Partial Number Theoretic Transform Masking in Post Quantum Cryptography Hardware: A Security Margin Analysis
For designers of post-quantum cryptography hardware, this work provides a methodology to audit and improve the security margin of partially masked NTT accelerators against side-channel attacks.
The paper evaluates the security claims of Adams Bridge, a partially masked hardware accelerator for ML-DSA and ML-KEM, finding that its shuffling provides only 6 bits of entropy per layer instead of the claimed 296 bits, and that full-scale belief propagation achieves 100% coefficient recovery on a single masked layer. The authors propose a countermeasure of strategically masking 3 consecutive mid-layers with 43% overhead to defeat soft-analytical attacks.
Adams Bridge, a hardware accelerator for ML-DSA and ML-KEM designed for the Caliptra root of trust, masks 1 of its Inverse Number Theoretic Transform (INTT) layers and relies on shuffling for the remainder, claiming per-butterfly Correlation Power Analysis (CPA) complexities of 2^46 (ML-DSA) and 2^96 (ML-KEM). We evaluate these claims against published side-channel literature across seven analysis tracks with confidence-rated evidence. Register-Transfer Level (RTL) analysis confirms that the design's Random Start Index (RSI) shuffling provides 6 bits of entropy per layer (64 orderings) rather than the 296 bits of a full random permutation assumed in its scaling argument, with effective margins below the designers' estimates. A soft-analytical attack pipeline demonstrates a 37-bit enumeration reduction, independent of Belief Propagation (BP) gains, quantifying the attack-model gap without achieving key recovery. Full-scale BP on the complete INTT factor graph achieves 100% coefficient recovery over the single-layer baseline, resolving whether BP gains scale to production-size Number Theoretic Transform (NTT) structures. A genie-aided information-theoretic bound shows observations contain sufficient mutual information for full recovery at SNRxN as low as 15. Layer-ablation analysis identifies four necessary conditions governing BP convergence. Observation topology, not count, determines recovery: 4 evenly spread layers achieve 100% while 4 consecutive layers achieve 0%, yielding a practical countermeasure design tool. Strategic masking of 3 consecutive mid-layers (43% overhead vs. full masking) creates an unrecoverable gap that defeats soft-analytical attacks. We contribute a reusable security margin audit methodology combining RTL verification, epistemic confidence tagging, sensitivity-scenario analysis, and experimental validation applicable to any partially masked NTT accelerator.