A formal analysis of symmetric encryption and keyed hash function

In this paper, the authors proposed a new deduction system called judgment deduction system (or JD-system), which can be used to formalize an idealized symmetric encryption scheme and keyed hash function. In this system, the principal\´s knowledge of equalities and non-equalities were formalized between contents (or keys) of either ciphertexts or keyed hash values, which is called "judgment" and as a property of the JD-system, the authors used the notion "unjudgment", which represent the situation where no knowledge about the equality and non-equality of a pair of terms exists. By using these notions, many security properties of symmetric encryption and keyed hash function are proved. A formal proof is given showing the sufficient conditions for these security properties and the relation among them. Another proof is also given showing some security properties can be achieved in case of keyed hash function and cannot be achieved in case of symmetric encryption