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 (Vigenere, 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 Vigenere 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.
Characterizing unknown ciphers is a central problem in cryptography. The comprehensive @cite_16 lists a wealth of methods, from frequency analysis to chosen-plaintext attacks. Papers such as @cite_4 offer additional methods. While these methods can be effective under the right conditions, they do not generalize well outside certain classes of ciphers. This has led researchers to propose several machine learning-based approaches. One work @cite_7 used genetic algorithms to recover the secret key of a simple substitution cipher. A review paper by @cite_0 proposes cipher classification with machine learning.
@cite_0 @cite_16 @cite_4 @cite_7
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This paper considers a new approach to cryptanalysis based on the application of a directed random search algorithm called a genetic algorithm. It is shown that such a algorithm could be used to discover the key for a simple substitution cipher. The best known cryptanalytic attack on McEliece's public-key cryptosystem based on algebraic coding theory is to repeatedly select k bits at random from an n-bit ciphertext vector, which is corrupted by at most t errors, in hope that none of the selected k bits are in error until the cryptanalyst recovers the correct message. The method of determining whether the recovered message is the correct one has not been throughly investigated. In this paper, we suggest a systematic method of checking, and describe a generalized version of the cryptanalytic attack which reduces the work factor sigdicantly (factor of 211 for the commonly used example of n=1024 Goppa code case). Some more improvements are also given. We also note that these cryptanalytic algorithms can be viewed as generalized probabilistic decoding algorithms for any linear error correcting codes. We demonstrate that, by using a recently proposed leveled homomorphic encryption scheme, it is possible to delegate the execution of a machine learning algorithm to a computing service while retaining confidentiality of the training and test data. Since the computational complexity of the homomorphic encryption scheme depends primarily on the number of levels of multiplications to be carried out on the encrypted data, we define a new class of machine learning algorithms in which the algorithm's predictions, viewed as functions of the input data, can be expressed as polynomials of bounded degree. We propose confidential algorithms for binary classification based on polynomial approximations to least-squares solutions obtained by a small number of gradient descent steps. We present experimental validation of the confidential machine learning pipeline and discuss the trade-offs regarding computational complexity, prediction accuracy and cryptographic security. In this paper we address the problem of solving substitution ciphers using a beam search approach. We present a conceptually consistent and easy to implement method that improves the current state of the art for decipherment of substitution ciphers and is able to use high ordern-gram language models. We show experiments with 1:1 substitution ciphers in which the guaranteed optimal solution for 3-gram language models has 38.6 decipherment error, while our approach achieves 4.13 decipherment error in a fraction of time by using a 6-gram language model. We also apply our approach to the famous Zodiac-408 cipher and obtain slightly better (and near to optimal) results than previously published. Unlike the previous state-of-the-art approach that uses additional word lists to evaluate possible decipherments, our approach only uses a letterbased 6-gram language model. Furthermore we use our algorithm to solve large vocabulary substitution ciphers and improve the best published decipherment error rate based on the Gigaword corpus of 7.8 to 6.0 error rate.