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Learning with Errors (LWE) is a hard math problem used in post-quantumcryptography. Homomorphic Encryption (HE) schemes rely on the hardness of theLWE problem for their security, and two LWE-based cryptosystems were recentlystandardized by NIST for digital signatures and key exchange (KEM). Thus, it iscritical to continue assessing the security of LWE and specific parameterchoices. For example, HE uses secrets with small entries, and the HE communityhas considered standardizing small sparse secrets to improve efficiency andfunctionality. However, prior work, SALSA and PICANTE, showed that ML attackscan recover sparse binary secrets. Building on these, we propose VERDE, animproved ML attack that can recover sparse binary, ternary, and narrow Gaussiansecrets. Using improved preprocessing and secret recovery techniques, VERDE canattack LWE with larger dimensions ($n=512$) and smaller moduli ($\log_2 q=12$for $n=256$), using less time and power. We propose novel architectures forscaling. Finally, we develop a theory that explains the success of ML LWEattacks.

SALSA VERDE: a machine learning attack on Learning With Errors with sparse small secrets