Primal implication as encryption

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 $\impφψ$ corresponds to the encryption of $\psi$ with a secret key $\phi$, primal disjunction $\vpφψ$ is a group key and $\perp$ reflects some backdoor constructions such as full superuser permissions or a universal decryption key. For the logic of $\perp$ 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.

16 pages