Schedule
The following is a tentative list of topics that may be covered. Some adjustments to the topics may occur over the course of the semester. Click on each topic for links to lecture notes and suggested readings.
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Topics
Introduction to cryptography
The one-time pad and perfect secrecy
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Pseudorandom generators (PRGs)
Cryptographic definitions and security reductions
Semantic security
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Examples of attacks and security reductions
Security of a stream cipher
Introduction to hybrid arguments
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The Blum-Micali PRG
Hybrid arguments
Stream cipher constructions
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Chosen-plaintext security (CPA-security)
Pseudorandom functions (PRFs) and permutations (PRPs)
PRF switching lemma
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Counter mode encryption (CTR)
Cipher block chaining mode encryption (CBC)
Introduction to message integrity
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Message authentication codes (MACs)
MACs from PRFs
Collision-resistant hash functions (CRHFs)
Birthday bound
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Merkle-Damgård construction
Davies-Meyer compression function
Hash-based MACs (HMAC)
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Domain extension for PRFs
rawCBC, ECBC, CMAC, and PMAC
Authenticated encryption
CCA-security
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Authenticated encryption from encrypt-then-MAC
One-time MAC and the Carter-Wegman MAC
Galois counter mode (GCM)
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Authenticated encryption with associated data
Even-Mansour cipher
Advanced Encryption Standard (AES)
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One-way functions
Merkle puzzles and key-agreement protocols
Prime-order groups: definitions and properties
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Discrete log, CDH, and DDH
Concrete instantiations of discrete log groups
Diffie-Hellman key exchange
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Public-key encryption
ElGamal encryption
CCA-secure public-key encryption
Hybrid encryption
Elliptic-curve groups
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Digital signatures
One-way functions
Lamport signatures
Merkle signatures
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Identification schemes
Signatures from identification schemes
Schnorr's identification scheme
Digital signature algorithm (DSA)
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Authenticated key exchange (AKE)
Transport Layer Security (TLS)
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Interactive proofs
Defining zero knowledge and the simulation paradigm
Zero-knowledge proof for 3-coloring
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Implications of quantum computing on cryptography
Introduction to lattices
Short integer solutions (SIS) problem
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Short integer solutions (SIS) problem
Collision-resistant hash functions from SIS
The leftover hash lemma (LHL)
Commitments from SIS
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Inhomogeneous SIS and gadget trapdoors
Lattice-based signatures in the random oracle model
Preimage-sampleable trapdoor functions
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Lattice-based signatures in the random oracle model
The learning with errors (LWE) assumption
Symmetric encryption from LWE
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Public-key encryption from LWE
Somewhat homomorphic encryption (SWHE)
The Gentry-Sahai-Waters (GSW) FHE scheme
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Bootstrapping SWHE to FHE
Key agreement from LWE
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Private information retrieval (PIR)