Technical report on Homomorphic Encryption (HE), a cryptographic method allowing computation directly on encrypted data to protect "data-in-use."

It details the evolution of HE schemes, from Partially Homomorphic Encryption (PHE) to Fully Homomorphic Encryption (FHE), explaining their mathematical underpinnings like the Learning with Errors (LWE) and Ring-LWE (RLWE) problems.

The report also analyzes the application of HE in privacy-preserving machine learning (PPML), highlighting its use in healthcare and finance for tasks like private inference and training, while addressing computational overheads and noise management techniques such as bootstrapping and modulus switching.

Ultimately, the text positions HE as a strategic tool for compliance with regulations like GDPR and HIPAA and a key post-quantum cryptography (PQC) technology for secure data collaboration.