Distributed Contingency Logic and Security

In information security, ignorance is not bliss. It is always stated that hiding the protocols (let the other be ignorant about it) does not increase the security of organizations. However, there are cases that ignorance creates protocols. In this paper, we propose distributed contingency logic, a proper extension of contingency (ignorance) logic. Intuitively, a formula is distributed contingent in a group of agent if and only if it does not follow from the knowledge of all individual agents put together. We formalize secret sharing scheme (a security property that is built upon ignorance of all agents), and a man in the middle attack to a weak protocol in our logic. We also illustrate a condition where disclose a secret may hide another one forever. Finally we prove the main theorems of every logic, soundness and completeness. We also prove that distributed contingency logic is more expressive than classical contingency logic and epistemic logic.