Paper 2026/1386

Key-Recovery Attacks on TALUS: A Cryptanalytic Note

Abstract

We present key-recovery attacks on the constructions of TALUS (Kao and Chang), a threshold ML-DSA (FIPS 204) construction available on arXiv and scheduled for presentation at the NIST Threshold Call Preview Talks Round 2 (TCPT-2, https://csrc.nist.gov/events/2026/tcpt). For TALUS-MPC, which is claimed EUF-CMA secure against an adversary corrupting up to $T − 1$ parties, we show the claim is false via two independent attacks, both exploiting the same root cause. TALUS-MPC uses Feldman commitments that apply the public matrix A to secret values: key shares of $s_1$ during key generation, and contributions to the nonce $y$ during signing. Since A is left-invertible in every ML-DSA parameter set, these images are invertible by Gaussian elimination, with no lattice problem to solve. A passive observer recovers all key shares of $s_1$ directly from the key-generation broadcast, and independently recovers the aggregate nonce y from the signing broadcast, which then yields $s_1 = c^{−1} \cdot (z − y)$ from a single signature. For TALUS-TEE and TALUS-MPC, we identify a persisting flaw: the rejection-sampling check that protects the error term $s_2$ in standard ML-DSA has been removed. Each signature leaks a noisy linear equation in $s_2$; applying least-squares recovery over the cyclotomic ring - an instance of LWE without modular reduction - recovers the full secret from a few hundred million signatures. The sample counts we derive are not optimized and we believe exploiting the bounded noise structure and lattice-reduction techniques would reduce them significantly, but we focus on establishing the structural flaw.