Paper 2026/1032

When Removing Reductions Goes Wrong: Auditing Reduction Placement in Production ML-DSA Implementations

Abstract

Implementing post-quantum signatures correctly in production cryptographic libraries remains challenging even after standardization. ML-DSA implementations rely on NTT-based polynomial arithmetic with lazy Montgomery reductions, and omitting a reduction may be either a valid optimization or a latent arithmetic defect. In practice, reduction calls are often removed for performance, memory, or embedded-deployment reasons, but the required correctness condition is inter-procedural: a site that appears redundant locally may be load-bearing for a later InvNTT stage. In this work, we present a certificate-backed audit methodology for reduction placement in production ML-DSA implementations. Starting from the conservative pq-crystals topology, our analysis propagates coefficient bounds across the full signing path and classifies reduction sites as redundant or necessary. The key technical ingredient is an exact-integer recovery result for sparse-challenge products, which tightens post-InvNTT bounds from (-Q,Q) to [-τη, τη] and separates safe omissions on sparse-product paths from load-bearing dense-product sites. Applying the methodology to eight ML-DSA libraries, we uncover a previously unreported defect in wolfSSL's memory-optimized WOLFSSL-DILITHIUM-SMALL path, where omitted post-matrix-multiplication reductions cause overflow, non-conformant arithmetic, and signing failure while surviving the implementation's existing KAT tests. The site classifications are backed by replayable SMT-LIB2 certificates, with the core integer-bound lemmas cross-checked in an axiom-free Coq development.