Syllabus

Topics (Lecture Notes, Video)

• Introduction to cryptography

• The one-time pad and perfect secrecy

References

• Boneh-Shoup (Chapter 2.1-2.2)

Topics (Lecture Notes, Video)

• Pseudorandom generators (PRGs)

• Cryptographic definitions and security reductions

References

• Boneh-Shoup (Chapter 2.3-2.4, 3.1-3.5)

Topics (Lecture Notes, Video)

• Semantic security

• The Blum-Micali PRG

• Hybrid arguments

References

• Boneh-Shoup (Chapter 3.4.2)

Topics (Lecture Notes, Video)

• Candidate stream cipher constructions

• Chosen-plaintext security (CPA-security)

• Pseudorandom functions (PRFs) and permutations (PRPs)

• PRF switching lemma

References

• Boneh-Shoup (Chapter 3.6, 3.9, 4.1, 4.4, 5.1-5.3)

Topics (Lecture Notes, Video)

• Block cipher modes of operation (CTR, CBC, ECB)

References

• Boneh-Shoup (Chapter 5.4-5.5)

Topics (Lecture Notes, Video)

• Even-Mansour cipher

• Advanced Encryption Standard (AES)

• Optional: Feistel networks, Luby-Rackoff, and DES/3DES

References

• Boneh-Shoup (Chapter 4.2, 4.5, 4.7)

Topics (Lecture Notes, Video)

• Message authentication codes (MACs)

• MACs from PRFs

• Domain extension for PRFs (rawCBC and ECBC)

References

• Boneh-Shoup (Chapter 6)

Topics (Lecture Notes, Video)

• Domain extension for PRFs (CMAC and PMAC)

• Collision resistant hash functions (CRHFs)

References

• Boneh-Shoup (Chapter 6, Chapter 8.1-8.2)

Topics (Lecture Notes, Video)

• Generic attacks on collision-resistant hash functions: birthday bound and Pollard rho

• Merkle-Damgård construction

• Davies-Meyer compression function

References

• Boneh-Shoup (Chapter 8.3-8.6)

Topics (Lecture Notes, Video)

• Hash-based MACs: HMAC and HKDF

• Authenticated encryption and CCA-security

References

• Boneh-Shoup (Chapter 8.7, Chapter 9.1-9.3)

Topics (Lecture Notes, Video)

• Constructing authenticated encryption

• 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)

Topics (Lecture Notes, Video)

• One-way functions (OWFs)

• Hard-core bits and Goldreich-Levin

References

• Boneh-Shoup (Chapter 3.4)

Topics (Lecture Notes, Video)

• Secure key-agreement protocols

• Merkle puzzles

• Black-box separations

• Prime-order groups: definitions and properties

References

• Boneh-Shoup (Chapter 10.4-10.5, 10.8)

• Limits on the Provable Consequences of One-way Permutations by Russel Impagliazzo and Steven Rudich

Topics (Lecture Notes, Video)

• 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)

Topics (Lecture Notes, Video)

• Diffie-Hellman key exchange

• Public-key encryption

• ElGamal encryption

References

• Boneh-Shoup (Chapter 11.2-11.3, 11.5)

Topics (Lecture Notes, Video)

• Random self-reducibility of discrete log and DDH

• Oblivious PRFs from DDH

• The random oracle model

References

• Boneh-Shoup (Chapter 8.10, 11.7)

Topics (Lecture Notes, Video)

• Digital signatures

• Composite-order groups: definitions and properties

• The RSA trapdoor permutation

References

• Boneh-Shoup (Chapter 10.2-10.3, 13.1)

Topics (Lecture Notes, Video)

• Signatures from RSA (RSA-FDH), PKCS1 signatures

• Insecurity of textbook RSA

• Public-key encryption from RSA

References

• Boneh-Shoup (Chapter 11.4, 13.2-13.4)

Topics (Lecture Notes, Video)

• Certificates and the public-key infrastructure (PKI)

• Authenticated key-exchange protocols: constructions and attacks

• Transport Layer Security (TLS)

References

• Boneh-Shoup (Chapter 21.1-21.6, 21.10)

Topics (Lecture Notes, Video)

• Implications of quantum computing on cryptography

• Signatures from one-way functions (Lamport signatures)

References

• Boneh-Shoup (Chapter 14.1-2)

Topics (Lecture Notes, Video)

• Winternitz signatures

• Merkle signatures

References

• Boneh-Shoup (Chapter 14.3, 14.6)

Topics (Lecture Notes, Video)

• 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)

Topics (Lecture Notes, Video)

• Definition of proof systems

• The class AM and IP

• IP = PSPACE

References

• Arora-Barak (Chapter 8)

Topics (Lecture Notes, Video)

• Defining zero knowledge and the simulation paradigm

• Zero knowledge for NP

References

• Boneh-Shoup (Chapter 20.1)

• The Knowledge Complexity of Interactive Proof Systems by Shafi Goldwasser, Silvio Micali, and Charles Rackoff

Topics (Lecture Notes, Video)

• Proofs of knowledge

• Schnorr's proof of knowledge of discrete log

• Proving relations in the exponent

References

• Boneh-Shoup (Chapter 19.1-19.3)

Topics (Lecture Notes, Video)

• The Fiat-Shamir heuristic

• Schnorr signatures and (EC)DSA signatures

References

• Boneh-Shoup (Chapter 20.3)

Topics (Lecture Notes, Video)

• Merkle trees

• Probabilistically-checkable proofs (PCPs)

• Kilian's protocol and CS proofs

References

• A Note on Efficient Zero-Knowledge Proofs and Arguments by Joe Kilian

Topics (Lecture Notes, Video)

• Linear PCPs

• SNARGs from linear PCPs

• Quadratic arithmetic programs

References

• Succinct Non-Interactive Arguments via Linear Interactive Proofs by Nir Bitansky, Alessandro Chiesa, Yuval Ishai, Rafail Ostrovsky, and Omer Paneth