Computational soundness for standard assumptions of formal cryptography

The Dolev–Yao model is a useful and well-known framework in which to analyze security protocols. However, it models the messages of the protocol at a very high level and makes extremely strong assumptions about the power of the adversary. The computational model of cryptography, on the other hand, takes a much lower-level view of messages and uses much weaker assumptions. Despite the large differences between these two models, we have been able to show that there exists a relationship between them. Previous results of ours demonstrate that certain kinds of computational cryptography can result in an equivalence of sorts between the formal and computational adversary. Specifically: • We gave an interpretation to the messages of the Dolev–Yao model in terms of computational cryptography, • We defined a computational security condition, called weak Dolev-Yao non-malleability, that translates the main assumptions of the Dolev-Yao model into the computational setting, and • We demonstrated that this condition is satisfied by a standard definition of computational encryption security called plaintext awareness. In this work, we consider this result and strengthen it in four ways: 1. Firstly, we propose a stronger definition of Dolev-Yao non-malleability which ensures security against a more adaptive adversary. 2. Secondly, the definition of plaintext awareness is considered suspect because it relies on a trusted third party called the random oracle. Thus, we show that our new notion of DolevYao non-malleability is satisfied by a weaker and less troublesome definition for computational encryption called chosen-ciphertext security. 3. Thirdly, we propose a new definition of plaintext-awareness that does not use random oracles, and an implementation. This implementation is conceptually simple, and relies only on general assumptions. Specifically, it can be thought of as a ‘self-referential’ variation on a well-known encryption scheme. 4. Lastly, we show how the computational soundness of the Dolev-Yao model can be maintained even as it is extended to include new operators. In particular, we show how the Diffie-Hellman key-agreement scheme and the computational Diffie-Hellman assumption can be added to the Dolev-Yao model in a computationally sound way. Thesis Supervisor: Ron Rivest Title: Professor, MIT