LLL Algorithm

Intro 0:00
The Algortihm 0:45
2D Example 6:30
3D Example 9:41
Algebraic Number Approximation 15:25
Cryptography 22:07
Mertens Conjecture 26:50

Lenstra-Lenstra-Lovasz (LLL) Lattice Basis Reduction Algorithm. A very useful algorithm for computational number theory.

Final project for M602 Algebraic Number Theory at Indiana University.

Special thanks to Grant Sanderson for creating the manim library, and to Jeff Suzuki for illuminating videos on the algorithm!

[pearbq]

At 7:51, the power of 2 should be placed at mu_[1, 0] instead of outside the bracket right?

[upliftingspirit]

Spent a couple hours to find resources on how these lattice reduction algorithms work. At last, found this video! Great job !!!

[alexzhu]

I have to do some tedious assignment on the Coppersmith attack on RSA which involves the LLL algorithm, much love from France

[charliekenney]

Excellent video. When "s" appears alone in Hungarian, it's often pronounced as a voiceless palato-alveolar fricative ("sh"). When "sz" appear together, as in Lovász's name, the noise they make is just "s" (as used in English). This is the reverse of the Polish, and may be confusing. "Low voss".

[mastercraft]

Nice work! Was just looking for a explanation of this algorithm to implement an Integer relation algorithm

[tuongnguyen]

How to do the algebraic number approximation in Matlab or Python or any other tools ?

[haoyu]

12:51 mu_[1, 0] = 1/3 and the rhs should be 0.52? Anyways this is a very well made and helpful video, thank you :)

[ahmedalbyati]

Please if can you help me I need a program algorithm about my design and evaluate cryptosystem based on braid groups

[brianbreitsch]

Thank you for this nice video! This was really helpful! Is this done with manim?

[nishinoya]

Can you put link of jeff Suzuki video of explaining Lavash condition?

[Barwani]

Hello! Could you please explain what the purpose of the line:
bk = bk - [uk, j]bj
is please?

[miikavuorio]

This clearly has that 3b1b look, did you create it with his python library?