Quantifying probabilistic information flow in computational reactive systems

Abstract

Information flow and non-interference are well-established techniques for expressing both integrity and privacy properties. Because of the enormous potential to transmit information using probabilistic methods of cryptography, interest has arisen in extending the traditional notions of information flow to fully reactive settings that allow for reasoning about arbitrary interactive systems, and in particular arbitrary cryptographic protocols. We propose definitions for quantifying the amount of information that users are able to transmit to each other in such reactive settings, and we in particular address computational restrictions and error probabilities so that our definitions are suited for complexity-theoretic reasoning about cryptographic systems. We show that our definitions are preserved under simulatability, which constitutes the cryptographic notion of a secure implementation, and we link our definitions to non-interference by showing that a zero or negligible quantity of information flow is equivalent to perfect or computational probabilistic non-interference, respectively. © Springer-Verlag Berlin Heidelberg 2005.