Intransitive non-interference for cryptographic purposes

Information flow and non-interference have recently become very popular concepts for expressing both integrity and privacy properties. Because of the enormous potential of transmitting information using probabilistic methods of cryptography, interest arose in capturing probabilistic non-interference. We investigate the notion of intransitive probabilistic non-interference in reactive systems, i.e., downgrading of probabilistic information and detection of probabilistic information flow by one or more involved third parties. Based on concrete examples, we derive several definitions that comprise cryptography-related details like error probabilities and computational restrictions. This makes the definitions applicable to systems involving real cryptography. Detection of probabilistic information flow is significantly more complicated to define if several third parties are involved because of the possibilities of secret sharing. We solve this problem by graph-theoretic techniques.