We propose POWERALERT, an efficient external integrity checker for untrusted hosts. Current attestation systems suffer from shortcomings, including requiring a complete checksum of the code segment, from being static, use of timing information sourced from the untrusted machine, or using imprecise timing information such as network round-trip time. We address those shortcomings by (1) using power measurements from the host to ensure that the checking code is executed and (2) checking a subset of the kernel space over an extended period. We compare the power measurement against a learned power model of the execution of the machine and validate that the execution was not tampered. Finally, POWERALERT randomizes the integrity checking program to prevent the attacker from adapting. We model the interaction between POWERALERT and an attacker as a time-continuous game. The Nash equilibrium strategy of the game shows that POWERALERT has two optimal strategy choices: (1) aggressive checking that forces the attacker into hiding, or (2) slow checking that minimizes cost. We implement a prototype of POWERALERT using Raspberry Pi and evaluate the performance of the integrity checking program generation.