Calculating Quantitative Integrity and Secrecy for Imperative Programs

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