# Learning the Enigma with Recurrent Neural Networks

arXiv: https://arxiv.org/abs/1708.07576 · HTML: https://mlsanity.com/paper/1708.07576/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Aug 2017.

## Built on by (most cited first, 2 of 2)

- [SALSA: Attacking Lattice Cryptography with Transformers](https://mlsanity.com/paper/2207.04785/) (2022)
- [Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on Learning With Errors](https://mlsanity.com/paper/2402.01082/) (2024)

## Abstract (arXiv)

Recurrent neural networks (RNNs) represent the state of the art in translation, image captioning, and speech recognition. They are also capable of learning algorithmic tasks such as long addition, copying, and sorting from a set of training examples. We demonstrate that RNNs can learn decryption algorithms -- the mappings from plaintext to ciphertext -- for three polyalphabetic ciphers (Vigen`ere, Autokey, and Enigma). Most notably, we demonstrate that an RNN with a 3000-unit Long Short-Term Memory (LSTM) cell can learn the decryption function of the Enigma machine. We argue that our model learns efficient internal representations of these ciphers 1) by exploring activations of individual memory neurons and 2) by comparing memory usage across the three ciphers. To be clear, our work is not aimed at 'cracking' the Enigma cipher. However, we do show that our model can perform elementary cryptanalysis by running known-plaintext attacks on the Vigen`ere and Autokey ciphers. Our results indicate that RNNs can learn algorithmic representations of black box polyalphabetic ciphers and that these representations are useful for cryptanalysis.