I have gone through quite a few articles over the last 12 months in my attempt to get a proper understanding of fully homomorphic encryption (FHE) schemes. The process was somewhat frustrating because most of the articles are either too basic, giving just very high-level intuitions, or too deep, assuming too much background on the part of the reader.
I did benefit tremendously from these two tutorial-style articles, which I recommend reading in sequence and iterate as necessary for those who want to get deep into FHEs.
- A brief survey of Fully Homomorphic Encryption, computing on encrypted data by Quarkslab
- Homomorphic Encryption by Shai Halevi
The latter is part of the edited volume Tutorials on the Foundations of Cryptography: Dedicated to Oded Goldreich, which I also highly recommend.
And in case you find yourself needing to read some prerequisites to read the above, the book An Introduction to Mathematical Cryptography by Jeffrey Hoffstein, Jill Pipher and Joseph H. Silverman should be quite helpful.