Abstract: In the research of information security and trusted computing, measuring dynamic integrity of codes under adversariesattacks is an important problem, especially in the context, such as wireless sensor network, cloud computing etc. In the open and less coupled systems, this issue is much more urgent. Hardware-based technologies of trusted computing and methods in (software based) code attestation can successfully measure some property of program, static or code oriented, but fail to measure integrity of certain behaviors during the executing of codes. This situation partially is due to the lack of proper theory of dynamic integrity, which can be changed with sound and precise concepts and models of measuring dynamic integrity. In this paper, we develop the concept of dynamic integrity after analysis of attacks and model of measuring dynamic integrity, and use the idea of provable secure from cryptography to give a formal notion of the concept. And we discuss its relationship with several other cryptography primitives, such as message authentication code schemes, code obfuscation etc. Based on the model, a complier-aided flow embedding method is proposed to achieve a weak form of dynamic integrity scheme, and security and efficiency are analyzed with some reasonable assumptions. Finally, we discuss how to compile any program enhanced by dynamic integrity measurable scheme and issues concerning the compiling process.