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.
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*Reference:*
Chris Peikert, *Lattices in Cryptography*, University of Michigan.
GitHub Repository: [github.com/cpe...](github.com/cpe...)
#lattice #cryptography #quantumcryptography
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[@RaahdheRaahdhe]

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

[@AdvancedMath]

That is incorrect. When -10 is added in the range [-2.5, 2.5) we should have get [-2.5-10, -10+2.5)=[-12.5, -7.5). Sorry about that.

[@RaahdheRaahdhe]

@@AdvancedMath yeah thanks for the clarification

[@Omaavelous]

It is Mumin I love you

[@AdvancedMath]

I love you too Mumin.