MATH 6302

Lattices: Geometry, Cryptography, and Algorithms

Course Description

Course information provided by the 2023-2024 Catalog.

A mathematically rigorous course on lattices. Lattices are periodic sets of vectors in high-dimensional space. They play a central role in modern cryptography, and they arise naturally in the study of high-dimensional geometry (e.g., sphere packings). We will study lattices as both geometric and computational objects. Topics include Minkowski's celebrated theorem, the famous LLL algorithm for finding relatively short lattice vectors, Fourier-analytic methods, basic cryptographic constructions, and modern algorithms for finding shortest lattice vectors. We may also see connections to algebraic number theory.

Prerequisites/Corequisites Prerequisite: MATH 4310 or permission of instructor.

Outcomes

• Demonstrate algorithmic techniques such as basis reduction and sieving.
• Identify Regev's lattice-based public-key encryption scheme.
• Understand how Fourier-analytic methods can be used to study the geometry of lattices.

When Offered Fall.

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