A Systematic Evaluation of Fault Attacks and Countermeasures on ML-DSA Rejection Sampling

What it is

A preprint by Yulong Meng (IACR ePrint 2026/2567, approved 21 October 2026) that evaluates fault attacks on ML-DSA (FIPS 204) rejection sampling and the countermeasures proposed against them. It tests the "third rejection test" of patent WO2025261784A1 against sign-then-verify across three fault models and two implementation variants (the reference implementation and a second variant the abstract does not name).

How it works

The proof uses the identity Az − ct = Ay − c·s2 = r. The value the third check compares is exactly r1, which signing already computes. Check 2 passing is what implies r1 = w1, so the third check re-verifies a condition check 2 already guarantees. The patent's six embodiments reduce to two independent conditions, and both cover only skips of check 2.

The z-norm check is the route that directly recovers the signing key s1. In 30,000 fault injections, all six embodiments detected a skipped z-norm check at a rate of zero. Using this gap, the author recovered s1 in full (all 1024 coefficients across four polynomials) from a third-check-protected implementation under randomized signing, the FIPS 204 default.

flowchart TD
    A[Fault in rejection sampling] --> B{Which check is skipped?}
    B -->|Check 2| C[Third check detects it]
    B -->|Check 2| D[Sign-then-verify misses it on reference code]
    B -->|z-norm check| E[Third check detects nothing]
    B -->|z-norm check| F[Sign-then-verify detects it]

What to do

The paper recommends deploying both the third check and sign-then-verify. Either one alone leaves a complete attack path open, and together they cover every path the author evaluated.

The third check is about 460–590 times cheaper than sign-then-verify on x86-64 and about 48 times cheaper on Cortex-M4. The combined cost is almost entirely that of sign-then-verify.

Caveats

• Sign-then-verify fails entirely against a check 2 skip on the reference implementation: every faulty signature passes verification.
• The cheapest third-check embodiment detects every exploitable signature from a check 2 skip, but it never detects a z-check skip.
• The page is a preprint with no stated peer review. It gives no details of the fault injection setup, and the abstract does not say whether the faults were simulated or physical.