We consider the problem of network-based attacks, such as Man-in-the-Middle attacks, on standard state estimators. To ensure graceful control degradation in the presence of attacks, existing results impose very strict integrity requirements on the number of noncompromised sensors. We study the effects of sporadic data integrity enforcement, such as message authentication, on control performance under stealthy attacks. We show that even with sporadic data integrity guarantees, the attacker cannot introduce an unbounded state estimation error while remaining stealthy. We present a design-time framework to derive safe integrity enforcement policies, and illustrate its use; we show that with even 20% of authenticated messages we can ensure satisfiable state estimation errors under attacks.