Homomorphic Encryption 101

Fully Homomorphic Encryption (FHE) is a groundbreaking cryptographic advancement that allows computations on encrypted data without decryption, maintaining data privacy throughout the process. Originally conceived in the late 1970s, FHE became a reality with Craig Gentry's 2009 scheme, which introduced bootstrapping to manage noise in ciphertexts. This technique has evolved into two main approaches: bootstrapped schemes, which focus on reducing bootstrapping time, and leveled schemes, which manage noise through parameterized circuits. Zama's work in programmable bootstrapping, particularly with their TFHE cryptosystem, has extended FHE capabilities to efficiently compute homomorphic non-linear functions, such as those found in neural networks. Recent advancements have enabled the evaluation of deep neural networks on encrypted data with improved speed and accuracy, demonstrating FHE's potential for secure cloud applications and privacy protection in machine learning.