Typical security models used for proving security of deployed cryptographic primitives do not allow adversaries to rewind or reset honest parties to an earlier state. Thus, it is common to see cryptographic protocols rely on the assumption that
random numbers can be continually generated. In this paper, we argue that because of the growing popularity of virtual machines and, specifically, their state snapshot and revert features, the security of cryptographic protocols proven under these assumptions is called into question. We focus on public-key encryption security in a setting where resetting is possible and random numbers might be reused. We show that existing schemes and security models are insufficient in this setting. We then provide new formal security models and show that making a simple and efficient modification to any existing PKE scheme gives us security under our new models.