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Motivated by cryptographic applications, we investigate two machine learning approaches to modular multiplication: namely circular regression and a sequence-to-sequence transformer model.
Solomon Kullback and Richard A. Leibler. On information and sufficiency. Annals of Mathematical Statistics . 22
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Taher ElGamal. A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms. IEEE Transactions on Information Theory 31
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Oded Regev. On lattices, learning with errors, random linear codes, and cryptography. Proceedings of the thirty-seventh annual ACM symposium on Theory of computing (Baltimore, MD, USA: ACM, 2005), 84–93
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Theodoros Palamas. Investigating the Ability of Neural Networks to Learn Simple Modular Arithmetic. MSc Thesis, Edinburgh, 2017. Available at https://project-archive.inf.ed.ac.uk/msc/20172390/msc_proj.pdf
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Alethea Power, Yuri Burda, Harri Edwards, Igor Babuschkin and Vedant Misra. Grokking: Generalization beyond overfitting on small algorithmic datasets. 1st Mathematical Reasoning in General Artificial Intelligence Workshop, ICLR 2021
2021
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François Charton. Linear algebra with transformers. Transactions on Machine Learning Research , 2835–8856 (2022)
2022
Cited alongside, same era.
Evrard Garcelon, Mohamed Malhou, Matteo Pirotta, Cathy Yuanchen Li, François Charton and Kristin Lauter. Solving Learning with Errors with Circular Regression. Preprint, Meta AI Papers, October 2022
2022
Cited alongside, same era.
Emily Wenger, Mingjie Chen, François Charton and Kristin Lauter. SALSA: Attacking Lattice Cryptography with Transformers. Proceedings of the 36th Conference on Neural Information Processing Systems (NeurIPS) , November 2022
2022
Cited alongside, same era.
2023
Cited alongside, same era.
Cathy Yuanchen Li, Jana Sotáková, Emily Wenger, Mohamed Malhou, Evrard Garcelon, François Charton and Kristin Lauter. SALSA PICANTE: a machine learning attack on LWE with binary secrets. Proceedings of the ACM Conference on Computer and Communications Security (CCS) , November 2023
2023
Later among the works it cites.
Cathy Yuanchen Li, Emily Wenger, Zeyuan Allen-Zhu, François Charton and Kristin Lauter. SALSA VERDE - A machine learning attack on LWE with small sparse secrets. Proceedings of the 37th Conference on Neural Information Processing Systems (NeurIPS) , November 2023
2023
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Neel Nanda, Lawrence Chan, Tom Lieberum, Jess Smith and Jacob Steinhardt. Progress measures for grokking via mechanistic interpretability. The Eleventh International Conference on Learning Representations , 2023
2023
Later among the works it cites.
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2023
Cited alongside, same era.
2023
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