From Qualitative to Quantitative Proofs of Security Properties Using First-Order Conditional Logic

TL;DR

This paper introduces a first-order conditional logic with epsilon-semantics for security protocols, enabling automatic conversion from qualitative to quantitative security proofs with super-polynomial convergence.

Contribution

It provides a complete axiomatization of the logic and a method to transform qualitative security proofs into quantitative ones suitable for concrete security analysis.

Findings

Complete axiomatization of the logic

Method for automatic proof conversion

Super-polynomial convergence in semantics

Abstract

A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is needed for reasoning about security protocols. A complete axiomatization is provided for this semantics, and it is shown how a qualitative proof of the correctness of a security protocol can be automatically converted to a quantitative proof appropriate for reasoning about concrete security.