A Formal System for Analysis of Cryptographic Encryption and Their Security Properties

Abstract

Providing a way to achieve the privacy and authenticity of information transmitted over or stored in an unreliable medium is a prime necessity in the world of computing and communication. In this paper, we propose a new deduction system called judgment deduction system (or JD-System), which can be used to formalize an idealized asymmetric (and symmetric) encryption scheme. In our system, deductive reasoning is used to identify the security properties of asymmetric and symmetric encryption. New notions are introduced for describing several security properties. For example, we use the notion of “judgment” in our system. Conversely, we also introduce the notion of “unjudgment” as a property of JD-system. By using these notions, we can express and prove the security properties content-indistinguishability, key-indistinguishability, content-non-malleability, content-length-indistinguishability, key-length-indistinguishability, content-length-non-malleability, and key-length-non-malleability of asymmetric (and symmetric) encryption schemes and the security property key-non-malleability of asymmetric encryption. Formal proofs are given showing the sufficient conditions for these security properties and showing formally the difference between asymmetric encryption and symmetric encryption scheme. Some security properties can be achieved in case of asymmetric encryption and cannot be achieved in case of symmetric encryption.