We propose a new deduction system which formalizes the principal's knowledgesof equalities and non-equalities between contents of ciphertexts or hashvalues, and keys of ciphertexts, which we call "judgment", and as ameta-property of the system, we propose the notion of "unjudgment", whichrepresents the situation where no knowledge about equality and non-equality ofa pair of terms exists. By using these notions, many security properties forcryptographic primitives such as content-indistinguishability,content-non-malleability, key-indistinguishability, key-non-malleability,content-length-non-malleability, and hash-collision-length-free are definedand we proved that the cryptographic primitives satisfy theseproperties.
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