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.
Past work has shown that RNNs can find general solutions to algorithmic tasks. Zaremba and Sutskever @cite_11 trained LSTMs to add 9-digit numbers with 99 In the 1930s, Allied nations had not yet captured a physical Enigma machine. Cryptographers such as the Polish Marian Rejewski were forced to compare plaintext, keyphrase, and ciphertext messages with each other to infer the mechanics of the machine. After several years of carefully analyzing these messages, Rejewski and the Polish Cipher Bureau were able to construct 'Enigma doubles' without ever having seen an actual Enigma machine @cite_19 . This is the same problem we trained our model to solve. Like Rejewski, our model uncovers the logic of the Enigma by looking for statistical patterns in a large number of plaintext, keyphrase, and ciphertext examples. We should note, however, that Rejewski needed far less data to make the same generalizations. Later in World War II, British cryptographers led by Alan Turing helped to actually crack the Enigma. As Turing's approach capitalized on operator error and expert knowledge about the Enigma, we consider it beyond the scope of this work @cite_9 .
@cite_19 @cite_9 @cite_11
1971846196 2188233853 2768347741 2135625884
The paper gives a personal view of work in the Polish Cipher Bureau from 1932 to 1939 as mathematicians worked to decipher the codes of the military version of the Enigma. The author, who was a participant, relates details of the device and the successes and frustrations involved in the work. He also describes mathematical principles that enabled him and his colleagues to break successive versions of the Enigma code and to construct technical devices (cyclometers and "bombs") that facilitated decipherment of Enigma-coded messages. This paper addresses the general problem of reinforcement learning (RL) in partially observable environments. In 2013, our large RL recurrent neural networks (RNNs) learned from scratch to drive simulated cars from high-dimensional video input. However, real brains are more powerful in many ways. In particular, they learn a predictive model of their initially unknown environment, and somehow use it for abstract (e.g., hierarchical) planning and reasoning. Guided by algorithmic information theory, we describe RNN-based AIs (RNNAIs) designed to do the same. Such an RNNAI can be trained on never-ending sequences of tasks, some of them provided by the user, others invented by the RNNAI itself in a curious, playful fashion, to improve its RNN-based world model. Unlike our previous model-building RNN-based RL machines dating back to 1990, the RNNAI learns to actively query its model for abstract reasoning and planning and decision making, essentially "learning to think." The basic ideas of this report can be applied to many other cases where one RNN-like system exploits the algorithmic information content of another. They are taken from a grant proposal submitted in Fall 2014, and also explain concepts such as "mirror neurons." Experimental results will be described in separate papers. Machine learning algorithms based on deep neural networks have achieved remarkable results and are being extensively used in different domains. However, the machine learning algorithms requires access to raw data which is often privacy sensitive. To address this issue, we develop new techniques to provide solutions for running deep neural networks over encrypted data. In this paper, we develop new techniques to adopt deep neural networks within the practical limitation of current homomorphic encryption schemes. More specifically, we focus on classification of the well-known convolutional neural networks (CNN). First, we design methods for approximation of the activation functions commonly used in CNNs (i.e. ReLU, Sigmoid, and Tanh) with low degree polynomials which is essential for efficient homomorphic encryption schemes. Then, we train convolutional neural networks with the approximation polynomials instead of original activation functions and analyze the performance of the models. Finally, we implement convolutional neural networks over encrypted data and measure performance of the models. Our experimental results validate the soundness of our approach with several convolutional neural networks with varying number of layers and structures. When applied to the MNIST optical character recognition tasks, our approach achieves 99.52 accuracy which significantly outperforms the state-of-the-art solutions and is very close to the accuracy of the best non-private version, 99.77 . Also, it can make close to 164000 predictions per hour. We also applied our approach to CIFAR-10, which is much more complex compared to MNIST, and were able to achieve 91.5 accuracy with approximation polynomials used as activation functions. These results show that CryptoDL provides efficient, accurate and scalable privacy-preserving predictions. 1. Summary In Part I, four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction. Almost all, if not all problems in induction can be put in this form. Some strong heuristic arguments have been obtained for the equivalence of the last three models. One of these models is equivalent to a Bayes formulation, in which a priori probabilities are assigned to sequences of symbols on the basis of the lengths of inputs to a universal Turing machine that are required to produce the sequence of interest as output. Though it seems likely, it is not certain whether the first of the four models is equivalent to the other three. Few rigorous results are presented. Informal investigations are made of the properties of these models. There are discussions of their consistency and meaningfulness, of their degree of independence of the exact nature of the Turing machine used, and of the accuracy of their predictions in comparison to those of other induction methods. In Part II these models are applied to the solution of three problems—prediction of the Bernoulli sequence, extrapolation of a certain kind of Markov chain, and the use of phrase structure grammars for induction. Though some approximations are used, the first of these problems is treated most rigorously. The result is Laplace's rule of succession. The solution to the second problem uses less certain approximations, but the properties of the solution that are discussed, are fairly independent of these approximations. The third application, using phrase structure grammars, is least exact of the three. First a formal solution is presented. Though it appears to have certain deficiencies, it is hoped that presentation of this admittedly inadequate model will suggest acceptable improvements in it. This formal solution is then applied in an approximate way to the determination of the “optimum” phrase structure grammar for a given set of strings. The results that are obtained are plausible, but subject to the uncertainties of the approximation used.