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
Topics
Pseudorandom generators (PRGs)
Cryptographic definitions and security reductions
Semantic security
Topics
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
Chosen-plaintext security (CPA-security)
Pseudorandom functions
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Pseudorandom functions (PRFs) and permutations (PRPs)
PRF switching lemma
Counter mode encryption (CTR)
Topics
Counter mode encryption (CTR)
Cipher block chaining mode encryption (CBC)
Introduction to message integrity
Topics
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
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Authenticated encryption
CCA-security
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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Authenticated key exchange (AKE)
Transport Layer Security (TLS)
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Identification schemes
Password-based authentication
Schnorr's identification scheme
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Signatures from identification schemes
Fiat-Shamir transformation
Digital signature algorithm (DSA)
Interactive proofs
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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 gadget matrix
Lattice trapdoors
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Lattice-based signatures in the random oracle model
The learning with errors (LWE) assumption
Symmetric encryption from LWE
Public-key encryption from LWE
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Key agreement from LWE
Identity-based encryption (IBE) from LWE
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Somewhat homomorphic encryption (SWHE)
The Gentry-Sahai-Waters (GSW) FHE scheme
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Private information retrieval (PIR)