Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on Learning With Errors

TL;DR

This paper introduces novel machine learning techniques, including angular embeddings and pre-training, to significantly enhance attacks on LWE problems, enabling recovery of secrets in larger dimensions with fewer samples and less preprocessing.

Contribution

It presents new methods that improve ML-based LWE attacks by speeding up preprocessing, increasing sample efficiency, and demonstrating success in higher dimensions.

Findings

Preprocessing speed increased by 25 times.

Model sample efficiency improved by 10 times.

First ML attack to recover secrets in dimension 1024.

Abstract

Learning with Errors (LWE) is a hard math problem underlying recently standardized post-quantum cryptography (PQC) systems for key exchange and digital signatures. Prior work proposed new machine learning (ML)-based attacks on LWE problems with small, sparse secrets, but these attacks require millions of LWE samples to train on and take days to recover secrets. We propose three key methods -- better preprocessing, angular embeddings and model pre-training -- to improve these attacks, speeding up preprocessing by $25\times$ and improving model sample efficiency by $10\times$. We demonstrate for the first time that pre-training improves and reduces the cost of ML attacks on LWE. Our architecture improvements enable scaling to larger-dimension LWE problems: this work is the first instance of ML attacks recovering sparse binary secrets in dimension $n=1024$, the smallest dimension used in practice for homomorphic encryption applications of LWE where sparse binary secrets are proposed.