Paper 2026/2137 Original: eprint.iacr.org/2026/2137 ↗

Too Small to Hide: Single-Trace Key Recovery from ML-KEM Key Generation

Abstract

Key generation in ML-KEM (CRYSTALS-Kyber) samples a short secret from a centered binomial distribution (CBD) and immediately transforms it with the number-theoretic transform (NTT). Each execution draws fresh randomness, so an attacker obtains a single trace and cannot average. We show that one power trace of the optimized pqm4 implementation on an Arm Cortex-M4 suffices, and that the two operations leak complementary information. The CBD sampler stores each coefficient as a signed $16$-bit two's-complement word, which reveals its sign almost without error but too little about its magnitude to yield long error-free hint sets. The missing magnitude leaks in the subsequent NTT, where coefficients are multiplied by public twiddle factors. Used as hints in a primal lattice attack, the combined leakage reduces the estimated BKZ block size for ML-KEM-768 from $624$ to $129$, corresponding to $2^{182.2}$ and $2^{37.7}$ in the core-SVP model. A control experiment shows that the same NTT code leaks the Hamming weight of a near-uniform operand as strongly as that of the secret, yet reveals almost nothing about its value. What makes a coefficient vulnerable is how few values it can take, not how small it is. That points to a countermeasure inside the CBD sampler. Each sample $v$ is stored as a random representative $\widetilde v = v + rq$ of its residue class, with $r$ nonzero, so the NTT and all later code run unchanged. This $q$-randomization drives the sign leakage to the noise floor, reduces the NTT magnitude leakage by $4.5\times$, and raises the block size from $129$ back to $611$, about four bits of estimated security lost instead of more than $140$. The sampler grows by $937$ bytes of firmware.