I am a last-year master student in pure mathematics and I am working on my thesis. I am working on a connection between lattice-based encryption and Ring LWE and between Ring LWE and Homomorphic encryption. For the second part, I manage to find an appropriate paper to provide me with some information. However, with the connection of the lattice-based encryption and LWE things seems to be messier. Apart from the assumptions of LWE that we have seen in a course of mine (search-LWE and decisional-LWE) I was able to find a Regev's definition where it presents that LWE is a sequence of approximations and the problem is to find the suitable vector to solve those approximations and also that this problem can be extended in the R-LWE to polynomials. I was also able to find a matrix form of the LWE definition. So let's say that I can understand how these three parts are connected, I still don't see how to connect them with lattices, so I kept searching. In many papers, I found that the hardness of the lattice-based problems, Shortest Vector Problem (SVP) and Closest Vector Problem (CVP), is connected with the LWE but nothing more. So I was wondering if anyone is familiar with any book/paper that explains how lattice-based cryptography is connected with LWE and explains the structure of R-LWE or at least guides me to a less chaotic path?
Thank you in advance.
