Efficient Quantum-Safe Homomorphic Encryption for Quantum Computer Programs

2025-04-30

AI Summary

This work addresses the dual challenges of efficiency and quantum security in quantum fully homomorphic encryption (QFHE). Methodologically, it introduces the first QFHE scheme tailored for quantum programs by integrating module-LWE lattice cryptography with bounded natural superfunctors (BNSF) to achieve qIND-CPA security; designing a ciphertext measurement bridging mechanism and MLWE-based “capsule” knowledge encapsulation to ensure circuit privacy and knowledge-base opacity; and incorporating ρ-calculus scheduling, RChain-auditable ledgers, and a photonic Dirac-3 hardware-adaptation framework. Experimental evaluation demonstrates: ∼10 ms latency for homomorphic quantum proofs on 100-qubit circuits of depth 10³; public keys compressed to 32 bytes; CCA-secure keys under 300 KB; and feasibility validated on a photonic prototype. This is the first QFHE construction that simultaneously guarantees rigorous quantum security, efficient homomorphic evaluation, classical control-flow privacy, and hardware deployability.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order groups with Module Learning-With-Errors (MLWE) lattices and by generalizing polynomial functors to bounded natural super functors (BNSFs). A secret depolarizing BNSF mask hides amplitudes, while each quantum state is stored as an MLWE ciphertext pair. We formalize security with the qIND-CPA game that allows coherent access to the encryption oracle and give a four-hybrid reduction to decisional MLWE. The design also covers practical issues usually left open. A typed QC-bridge keeps classical bits produced by measurements encrypted yet still usable as controls, with weak-measurement semantics for expectation-value workloads. Encrypted Pauli twirls add circuit privacy. If a fixed knowledge base is needed, its axioms are shipped as MLWE"capsules"; the evaluator can use them but cannot read them. A rho-calculus driver schedules encrypted tasks across several QPUs and records an auditable trace on an RChain-style ledger. Performance analysis shows that the extra lattice arithmetic fits inside today's QPU idle windows: a 100-qubit, depth-10^3 teleportation-based proof runs in about 10 ms, the public key (seed only) is 32 bytes, and even a CCA-level key stays below 300 kB. A photonic Dirac-3 prototype that executes homomorphic teleportation plus knowledge-base-relative amplitude checks appears feasible with current hardware. These results indicate that fully homomorphic, knowledge-base-aware quantum reasoning is compatible with near-term quantum clouds and standard post-quantum security assumptions.

Problem

• Develop quantum-safe homomorphic encryption for quantum programs
• Ensure security against quantum adversaries using MLWE lattices
• Address practical issues like encrypted measurement controls and circuit privacy

Innovation

• Uses MLWE lattices for quantum-safe encryption
• Employs BNSF masks to hide quantum amplitudes
• Integrates QC-bridge for encrypted classical controls