Machine learning for modular multiplication

2024/02/29 by Lauter, Kristin, Li, Cathy Yuanchen, Maughan, Krystal +2
#Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Machine Learning (cs.LG)

paper · doi:10.48550/arxiv.2402.19254

Abstract

Motivated by cryptographic applications, we investigate two machine learning approaches to modular multiplication: namely circular regression and a sequence-to-sequence transformer model. The limited success of both methods demonstrated in our results gives evidence for the hardness of tasks involving modular multiplication upon which cryptosystems are based.

Related

• Learning Modular Exponentiation with Transformers
• Making Hard Problems Easier with Custom Data Distributions and Loss Regularization: A Case Study in Modular Arithmetic
• Why Can't Transformers Learn Multiplication? Reverse-Engineering Reveals Long-Range Dependency Pitfalls
• Fourier Circuits in Neural Networks and Transformers: A Case Study of Modular Arithmetic with Multiple Inputs
• Learning Pseudorandom Numbers with Transformers: Permuted Congruential Generators, Curricula, and Interpretability