Fully Homomorphic Encryption (FHE) Strategy

Abstract

This LP defines Lux Network's Fully Homomorphic Encryption (FHE) strategy, documenting our independent Go-based TFHE implementation built from first principles to avoid patent encumbrance while delivering superior performance and blockchain-native design.

Motivation

Greenfield Implementation

Lux Industries chose to implement TFHE from first principles in Go, based solely on published academic research. This ensures:

1. Independence: No dependencies on third-party FHE implementations
2. Academic Foundation: Built on peer-reviewed cryptographic research
3. Full Control: Complete ownership of our cryptographic stack
4. Blockchain-Native: Designed specifically for blockchain use cases

Specification

1. Independent TFHE Implementation

Repository: github.com/luxfi/tfhe

Key Characteristics:

• Pure Go: No CGO dependencies, compiles anywhere Go runs
• Original Code: Written from scratch, not derived from any existing implementation
• Academic Foundation: Based on peer-reviewed publications only:
  • Chillotti et al. "TFHE: Fast Fully Homomorphic Encryption Over the Torus" (Journal of Cryptology, 2020)
  • Ducas & Micciancio "FHEW: Bootstrapping Homomorphic Encryption in Less Than a Second" (EUROCRYPT 2015)

Technology Stack:

github.com/luxfi/tfhe          <- TFHE operations
    └── github.com/luxfi/lattice   <- Custom lattice crypto library
        └── Standard Go crypto      <- No external dependencies

2. Performance Comparison

Operation	Lux Go TFHE	OpenFHE (CGO)	Advantage
Bootstrap Key Gen	132 ms	2,413 ms	18x faster
Boolean Gate (AND)	51 ms	56 ms	1.10x faster
Boolean Gate (XOR)	51 ms	56 ms	1.10x faster
Encrypt Bit	21 µs	28 µs	1.3x faster
NOT Gate	1.2 µs	1.4 µs	~Same

Platform: Apple M1 Max

3. Blockchain-Native Design

Type	Bits	Use Case
FheBool	1	Boolean flags, comparisons
FheUint8	8	Bytes, small values
FheUint32	32	Standard integers
FheUint64	64	Large integers
FheUint128	128	UUIDs
FheUint160	160	Ethereum addresses
FheUint256	256	EVM word size

4. Patent Portfolio

Lux Industries has filed patent applications for novel innovations developed independently:

Patent ID	Title	Innovation
PAT-FHE-001	Consensus-Integrated Threshold FHE	Decryption shares in consensus votes
PAT-FHE-002	Deterministic FHE RNG	Blockchain-compatible random numbers
PAT-FHE-003	Transaction-Batch Amortized Bootstrapping	Block-level optimization
PAT-FHE-004	Lazy Carry Propagation	Deterministic noise tracking
PAT-FHE-005	Batch DAG Execution	GPU-accelerated FHE ops
PAT-FHE-006	GPU Backend Abstraction	Multi-vendor GPU support
PAT-FHE-007	Packed Device Formats	Memory-efficient ciphertext
PAT-FHE-008	Multi-GPU Coordination	Distributed FHE compute
PAT-FHE-009	Gas Metering	Variable-cost FHE precompiles

5. Licensing Model

Lux Research License with Patent Reservation:

Use Case	License Required	Cost
Research/Academic	✅ Free	$0
Lux Network Mainnet	✅ Free	$0
Lux Network Testnet	✅ Free	$0
Other Commercial	Commercial License	Contact

This model:

• Encourages academic research and peer review
• Protects Lux Network ecosystem
• Prevents competitors from free-riding on our investment
• Mirrors successful models (MySQL, Qt, etc.)

Rationale

Why Not Use Existing Libraries?

1. Patent Risk: [third-party]'s active litigation demonstrates real legal exposure
2. Licensing Uncertainty: Commercial use requires negotiation with uncertain outcomes
3. Dependency Risk: Reliance on third-party codebase for critical infrastructure
4. Performance: Our implementation is faster due to Go's compilation and our optimizations
5. Integration: Native Go enables seamless Lux node integration without CGO complexity

Why Go?

