From Gentry's blueprint through Ring-LWE, BFV, BGV, CKKS, TFHE, bootstrapping, and practical FHE applications — the mathematics and engineering of computing on ciphertexts.
Homomorphic encryption lets a server compute on data it cannot see. This course builds the complete mathematical and engineering stack: the hardness of Ring-LWE and noise management, the BFV and BGV schemes for exact integer arithmetic, CKKS for approximate real-number arithmetic, TFHE for Boolean circuits via programmable bootstrapping, the bootstrapping theorem (Gentry 2009), multi-key and threshold FHE, practical FHE libraries (OpenFHE, SEAL, Concrete), and applications in private machine learning, private database queries, genomics, and blockchain.
Built by Lakshya Kumar
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Sign in to applyComplete all modules, then submit the required number of capstone projects. Each must earn a passing rating from an admin reviewer.
Choose one: implement a private mean/variance computation for 100 floats using CKKS (OpenFHE); implement a private comparison circuit for 8-bit integers using TFHE (Concrete); or implement a private voting tally with threshold decryption using Paillier. Include benchmarks, a noise-budget analysis, and a 5-page report on when your chosen scheme is appropriate.
I'm studying Homomorphic Encryption: Ring-LWE hardness and noise management, the BFV scheme for exact integer arithmetic, BGV, CKKS for approximate arithmetic, TFHE for Boolean circuits via programmable bootstrapping, bootstrapping (Gentry 2009), multi-key FHE, threshold decryption, FHE libraries (OpenFHE, SEAL, Zama Concrete), and applications in private ML, PIR, genomics, and blockchain. Context: 1. My goal: [e.g. "use FHE for private ML inference", "understand TFHE for a blockchain project", "build a privacy-preserving system"] 2. My background: [e.g. "completed Advanced Cryptography module", "engineer wanting to use FHE libraries"] 3. One concept to understand: [e.g. "how does CKKS rescaling work?", "when should I choose TFHE vs BFV?"] Answer: - For (3): the precise mathematical explanation and a Python snippet showing the effect. - What's the minimal path through this course for my goal? - What FHE scheme and library for my use case, and what are the performance implications?
Build a service that computes statistics (mean, variance, count) on encrypted data without seeing the plaintext. Use BFV or CKKS for the encryption layer; clients encrypt + upload; server aggregates + returns encrypted result. Benchmark for 10k records.
Implement a 2-party PSI protocol: both parties have sets of 100k items; compute the intersection without revealing non-intersecting items. Compare PSI-via-FHE to a hash-based PSI; document the trade-offs.
Run inference for a small ML model (logistic regression or 2-layer neural net) under FHE. Client encrypts input; server runs inference; client decrypts the result. Benchmark the latency for one prediction; document the accuracy degradation vs floating-point.
Take a real-world privacy use case (e.g., census-style aggregate queries). Implement two solutions: differential-privacy (with Laplace noise) and FHE. Compare query accuracy, latency, and trust assumptions. Produce a recommendation memo for which technique to ship.
The TFHE paper. Read after Module 7.