Calculating Quantitative Integrity and Secrecy for Imperative Programs

Abstract

This paper presents a framework for calculating measures of data integrity for programs in a small imperative language. The authors develop a Markov chain semantics for their language which calculates Clarkson and Schneider's definitions of data contamination, data suppression, program suppression and program transmission. The authors then propose their own definition of program integrity for probabilistic specifications. These definitions are based on conditional mutual information and entropy; they present a result relating them to mutual information, which can be calculated by a number of existing tools. The authors extend a quantitative information flow tool CH-IMP to calculate these measures of integrity and demonstrate this tool with examples including error correcting codes, the Dining Cryptographers protocol and the attempts by a number of banks to influence the Libor rate.