CS 6802

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  • Schedule of Classes - September 10, 2024 10:17AM EDT
  • Course Catalog - September 10, 2024 9:19AM EDT
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CS 6802
Lattices: Geometry, Cryptography, and Algorithms

Course information provided by the Courses of Study 2023-2024.

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.

When Offered Spring.

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.

View Enrollment Information

Syllabi: none

  •   Regular Academic Session.  Combined with: MATH 6302

  • 3 Credits Graded

  • 19525 CS 6802   LEC 001

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  • Enrollment is restricted to graduate students only. All others must add themselves to the waitlist during add/drop in January.