## SyllabusThe following is a list of topics that are covered. Click on each topic for links to lecture notes and suggested readings. The scribed lecture notes are available here. ## Jan 19: Introduction to Lattices**Topics**(**Lecture Notes**)Why lattices? Definitions and computational problems
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## Jan 24: Short Integer Solutions (SIS)**Topics**(**Lecture Notes**)Complexity and algorithms for lattice problems The short integer solutions (SIS) problem
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## Jan 26: Cryptographic Constructions from SIS**Topics**(**Lecture Notes**)Collision-resistant hash functions from SIS The leftover hash lemma (LHL) Commitments from SIS
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## Jan 31: Lattice Trapdoors and Digital Signatures**Topics**(**Lecture Notes**)Inhomogeneous SIS and gadget trapdoors Lattice-based signatures in the random oracle model
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## Feb 2: Preimage-Sampleable Trapdoor Functions**Topics**(**Lecture Notes**)Preimage-sampleable trapdoor functions Discrete Gaussians over lattices
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## Feb 7: Discrete Gaussian Sampling**Topics**(**Lecture Notes**)The smoothing parameter Rounded Gaussians vs. discrete Gaussians
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## Feb 9: Discrete Gaussian Sampling (Continued)**Topics**(**Lecture Notes**)Discrete Gaussian sampling over the integers Discrete Gaussian sampling over an arbitrary lattice
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## Feb 14: Learning with Errors (LWE)**Topics**(**Lecture Notes**)The learning with errors (LWE) assumption Public-key encryption from LWE Key exchange from LWE
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## Feb 16: Fully Homomorphic Encryption (FHE)**Topics**(**Lecture Notes**)Somewhat homomorphic encryption (SWHE) The Gentry-Sahai-Waters (GSW) FHE scheme
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## Feb 21: FHE Bootstrapping**Topics**(**Lecture Notes**)Bootstrapping SWHE to FHE Bootstrapping the GSW encryption scheme
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## Feb 23: Lattice-Based Key Exchange**Topics**(**Lecture Notes**)Key exchange from LWE
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## Feb 28: Homomorphic Signatures**Topics**(**Lecture Notes**)Homomorphic signatures Lattice homomorphisms
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## Mar 2: Homomorphic Signatures and Commitments**Topics**(**Lecture Notes**)Context-hiding for homomorphic signatures Homomorphic commitments
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## Mar 7: Homomorphic Commitments**Topics**(**Lecture Notes**)Dual-mode homomorphic commitments Designated-prover NIZKs
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## Mar 9: Attribute-Based Encryption (ABE)**Topics**(**Lecture Notes**)Dual Regev encryption Attribute-based encryption (ABE)
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## Mar 14: Spring Break (No Class)## Mar 16: Spring Break (No Class)## Mar 21: Attribute-Based Encryption (ABE)**Topics**(**Lecture Notes**)Attribute-based encryption Punctured trapdoors
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## Mar 23: Predicate Encryption (PE)**Topics**(**Lecture Notes**)Predicate encryption The dual-use approach
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## Mar 28: Functional Encryption (FE)**Topics**(**Lecture Notes**)Functional encryption Garbled circuits
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## Mar 30: Succinct Functional Encryption**Topics**(**Lecture Notes**)Functional encryption from public-key encryption Succinct FE from garbled circuits, ABE and FHE
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## Apr 4: Designated-Verifier NIZKs**Topics**(**Lecture Notes**)Blum's protocol for graph Hamiltonicity One-time NIZK from PKE
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## Apr 6: Reusable Designated-Verifier NIZKs**Topics**(**Lecture Notes**)Reusable designated-verifier NIZKs from ABE
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## Apr 11: Correlation Intractability and NIZKs**Topics**(**Lecture Notes**)Correlation-intractable hash functions NIZKs from circular-secure FHE
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## Apr 13: NIZKs from LWE**Topics**(**Lecture Notes**)Correlation-intractable hash functions from LWE NIZKs from LWE
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## Apr 18: Multi-Key Fully Homomorphic Encryption**Topics**(**Lecture Notes**)Multi-key FHE
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## Apr 20: Homomorphic Secret Sharing (HSS)**Topics**(**Lecture Notes**)Secret sharing Homomorphic secret sharing
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## Apr 25: Distributed Point Functions (DPFs)**Topics**(**Lecture Notes**)Function secret sharing Distributed point functions DPFs from one-way functions Using DPFs for private database queries
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## Apr 27: Guest Lecture – Brent Waters## May 2: Private Information Retrieval (PIR)**Topics**(**Lecture Notes**)Private information retrieval (PIR) Single-server PIR from homomorphic encryption Ring learning with errors (RLWE)
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## May 4: Course Wrapup: Lattices and Beyond |