Statistical cryptanalysis of block ciphers as channel communication

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Abstract: Block ciphers are indispensable components of the communication infrastructure, yet few unifying principles for their design and analysis exist. As a result, it is not possible to easily characterize good and bad ciphers, and the design of good ciphers is difficult. While notable general treatments of the problem do exist and have contributed valuable insights, it has been difficult to combine the individual treatments of specific attacks and specific cipher designs into an overarching theory, and much remains to be done.This project studies a large class of attacks known as statistical cryptanalysis, which exploits probabilistic relationships among the plaintext, key and ciphertext to determine the key. The research extends existing communication channel models of statistical cryptanalysis---where low capacity channels carry encoded symbols of the key to the adversary---which have been used very successfully to design attacks on stream ciphers, but are not as widely used for block cipher cryptanalysis. A key insight exploited by the project is as follows: existing cryptanalytic models do not provide a means of studying the combination of related-key attacks and statistical attacks. The PI observed that related secrets form codes over information leakage channels, improving adversary communication efficiency. Using this approach, the project obtains general results on attack efficiency---experimentally verified as far as possible---and related cipher design criteria. Through an established r elationship with local high school Chantilly Academy, where the PI teaches cryptography modules, the project contributes to K-12 education, and inspires high school students to study mathematics, engineering and computer science.