End-to-end encryption (E2EE) by messaging platforms enable people to securely and privately communicate with one another. Its widespread adoption however raised concerns that illegal content might now be shared undetected. Following the global pushback against key escrow systems, client-side scanning based on perceptual hashing has been recently proposed by tech companies, governments and researchers to detect illegal content in E2EE communications. We here propose the first framework to evaluate the robustness of perceptual hashing-based client-side scanning to detection avoidance attacks and show current systems to not be robust. More specifically, we propose three adversarial attacks--a general black-box attack and two white-box attacks for discrete cosine transform-based algorithms--against perceptual hashing algorithms. In a large-scale evaluation, we show perceptual hashing-based client-side scanning mechanisms to be highly vulnerable to detection avoidance attacks in a black-box setting, with more than 99.9% of images successfully attacked while preserving the content of the image. We furthermore show our attack to generate diverse perturbations, strongly suggesting that straightforward mitigation strategies would be ineffective. Finally, we show that the larger thresholds necessary to make the attack harder would probably require more than one billion images to be flagged and decrypted daily, raising strong privacy concerns. Taken together, our results shed serious doubts on the robustness of perceptual hashing-based client-side scanning mechanisms currently proposed by governments, organizations, and researchers around the world.