Logical concepts in cryptography

Abstract

The thesis is about a breadth-first exploration of logical concepts in cryptography and their linguistic abstraction and model-theoretic combination in a comprehensive logical system, called CPL (for Cryptographic Protocol Logic). We focus on two fundamental aspects of cryptography. Namely, the security of communication (as opposed to security of storage) and cryptographic protocols (as opposed to cryptographic operators). The logical concepts explored are the following. Primary concepts: the modal concepts of belief, knowledge, norms, provability, space, and time. Secondary concepts: belief with error control, individual and propositional knowledge, confidentiality norms, truth-functional and relevant (in particular, intuitionistic) implication, multiple and complex truth values, and program types. The distinguishing feature of CPL is that it unifies and refines a variety of existing approaches. This feature is the result of our wholistic conception of property-based (modal logics) and model-based (process algebra) formalisms. We illustrate the expressiveness of CPL on representative requirements engineering case studies. Further, we extend (core) CPL (qualitative time) with rational-valued time, i.e., time stamps, timed keys, and potentially drifting local clocks, to tCPL (quantitative time). Our extension is conservative and provides further evidence for Lamport's claim that adding real time to an untimed formalism is really simple. Furthermore, we sketch an extension of (core) CPL with a notion of probabilistic polynomial-time (PP) computation. We illustrate the expressiveness of this extended logic (ppCPL) on tentative formalisation case studies of fundamental and applied concepts. Fundamental concepts: (1) one-way function, (2) hard-core predicate, (3) computational indistinguishability, (4) (n-party) interactive proof, and (5) (n-prover) zero-knowledge. Applied concepts: (1) security of encryption schemes, (2) unforgeability of signature schemes, (3) attacks on encryption schemes, (4) attacks on signature schemes, and (5) breaks of signature schemes. In the light of logic, adding PP to a formalism for cryptographic protocols is perhaps also simple and can be achieved with an Ockham's razor extension of an existing core logic, namely CPL.

Index Terms

• General and reference

  • Document types

    • Surveys and overviews

• Information systems

  • Data management systems

    • Data structures

      • Data layout

        • Data encryption

• Security and privacy

  • Cryptography

• Theory of computation

  • Computational complexity and cryptography