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Advanced healthcare applications such as telemedicine, smart health, and e-health transmit digital images over an open and insecure communication network. Hence, it becomes mandatory to protect these images from eavesdropping to protect patients’ sensitive data. In last two decades, researchers have proposed many chaotic map based medical image cryptosystems. However, many of these systems have used chaotic maps that have a small chaotic range, and suffer from the issue of blank and stable windows. Motivated by the fact, the work in this paper proposes a new chaotic map referred to as an Improved Cosine Fractional Chaotic Map (ICFCM). This proposed map has wider and uniform chaotic range, more positive Lyapunov exponent, and does not have blank and stable windows. Also, we design a medical image encryption scheme using combination of ICFCM and DNA operation. The scheme takes four steps …