Telepresence surgical training based on mixed reality over the Internet is exposed to various cyber-attacks. Providing an adequate level of security against such attacks becomes an essential requirement for implementing this technology. The aim of this work is to improve the security of data transmission against several potential attacks while reducing the required execution time for encryption and decryption during real-time surgical telepresence training. In this research, a cryptosystem based on an enhanced chaotic map with Markov property using the Secure Hash Algorithm with 256-bit (SHA-256) is proposed to secure data during transmission. The enhanced chaotic map governs the diffusion process for image ciphering. The proposed scheme reduces the average processing time by 23.49%, i.e., from 83.99 ms (millisecond) to 64.33 ms, compared to the current state of the art solution, which is used as a benchmark in this work. Moreover, the Peak Signal to Noise Ratio (PSNR), which is used for measuring the encryption strength, is reduced by 17.33%, i.e., from 36.13 dB (decibel) to 29.87 dB compared to the same benchmark. The proposed solution demonstrates significant improvement in securing data against brute force attack, known-plaintext attack, chosen-plaintext attack and other statistical attacks. Also, the solution reduces the processing time required for both encryption and decryption.