Formal Framework for Reasoning About the Precision of Dynamic Analysis

Dynamic program analysis is extremely successful both in code debugging and in malicious code attacks. Fuzzing, concolic, and monkey testing are instances of the more general problem of analysing programs by dynamically executing their code with selected inputs. While static program analysis has a beautiful and well established theoretical foundation in abstract interpretation, dynamic analysis still lacks such a foundation. In this paper, we introduce a formal model for understanding the notion of precision in dynamic program analysis. It is known that in sound-by-construction static program analysis the precision amounts to completeness. In dynamic analysis, which is inherently unsound, precision boils down to a notion of coverage of execution traces with respect to what the observer (attacker or debugger) can effectively observe about the computation. We introduce a topological characterisation of the notion of coverage relatively to a given (fixed) observation for dynamic program analysis and we show how this coverage can be changed by semantic preserving code transformations. Once again, as well as in the case of static program analysis and abstract interpretation, also for dynamic analysis we can morph the precision of the analysis by transforming the code. In this context, we validate our model on well established code obfuscation and watermarking techniques. We confirm the efficiency of existing methods for preventing control-flow-graph extraction and data exploit by dynamic analysis, including a validation of the potency of fully homomorphic data encodings in code obfuscation.