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.

翻译：受密码学应用驱动，我们研究了两种模乘的机器学习方法：循环回归模型和序列到序列Transformer模型。两种方法的有限成功结果表明，基于模乘的密码系统所依赖的任务具有困难性。