Overview of Major Fully Homomorphic Encryption (FHE) Schemes

Main FHE Schemes and Their Traits

BGV (Brakerski–Gentry–Vaikuntanathan)

• Type: Exact integer arithmetic (mod t)
• Noise management: Relies on modulus switching to control noise growth
• Use case: Secure computation over integers with good performance for deep circuits
• Trait: Flexible parameter selection, supports leveled and bootstrapped modes

CKKS (Cheon–Kim–Kim–Song)

• Type: Approximate arithmetic over complex numbers
• Noise management: Rescaling operation to maintain precision
• Use case: Privacy-preserving machine learning, statistics, signal processing
• Trait Supports controlled precision loss, trades exactness for efficiency

BFV (Brakerski–Fan–Vercauteren)

• Type: Exact integer arithmetic (mod t)
• Noise management: Uses relinearization and modulus switching
• Use case: Applications requiring exact integer results (e.g., voting, counters)
• Trait: Conceptually simpler than BGV, popular in Microsoft SEAL

FHEW (Fast Fully Homomorphic Encryption over the Torus)

• Type: Bit-level FHE, boolean gate operations
• Noise management: Extremely fast bootstrapping (~0.1s per gate in original)
• Use case: Low-latency evaluation of small boolean circuits
• Trait: Pioneered ultra-fast gate bootstrapping, foundation for TFHE, one ciphertext per bit

TFHE (Fast Fully Homomorphic Encryption over the Torus — extended)

• Type: Bit-level FHE, boolean and arithmetic gates
• Noise management: Bootstrapping in tens of microseconds per gate
• Use case: Encrypted decision trees, conditional branching, crypto protocols
• Trait: Industry’s fastest bootstrapping; practical for real-time logic evaluation, one ciphertext per bit