Lattice Cryptography: What is a Fundamental Region and How to Compute It

In this video, we explore the essential concept of a fundamental region in lattice theory, a key building block for understanding both the geometric and algebraic properties of lattices. We begin by defining what a fundamental region is and why it matters, using simple examples to make the concept clear. From one-dimensional integer lattices to two-dimensional grids, we show how fundamental regions divide space into non-overlapping sections that perfectly fit together when shifted by lattice points. You'll also learn how to calculate the boundaries and volume of a fundamental region using basis vectors, and why these calculations are crucial for understanding lattice cryptography.
Here’s how you can include the reference in your YouTube video description:

**Reference:**

Chris Peikert, *Lattices in Cryptography*, University of Michigan.

#lattice #cryptography #quantumcryptography

**Support This Channel:**
I would greatly appreciate it if you could treat me to a cup of coffee or show support for my channel through any other means. You can do so by visiting:

[RaahdheRaahdhe]

At 2:40 how did we get the range ending with 9.5? May you please explain