Foreword I was struggling a lot with lattices in CTF challenges, so I spent some time learning about what are lattices and how to use them in solving CTF Challenges. Great resource to get started A Gentle Tutorial for Lattice-Based Cryptanalysis: highly recommend Lightweight Introduction to Lattices Coppersmith’s Method and Related Applications Finding Small Roots of Bivariate Integer Polynomial Equations: a Direct Approach The following will be about this paper: Recovering cryptographic keys from partial information, by example which heavily employs lattices for recovering cryptographic secrets.