Twisting Additivity in Program Obfuscation

Abstract : Additivity plays a key role in program analysis. It is the basis for designing Galois connection based abstract interpretations, it makes a Data-Flow Analysis (DFA) problem easy being convertible into a Kildall's general form, and provides a lattice-theoretic model for disjunctive analysis. In this paper we consider reversible transformers respectively making any monotone function additive and maximally non-additive. We show that, under non restrictive hypothesis, these transformers exist and that they provide a theoretical foundation for the obfuscation of DFA.