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E-Health systems based on the internet of things belong to real-time diagnosis and monitoring systems require optimizing solutions. Performing the quality of service and security of large-scale sensor network data developed for e-health-aware applications becomes a great challenge. To provide real-time effective solution, this paper introduces a novel generalized chaotic function expressed as a form of discrete mapping with a new approach for enhancing structure complexity. While the control parameters vary in a wide range of values, the structure exhibits several new one-dimensional discrete-time maps, including known ones namely Wavelet and Gaussian maps. Optimized values of the operands depending on excellent chaotic dynamic proprieties were chosen for highly random and secure keys. Simulation is conducted for different encryption algorithms applied to NIH chest X-ray data set to prove the new map efficiency in terms of speed and accuracy. The results show an excellent and satisfactory encryption time and security performances record that has reached; 0.0001s, supplemented by an entropy value of 7.9999947.