1. Determinism: Critical for blockchain consensus - same inputs produce same outputs
2. Cross-Platform: Single binary deployment, no shared library dependencies
3. Memory Safety: Garbage collection prevents entire classes of vulnerabilities
4. Concurrency: Native goroutines for parallel FHE operations
5. Ecosystem: Matches Lux node implementation language

Academic Basis

Our implementation uses techniques from published academic literature:

• Boolean Gates: FHEW bootstrapping (Ducas & Micciancio, 2015)
• Programmable Bootstrapping: TFHE scheme (Chillotti et al., 2020)
• Ring-LWE: Well-established lattice cryptography

These techniques predate recent patent filings and represent established cryptographic knowledge.

Implementation

fhEVM Architecture

┌─────────────────────────────────────────────────────────────┐
│                      Lux fhEVM Stack                         │
├─────────────────────────────────────────────────────────────┤
│  Solidity Layer (lux/standard/contracts/fhe/)               │
│    ├── FHE.sol      - High-level encrypted types            │
│    ├── FheOS.sol    - Precompile interface                  │
│    └── Tokens/      - ConfidentialERC20, etc.               │
├─────────────────────────────────────────────────────────────┤
│  EVM Precompiles (lux/evm/precompile/contracts/fhe/)        │
│    ├── FheAdd, FheSub, FheMul   - Arithmetic                │
│    ├── FheEq, FheLt, FheGt      - Comparison                │
│    └── FheDecrypt               - Threshold decryption      │
├─────────────────────────────────────────────────────────────┤
│  Go TFHE Library (github.com/luxfi/tfhe)                    │
│    ├── Encryptor    - Public key encryption                 │
│    ├── Evaluator    - Homomorphic operations                │
│    └── Decryptor    - Secret key decryption                 │
├─────────────────────────────────────────────────────────────┤
│  Lattice Primitives (github.com/luxfi/lattice)              │
│    ├── RLWE         - Ring-LWE encryption                   │
│    ├── NTT          - Number theoretic transform            │
│    └── Sampling     - Gaussian/uniform sampling             │
└─────────────────────────────────────────────────────────────┘

KMS Virtual Machine

The K-Chain VM (lux/node/vms/kmsvm) provides:

• Post-quantum key management (ML-KEM)
• Threshold key sharing
• Integration with consensus for decryption

Security Considerations

1. Implementation Security: Code undergoes continuous testing and will receive third-party audit
2. Parameter Security: Using well-studied security parameters from literature
3. Side-Channel Resistance: Constant-time operations where cryptographically necessary
4. Key Management: Threshold scheme prevents single-point-of-failure

Timeline

Date	Milestone
2024-Q3	Initial Go TFHE implementation
2024-Q4	Patent portfolio filed
2024-Q4	Lattice library production-ready
2025-Q1	fhEVM precompiles integrated
2025-Q2	Testnet deployment
2025-Q3	Security audit
2025-Q4	Mainnet activation

Backwards Compatibility

This LP introduces new FHE capabilities and does not affect existing chain functionality. The implementation is additive and opt-in for applications requiring confidential computation.

Security Considerations

FHE implementations must undergo cryptographic audit before mainnet deployment. Key security aspects:

• Parameter selection must ensure adequate security margins
• Key management follows existing chain security practices
• Bootstrapping key generation uses audited random number sources

References

1. Chillotti, I., Gama, N., Georgieva, M., & Izabachène, M. (2020). "TFHE: Fast Fully Homomorphic Encryption Over the Torus." Journal of Cryptology.

2. Ducas, L., & Micciancio, D. (2015). "FHEW: Bootstrapping Homomorphic Encryption in Less Than a Second." EUROCRYPT 2015.

3. Rekt News. (2024, December 23). "Patently Absurd." https://rekt.news/patently-absurd

Copyright (c) 2024-2025 Lux Industries Inc. All rights reserved. Patent rights reserved. See LICENSE for terms.