Course Details - Fall 2025
- Instructor: Akshayaram Srinivasan
- Lecture Timings: Monday 11 am - 1 pm
- Location: AB114 (View on Map)
- Office Hours: By appointment.
- Class Discussion: See Piazza for details.
Course Description
Lattices have revolutionized cryptography by enabling constructions of advanced cryptographic primitives that were unimaginable a few years back. In this course, we will study the (i) mathematical properties of lattices, (ii) discuss several lattice problems which we believe are hard (even against quantum computers), and (iii) use these hard problems to construct cryptographic applications. The major focus of this course would be on part (iii), with a particular emphasis on recent results.
Prerequisites
Students are expected to have completed undergraduate-level courses on discrete mathematics, linear algebra, algorithms, and complexity theory. As this course will be theoretical, students are expected to have good mathematical maturity and should be comfortable with writing proofs.
Evaluation
- Scribe Notes (15%)
- Problem Sets (45%)
- Final Project (40%)
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 Schedule
| Date | Topics Covered | Scribe Notes | Additional Reading |
|---|---|---|---|
| Sept 8, 2025 | Short Integer Solutions (SIS) and Collison-Resistant Hashing (CRH) | Lecture-1 | Introduction to Lattices SIS Problem and CRH Optional: Micciancio-Regev'04 |
| Sept 15, 2025 | Learning with Errors (LWE) and Public-key Encryption |
LWE and PKE Search-to-Decision (Lemma 4.1 and 4.2) Optional: Regev's survey of LWE |