Salsa Picante: A Machine Learning Attack On LWE with Binary Secrets

Abstract

Learning With Errors (LWE) is a hard math problem underpinning many proposed post-quantum cryptographic (PQC) systems. The only PQC Key Exchange Mechanism (KEM) standardized by NIST [13] is based on module LWE, and current publicly available PQ Homomorphic Encryption (HE) libraries are based on ring LWE [2]. The security of LWE-based PQ cryptosystems is critical, but certain implementation choices could weaken them. One such choice is sparse binary secrets, desirable for PQ HE schemes for efficiency reasons. Prior work Salsa [51] demonstrated a machine learning based attack on LWE with sparse binary secrets in small dimensions (𝑛 ≤ 128) and low Hamming weights (ℎ ≤ 4). However, this attack assumes access to millions of eavesdropped LWE samples and fails at higher Hamming weights or dimensions. We present Picante, an enhanced machine learning attack on LWE with sparse binary secrets, which recovers secrets in much larger dimensions (up to 𝑛 = 350) and with larger Hamming weights (roughly 𝑛/10, and up to ℎ = 60 for 𝑛 = 350). We achieve this dramatic improvement via a novel preprocessing step, which allows us to generate training data from a linear number of eavesdropped LWE samples (4𝑛) and changes the distribution of the data to improve transformer training. We also improve the secret recovery methods of Salsa and introduce a novel cross-attention recovery mechanism allowing us to read off the secret directly from the trained models. While Picante does not threaten NIST’s proposed LWE standards, it demonstrates significant improvement over Salsa and could scale further, highlighting the need for future investigation into machine learning attacks on LWE with sparse binary secrets.