Over the past two decades, several microarchitectural side channels have been exploited to create sophisticated security attacks. Solutions to this problem have mainly focused on fixing the source of leaks either by limiting the flow of information through the side channel by modifying hardware, or by refactoring vulnerable software to protect sensitive data from leaking. These solutions are reactive and not preventative: while the modifications may protect against a single attack, they do nothing to prevent future side channel attacks that exploit other microarchitectural side channels or exploit the same side channel in a novel way. In this paper we present a general mitigation strategy that focuses on the infrastructure used to measure side channel leaks rather than the source of leaks, and thus applies to all known and unknown microarchitectural side channel leaks. Our approach is to limit the fidelity of fine grain timekeeping and performance counters, making it difficult f...