin Luther King, Jr. Day (No Class)

Jan 22: Attacks and Reductions in Cryptography

Topics (Lecture Notes)
- Examples of attacks and security reductions
- Security of a stream cipher
- Introduction to hybrid arguments
References
- Examples of Proofs in Cryptography

Jan 27: PRG Composition and Hybrid Arguments

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

Jan 29: CPA-Security and Pseudorandom Functions

Topics
- 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)

Feb 3: Block Ciphers Modes of Operation

Topics
- Counter mode encryption (CTR)
- Cipherblock chaining mode encryption (CBC)
References
- Boneh-Shoup (Chapter 5.4-5.5)

Feb 5: Block Cipher Constructions

Topics
- Even-Mansour cipher
- Advanced Encryption Standard (AES)
References
- Boneh-Shoup (Chapter 4.2, 4.5, 4.7)

Feb 10: Message Integrity

Topics
- Message authentication codes (MACs)
- MACs from PRFs
- Collision resistant hash functions (CRHFs)
References
- Boneh-Shoup (Chapter 6)

Feb 12: Collision-Resistant Hash Functions

Topics
- Merkle-Damgård construction
- Davies-Meyer compression function
- Birthday bound
References
- Boneh-Shoup (Chapter 8.1-8.4)

Feb 17: HMAC, Key Derivation, and Domain Extension

Topics
- Hash-based MACs
- HMAC and HKDF
- Domain extension for PRFs (rawCBC, ECBC, PMAC)
References
- Boneh-Shoup (Chapter 6, 8.5-8.7)

Feb 19: Authenticated Encryption and CCA Security

Topics
- Authenticated encryption and CCA-security
- Authenticated encryption from encrypt-then-MAC
- Authenticated encryption with associated data
References
- Boneh-Shoup (Chapter 9.1-9.7)

Feb 24: Secure Key Agreement and Prime-Order Groups

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

Feb 26: Diffie-Hellman Key Exchange

Topics
- Discrete log, CDH, and DDH
- Concrete instantiations of discrete log groups
- Diffie-Hellman Key Exchange
References
- Boneh-Shoup (Chapter 10.4-10.5)

Mar 3: Public-Key Encryption

Topics
- Elliptic-curve groups
- Public-key encryption
References
- Boneh-Shoup (Chapter 11.2-11.3, 15.1-15.3)

Mar 5: ElGamal Encryption and Digital Signatures

Topics
- ElGamal encryption
- CCA-secure public-key encryption
- Digital signatures
References
- Boneh-Shoup (Chapter 11.5, 12.1-12.2, 12.4, 13.1)

Mar 10: The RSA Problem and Digital Signatures

Topics
- Composite-order groups: definitions and properties
- The RSA problem
- RSA-FDH signatures
- PKCS1 signatures
References
- Boneh-Shoup (Chapter 10.2-10.3, 13.1, 13.3, 13.6)

Mar 12: Exam 1 (In Class)

Mar 17: Spring Break (No Class)

Mar 19: Spring Break (No Class)

Mar 24: Public-Key Cryptography from RSA

Topics
- Public-key encryption from RSA
- RSA-OAEP
- Public-key infrastructure (PKI)
References
- Boneh-Shoup (Chapter 11.4)

Mar 26: Authenticated Key Exchange and TLS

Topics
- Threshold signatures
- Transport Layer Security (TLS)
- Authenticated key exchange (AKE) and TLS 1.3
References
- Boneh-Shoup (Chapter 12.8, 13.8)

Mar 31: Authenticated Key Exchange: Constructions and Attacks

Topics
- AKE protocols: constructions and attacks
- Identification protocols
References
- Boneh-Shoup (Chapter 21.1, 21.10)

Apr 2: Schnorr's Identification Protocol and Fiat-Shamir

Topics
- Schnorr's identification scheme
- Fiat-Shamir heuristic
- Schnorr signatures
- ECDSA signatures
References
- Boneh-Shoup (Chapter 19.1-19.3)

Apr 7: Post-Quantum Cryptography

Topics
- Implications of quantum computing on cryptography
- The learning with errors (LWE) assumption
References
- A Decade of Lattice Cryptography, by Chris Peikert (Chapter 4.2)

Apr 9: Post-Quantum Key Exchange and PKE from LWE

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

Apr 14: Fully Homomorphic Encryption

Topics
- Fully homomorphic encryption (FHE)
- Gentry-Sahai-Waters (GSW) FHE scheme
References
- A Decade of Lattice Cryptography, by Chris Peikert (Chapter 6.1)
- Homomorphic Encryption from Learning with Errors: Conceptually-Simpler, Asymptotically-Faster, Attribute-Based by Craig Gentry, Amit Sahai, and Brent Waters

Apr 16: Short Integer Solutions and Digital Signatures

Topics
- Short integer solutions (SIS) problem
- Lattice trapdoors
- Digital signatures from SIS
References

Apr 21: Identity-Based Encryption from Lattices

Topics
- Identity-based encryption (IBE)
- Gentry-Peikert-Vaikuntanathan IBE scheme
References
- A Decade of Lattice Cryptography, by Chris Peikert (Chapter 4.1, 5.5)
- How to Use a Short Basis: Trapdoors for Hard Lattices and New Cryptographic Constructions, by Craig Gentry, Chris Peikert, and Vinod Vaikuntanathan

Apr 23: Course Wrap-up

Apr 28: Exam 2 (In Class)

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