Cyberattacks pose a serious threat to the wireless transfer of sensitive healthcare data, hampering the level of privacy offered. Numerous cyber-security modules have been developed. However, many of these methods are unsuitable for real-time medical data processing. In this article, we present a cybersecurity framework developed for medical images in a smart healthcare system. We propose two novel two-dimensional chaotic maps, called the logistic regulated quadratic map (LRQ) and quadratic regulated quadratic map (QRQ), which have compound chaotic properties and a large chaotic range. We present an encryption technique based on the LRQ and QRQ map and demonstrate that the exceedingly chaotic pseudorandom number sequence generated by the maps results in a highly robust cipher image. Our fast cryptosystem can encrypt an image of size 128 × 128 in approximately 0.03 s. The proposed cybersecurity solution protects data against cyberattacks and ensures a seamless treatment experience.