mlsanityData to 7 Oct 2026

SALSA: Attacking Lattice Cryptography with Transformers

arXiv 2207.04785 ↗First posted 11 Jul 2022cs.CR cs.LGcited by 28

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Abstract (arXiv)

Currently deployed public-key cryptosystems will be vulnerable to attacks by full-scale quantum computers. Consequently, "quantum resistant" cryptosystems are in high demand, and lattice-based cryptosystems, based on a hard problem known as Learning With Errors (LWE), have emerged as strong contenders for standardization. In this work, we train transformers to perform modular arithmetic and combine half-trained models with statistical cryptanalysis techniques to propose SALSA: a machine learning attack on LWE-based cryptographic schemes. SALSA can fully recover secrets for small-to-mid size LWE instances with sparse binary secrets, and may scale to attack real-world LWE-based cryptosystems.

Key facts. Cited by 28 papers in the map (data through 7 Oct 2026). Builds on 26 of its 72 references that are in the map. First posted on arXiv 11 Jul 2022.

Builds on

26 of 72 references.

References · 26

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14 more
  1. 2021The Neural Data Router: Adaptive Control Flow in Transformers Improves Systematic Generalizationcited by 62
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  6. 2020Can Sequence-to-Sequence Models Crack Substitution Ciphers?cited by 9
  7. 2021Transformer-based Machine Learning for Fast SAT Solvers and Logic Synthesiscited by 8
  8. 2021Solving Arithmetic Word Problems with Transformers and Preprocessing of Problem Textcited by 7
  9. 2021A deep language model to predict metabolic network equilibriacited by 3
  10. 2015Provably weak instances of Ring-LWEcited by 2
  11. 2017Learning the Enigma with Recurrent Neural Networkscited by 2
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 6; 2024: 6; 2025: 13; 2026: 3.

28 papers.

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  1. 2024Formal Mathematical Reasoning: A New Frontier in AIcited by 80
  2. 2023Length Generalization in Arithmetic Transformerscited by 64
  3. 2024Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformerscited by 29
  4. 2024Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theorycited by 17
  5. 2023SALSA PICANTE: a machine learning attack on LWE with binary secretscited by 11
  6. 2023Learning to Compute Gr"obner Basescited by 7
  7. 2024Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on Learning With Errorscited by 7
  8. 2025Computational Algebra with Attention: Transformer Oracles for Border Basis Algorithmscited by 7
  9. 2025Should LLM Safety Be More Than Refusing Harmful Instructions?cited by 6
  10. 2025Benchmarking Large Language Models for Cryptanalysis and Side-Channel Vulnerabilitiescited by 5
  11. 2024Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmeticcited by 4
  12. 2025Geometric Generality of Transformer-Based Gr"obner Basis Computationcited by 3
16 more
  1. 2023Gradient Descent Fails to Learn High-frequency Functions and Modular Arithmeticcited by 2
  2. 2024Machine learning for modular multiplicationcited by 2
  3. 2025Local Look-Ahead Guidance via Verifier-in-the-Loop for Automated Theorem Provingcited by 2
  4. 2025Discovering Learning-Friendly Generation Orders for Sequential Computationcited by 1
  5. 2023Practically Solving LPN in High Noise Regimes Faster Using Neural Networkscited by 0
  6. 2023Memorization for Good: Encryption with Autoregressive Language Modelscited by 0
  7. 2025Prime Convolutional Model: Breaking the Ground for Theoretical Explainabilitycited by 0
  8. 2025The informativeness of the gradient revisitedcited by 0
  9. 2025CALT: A Library for Computer Algebra with Transformercited by 0
  10. 2025Learning Moderately Input-Sensitive Functions: A Case Study in QR Code Decodingcited by 0
  11. 2025NoMod: A Non-modular Attack on Module Learning With Errorscited by 0
  12. 2025TAPAS: Datasets for Learning the Learning with Errors Problemcited by 0
  13. 2025Learning Pseudorandom Numbers with Transformers: Permuted Congruential Generators, Curricula, and Interpretabilitycited by 0
  14. 2026Improving ML Attacks on LWE with Data Repetition and Stepwise Regressioncited by 0
  15. 2026Discovering Lattice Reduction Strategies via Self-Playcited by 0
  16. 2026CARTS: Contextual Autoregressive Rank Transcoding Steganography for Full-Capacity Keyed Text Encodingcited by 0