# TAPAS: Datasets for Learning the Learning with Errors Problem

arXiv: https://arxiv.org/abs/2510.08797 · HTML: https://mlsanity.com/paper/2510.08797/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 38 references that are in the map.
- First posted on arXiv 9 Oct 2025.

## Builds on (most cited first, 12 of 12)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [SALSA: Attacking Lattice Cryptography with Transformers](https://mlsanity.com/paper/2207.04785/) (2022)
- [SALSA PICANTE: a machine learning attack on LWE with binary secrets](https://mlsanity.com/paper/2303.04178/) (2023)
- [SALSA VERDE: a machine learning attack on Learning With Errors with sparse small secrets](https://mlsanity.com/paper/2306.11641/) (2023)
- [Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on Learning With Errors](https://mlsanity.com/paper/2402.01082/) (2024)
- [The cool and the cruel: separating hard parts of LWE secrets](https://mlsanity.com/paper/2403.10328/) (2024)
- [Benchmarking Attacks on Learning with Errors](https://mlsanity.com/paper/2408.00882/) (2024)
- [Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmetic](https://mlsanity.com/paper/2410.03569/) (2024)
- [An efficient algorithm for integer lattice reduction](https://mlsanity.com/paper/2303.02226/) (2023)
- [Provably weak instances of Ring-LWE](https://mlsanity.com/paper/1502.03708/) (2015)

## Abstract (arXiv)

AI-powered attacks on Learning with Errors (LWE), an important hard math problem in post-quantum cryptography, rival or outperform "classical" attacks on LWE under certain parameter settings. Despite the promise of this approach, a dearth of accessible data limits AI practitioners' ability to study and improve these attacks. Creating LWE data for AI model training is time- and compute-intensive and requires significant domain expertise. To fill this gap and accelerate AI research on LWE attacks, we propose the TAPAS datasets, a Toolkit for Analysis of Post-quantum cryptography using AI Systems. These datasets cover several LWE settings and can be used off-the-shelf by AI practitioners to prototype new approaches to cracking LWE. This work documents TAPAS dataset creation, establishes attack performance baselines, and lays out directions for future work.