Explore the intricacies of Fully Homomorphic Encryption (FHE) in this 45-minute talk by Rachel Player from Sorbonne Université. Delve into the security aspects of lattice-based cryptography, focusing on Ring Learning with Errors (Ring-LWE) problem-based FHE schemes. Examine the selection of secure Ring-LWE parameters and compare differing estimates used in NIST post-quantum cryptography process submissions. Investigate the impact of encoding raw data into plaintext space on efficiency, and learn about a Fan-Vercauteren FHE scheme variant that offers a convenient plaintext space for encoding and enables higher-depth circuit evaluation. Gain insights into topics such as the Learning with Errors problem, Bounded Distance Decoding, security arguments for the FV scheme, algorithms for solving LWE, and the NIST post-quantum standardization process.