CSE 599: Lattices and Lattice-based Cryptography

CSE 599: Lattices and Lattice-based Cryptography (Spring 2022)

General Information

Instructor: Huijia (Rachel) Lin, rachel(at)cs

Time and location:

Class: Monday/Wednesday 10:00am-11:20pm, Location TBA

Office hours:

Rachel Lin: Monday 4:00pm-5:00pm, CSE 652 and on Zoom

Discussion: We are going to use Edstem Board. Notes and reading material will also be posted at Edstem.

Topics

Point Lattices over the reals are remarkably useful in cryptography. Among many others, the Learning With Errors (LWE) assumption has changed the landscape of cryptography in recent years. Nearly every known cryptographic objective, from signatures, non-interactive zero-knowledge, fully homomorphic encryption, to attribute based encryption, can be based on LWE. Lattices is also one of the most widely used bases for developing post-quantum and quantum cryptography, and it is a unique source of computational hardness with worst-case to average-case connections. In this course, we will delve into lattices and lattice-based cryptography. Topics covered, depending on time and interests, may include:

basic properties of lattices,
basic algorithms for attacking lattice problems and LWE,
worst-case to average-case, decision to search, reduction,
basic cryptographic constructions: pseudo-random functions, signatures, chosen-ciphertext secure encryption, etc,
powerful cryptographic constructions: fully homomorphic encryption, attribute-based encryption, constraint pseudo-random function etc,
lattices and quantum computation.

Prerequisite: This class is intended for graduate students or upper level undergraduate CS or Math students. The most important prerequisite is (some) mathematical maturity and familiarity with linear algebra. Students should be ready to read and write (and even enjoy!) mathematical definitions and proofs. Courses in theory of computation and cryptography would help, but are not necessary.

Resources

There is no mandatory textbook. Notes and reading material will be posted on Edstem. Following is a list of great resources to reference to for lattice based cryptography and cryptography in general.

Chris Peikert A Decade of Lattice Cryptography
Vinod Vaikuntanathan Lecture notes for lattice-based cryptography
Boaz Barak. An Intensive Introduction to Cryptography (Recommended! we will follow a similar pace as this class.)
R. Pass and a. shelat. A Course in Cryptography (fun and intuitive lecture notes for an undergrad crypto class, focusing on theory)
O. Goldreich. The Foundations of Cryptography (a thorough and formal textbook on foundations.)
J. Katz and Y. Lindell. Introduction to Modern Cryptography (a textbook, relatively easy entry)
D. Boneh and V. Shoup A Graduate Course in Applied Cryptography (a textbook on applied cryptography)

Grading:

Grading is based on class participation and a final project. For the final project, you can either choose to prove something new or write a short survey on a topic of your choice that will be useful for future research. You are welcomed to discuss project ideas with me.

On-going Pandemic:

We are having this class during an on-going pandemic. If any student feels sick, please do not hesitate to attend the class virtually, or skip the class. If any student has any circumstances, we will accommodate flexibly. Please reach out the instructor and the TA directly. We are here to learn and to support each other.