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Symposium on logic and computability "Logic and Computation Day"
June 7, 2013 14:30–13:15, Moscow, Steklov Mathematical Institute of RAS

Primal implication as encryption

V. N. Krupski

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: We propose a “cryptographic” interpretation for the propositional connectives of primal infon logic introduced by Y. Gurevich and I. Neeman and prove the corresponding soundness and completeness results. Primal implication $\varphi \to \psi$ corresponds to the encryption of $\psi$ with a secret key $\varphi$, primal disjunction is a group key and $\bot$ reflects some backdoor constructions such as full superuser permissions or a universal decryption key. For the logic of $\bot$ as a universal key (it was never considered before) we prove that the derivability problem has linear time complexity. We also show that the universal key can be emulated using primal disjunction.