The standard pipeline for many vision tasks uses a conventional camera to capture an image that is then passed to a digital processor for information extraction. In some deployments, such as private locations, the captured digital imagery contains sensitive information exposed to digital vulnerabilities such as spyware, Trojans, etc. However, in many applications, the full imagery is unnecessary for the vision task at hand. In this paper we propose an optical and analog system that preprocesses the light from the scene before it reaches the digital imager to destroy sensitive information. We explore analog and optical encodings consisting of easily implementable operations such as convolution, pooling, and quantization. We perform a case study to evaluate how such encodings can destroy face identity information while preserving enough information for face detection. The encoding parameters are learned via an alternating optimization scheme based on adversarial learning with deep neural networks. We name our system CAnOPIC (Camera with Analog and Optical Privacy-Integrating Computations) and show that it has better performance in terms of both privacy and utility than conventional optical privacy-enhancing methods such as blurring and pixelation.