FHE Overview

Why Existing FHE Schemes Fall Short

Fully Homomorphic Encryption enables computation on encrypted data without decryption. The theoretical breakthrough (Gentry, 2009) has been refined through four generations of schemes, but all share a fundamental bottleneck: bootstrapping — the process of refreshing ciphertext noise to enable further computation. Bootstrapping is the most expensive operation in FHE, typically consuming 80-90% of total computation time.

First generation schemes (Gentry's original) used ideal lattices but suffered from impractical noise growth. Second generation (BGV, BFV) introduced ring-LWE but required complex bootstrapping. Third generation (GSW, TFHE) used approximate eigenvectors but remained slow with gate-by-gate evaluation. Fourth generation (CKKS) enabled approximate arithmetic but introduced precision loss.

None of these approaches can operate within Solana's 400ms block time constraints.

The AFHE Innovation: Eliminating Bootstrapping

AFHE takes a fundamentally different approach. Instead of encrypting data and computing gates on ciphertexts (requiring periodic bootstrapping to manage noise), AFHE precomputes encrypted lookup tables for every operation needed, evaluates functions by table lookup rather than gate-by-gate homomorphic computation, and eliminates noise accumulation because each lookup is a single-step operation.

For a function f(x, y), AFHE precomputes a table T where T[Enc(x)][Enc(y)] = Enc(f(x, y)). At runtime, evaluating f on encrypted inputs requires only a table lookup — constant time, no bootstrapping.

The Trade-off: Storage for Speed

LUT-based FHE trades storage for speed. Precomputed tables for operations over large domains require significant memory. AFHE manages this through domain partitioning, hierarchical table structures, and lazy evaluation.

Security Foundation

AFHE's security reduces to the Multivariate Quadratic (MQ) problem, which is proven NP-hard in the worst case (Garey & Johnson, 1979). Unlike the Learning With Errors (LWE) assumption underlying lattice-based FHE schemes — which is conjectured hard but not proven — MQ-hardness is a proven mathematical result. There is no known efficient quantum attack against the general MQ problem: Shor's algorithm does not apply, and Grover's provides at most a quadratic speedup addressable by standard parameter adjustment. The scheme provides 128-bit post-quantum security.

Performance Profile

The following are internal benchmarks conducted by the AURA engineering team and have not yet been independently reproduced. AFHE achieves approximately 1000x performance improvement over TFHE-based alternatives across standard arithmetic operations. Binary gate evaluation takes approximately 0.01ms (vs 10ms TFHE). 8-bit addition completes in approximately 0.1ms (vs 100ms). Comparison operations take approximately 0.05ms (vs 50ms). 64-bit multiplication completes in approximately 5ms (vs 5000ms). Benchmark methodology, hardware specifications, and reproduction instructions are available in the technical appendix. Independent third-party verification is being pursued. AFHE's performance enables encrypted computation within Solana's block time constraints — something no bootstrapping-based scheme can achieve today.