# Is there a source(book, thesis, paper) that explains Lattice basis reduction algorithms (LLL, HKZ) and provides an in depth analysis of the same?

I want to give a slight background about me: I've Bachelors in Computer Engineering and I've been interested in Cryptography since my college days and have been following the field ever since. I'm also actively following the state-of-the-art, particularly in the area of Lattice-based-cryptography. I'm independently researching in this field and have been particularly interested in Lattice basis reduction algorithms and their involvement in cryptanalysis. I've been trying to get a feel of Lattice basis reduction algorithms since somedays and would like to share the timeline that I followed up until this point.

1. Motivation for why lattices are important from a cryptographers standpoint.
2. Introduction to Lattices, sub-lattices and related terminology.
3. Hard Problems in Lattice based Cryptography
4. Lattice basis Reduction Algorithms
• Q1. I'm stuck at HKZ and haven't been able to get a feel of these concepts in particular. I haven't found some resources that could possibly help me in understanding it a bit better.
• Q2. I have usually found problems in 2 dimensions. Is there a resource where someone has worked out on problems for a few more dimensions (maybe, 3,4,5 and 6)?

The resources that I've been taking help from are:

1. LLL Algorithm
2. Chapter 10 and 13 of Algorithmic Cryptanalysis by Antoine Joux
3. Regev's Lecture Notes
4. Also from Nigel Smart's Crypto Made Simple for the basics of Lattice based Cryptography.
5. A Complete Analysis of the BKZ Lattice Reduction Algorithm