As humanity struggles to contain the global COVID-19 pandemic, privacy concerns are emerging regarding confinement, tracing and testing. The scientific debate concerning privacy of the COVID-19 tracing efforts has been intense, especially focusing on the choice between centralised and decentralised tracing apps. The privacy concerns regarding COVID-19 testing, however, have not received as much attention even though the privacy at stake is arguably even higher. COVID-19 tests require the collection of samples. Those samples possibly contain viral material but inevitably also human DNA. Patient DNA is not necessary for the test but it is technically impossible to avoid collecting it. The unlawful preservation, or misuse, of such samples at a massive scale may hence disclose patient DNA information with far-reaching privacy consequences. Inspired by the cryptographic concept of "Indistinguishability under Chosen Plaintext Attack", this paper poses the blueprint of novel types of tests allowing to detect viral presence without leaving persisting traces of the patient's DNA.