Constant-Depth NTT for FHE-Based Private Proof Delegation (pse.dev)

Takamichi Tsutsumi announces a constant-depth construction of the Number Theoretic Transform (NTT) tailored for fully homomorphic encryption (FHE) based private proof delegation. The work shows how to perform the key polynomial/FFT-like linear algebra primitive underlying convolutions and polynomial multiplications in a circuit whose multiplicative depth does not grow with transform size. That constant depth is achieved via new circuit structuring and packing strategies that move complexity into cheap linear (ciphertext-to-ciphertext) operations rather than deep multiplicative chains. This matters because multiplicative depth is the chief bottleneck in leveled FHE: depth determines noise growth and the need for expensive bootstrapping. A constant-depth homomorphic NTT lets large polynomial operations be executed under encryption with far less bootstrapping, lower latency, and smaller noise budgets—directly benefiting FHE-backed private proof delegation and ZK workflows that rely on polynomial arithmetic (e.g., polynomial commitments, arithmetization of circuits, and homomorphic proof aggregation). Practically, this could make FHE+ZKP hybrid protocols much more efficient and scalable, enabling larger delegated proofs, cheaper server-side computation, and tighter integration between encrypted computation and zero-knowledge proof generation.