In recent years code obfuscation has attracted research interest as a promising technique for protecting secret properties of programs. The basic idea of code obfuscation is to transform programs in order to hide their sensitive information while preserving their functionality. One of the major drawbacks of code obfuscation is the lack of a rigorous theoretical framework that makes it difficult to formally analyze and certify the effectiveness of obfuscating techniques. We face this problem by providing a formal framework for code obfuscation based on abstract interpretation and program semantics. In particular, we show that what is hidden and what is preserved by an obfuscating transformation can be expressed as abstract interpretations of program semantics. Being able to specify what is masked and what is preserved by an obfuscation allows us to understand its potency, namely the amount of obscurity that the transformation adds to programs. In the proposed framework, obfuscation and attackers are modeled as approximations of program semantics and the lattice of abstract interpretations provides a formal tool for comparing obfuscations with respect to their potency. In particular, we prove that our framework provides an adequate setting to measure not only the potency of an obfuscation but also its resilience, i.e., the difficulty of undoing the obfuscation. We consider code obfuscation by opaque predicate insertion and we show how the degree of abstraction needed to disclose different opaque predicates allows us to compare their potency and resilience.