Course Details
- Instructor: Akshayaram Srinivasan
- Lecture Timings: Tuesday and Thursday at 2 - 3.30 PM.
- Prerequisites: Basics of discrete probability and linear algebra.
- Assignments and Lecture Notes: Piazza
References
- Lattices in Computer Science by Oded Regev.
- Lattices, Learning with Errors and Post-Quantum Cryptography by Vinod Vaikuntanathan.
- Lattices in Cryptography by Chris Peikert.
- Lattice-based Cryptosystems by Dakshita Khurana.
- A Decade of Lattice Cryptography by Chris Peikert.
Course Summary
| Date | Topics Covered | References |
|---|---|---|
| 09/08/22 | Introduction to Lattices | Regev: Lecture-1 |
| 16/08/22 | Minkowski's Theorem LLL Reduced Basis |
Regev: Lecture-1 Regev: Lecture-2 |
| 18/08/22 | LLL Algorithm Babai's Nearest Plane Algorithm |
Regev: Lecture-2 Regev: Lecture-3 |
| 23/08/22 | Attacks on Low Exponent RSA with Deterministic Padding | Regev: Lecture-4 |
| 25/08/22 | SIS assumption Collision-Resistance from SIS |
Peikert: Chapter-4.1 Micciancio-Regev: Worst-case to Average-case Reductions |
| 30/08/22 | LWE assumption Secret-Key Encryption from LWE |
Peikert: Chapter-4.2 Regev: Learning with Errors Survey |
| 06/09/22 | Completing proof of SKE Public-Key Encryption from LWE |
Vaikuntanathan: Lecture-1 Leftover Hash Lemma |
| 08/09/22 | Dual-Regev Encryption GSW Fully Homomorphic Encryption |
Vaikuntanathan: Lecture-1 Khurana: Lecture-11 Khurana: Lecture-12 |
| 13/09/22 | Bootstrapping Applications of FHE: PIR and Secure Computation |
Khurana: Lecture-11 Gentry: Computing Arbitrary Functions of Encrypted Data |
| 20/09/22 | Trapdoor Functions Introduction to Lattice Trapdoors |
Jain: Chapter-6 Vaikuntanathan: Lecture-6 |
| 22/09/22 | Type-1 and Type-2 Lattice Trapdoors | Vaikuntanathan: Lecture-6 |
| 27/09/22 | Trapdoors for SIS Introduction to Digital Signatures |
Vaikuntanathan: Lecture-6 |
| 29/09/22 | Pre-Image Sampler and Digital Signatures | Halevi-Malkin: SIS-based Signatures Gentry-Peikert-Vaikuntanathan |
| 04/10/22 | Sampling from Discrete Gaussians | Gentry-Peikert-Vaikuntanathan Micciancio-Regev |
| 06/10/22 | Identity-based Encryption | Gentry-Peikert-Vaikuntanathan |
| 11/10/22 | CCA-2 Security from IBE | Boneh-Canetti-Halevi-Katz |
| 13/10/22 | Selective Secure IBE without Random Oracles | Cash-Hofheinz-Kiltz-Peikert |
| 18/10/22 | Attribute-based Encryption | Boneh et al. |
| 20/10/22 | Attribute-based Encryption Contd. | Boneh et al. |
| 25/10/22 | Zero-Knowledge Proofs | Pass-shelat: Chapter-4 Rosen: Introduction to ZK |
| 27/10/22 | Zero-Knowledge Proofs contd. | Pass-shelat: Chapter-4 |
| 1/11/22 | NIZKs in the Random Oracle Model | |
| 3/11/22 | NIZKs from circular-secure LWE | Canetti-Lombardi-Wichs |
| 10/11/22 | NIZKs from LWE | Peikert-Shiehian |
| 15/11/22 | Review Lecture |