The broadcast nature of the wireless spectrum necessarily implies the possibility of eavesdropping, as well as malicious modification of waveforms through inexpensive, widely available software-defined radios (SDRs). This paper proposes a method for covert wireless communications that can be used to authenticate a device or exchange private information between devices. Our approach, called Impairment Shift Keying (ISK), introduces small yet controlled modifications to the radio transmitter hardware, which distorts regular standards-compliant waveforms, such as WiFi, with only 1% increase in bit error rate. A deep convolutional neural network (CNN) is trained to learn these overlay signal variations, which serves as a low-overhead classifier returning a binary 0 or 1 per detected impairment pattern. By mapping device-specific injected impairment patterns to signal variations, ISK validates device IDs with only few inphase (I) and quadrature (Q) samples. Furthermore, through an experimental testbed, ISK is shown to be resilient to channel and SNR level variations, allowing a throughput of 93-1500 Kbps on the covert channel that is undetected by other receivers.