In this paper, we investigate the conditions for the existence of dynamically undetectable attacks and perfectly undetectable attacks. Then we provide a quantitative measure on the security for discrete-time linear time-invariant (LTI) systems under both actuator and sensor attacks based on undetectability. Finally, the computation of proposed security index is reduced to a min-cut problem for the structured systems by graph theory. Numerical examples are provided to illustrate the theoretical results.