The security of ML-DSA, like most signature schemes, is partially based on the fact that the nonce used to generate the signature is unknown to any attacker. In this work, we exhibit a lattice-based attack that is possible if the nonces share implicit or explicit information. From a collection of signatures whose nonces share certain coefficients, it is indeed possible to build a collection of non full-rank lattices. Intersecting them, we show how to create a low-rank lattice that contains one of the polynomials of the secret key, which in turn can be recovered using lattice reduction techniques. There are several interpretations of this result: firstly, it can be seen as a generalization of a fault-based attack on BLISS presented at SAC’16 by Thomas Espitau et al.. Alternatively, it can be understood as a side-channel attack on ML-DSA, in the case where an attacker is able to recover only one of the coefficients of the nonce used during the generation of the signature. For ML-DSA-II, we show that \(4 \times 160\) signatures and few hours of computation are sufficient to recover the secret key on a desktop computer. Lastly, our result shows that simple countermeasures, such as permuting the generation of the nonce coefficients, are not sufficient.