The security of the healthcare system is a significant concern that requires thorough investigation. Consequently, medical image encryption is a crucial endeavor in healthcare applications. In the past, conventional image encryption schemes were primarily used to convert original images into encrypted ones. Although this approach ensures image privacy, it does not achieve cloud-based usability. Researchers have recently suggested Thumbnail-Preserving Encryption (TPE) to balance image usability and security on cloud platforms. Existing TPE techniques for intra-block grouping often use several pseudo-random functions with significant computing complexity, resulting in prolonged encryption and decryption times. A new TPE scheme employed by advanced SPE based on chaotic maps (known as TPE-ASPEC) is introduced to overcome this issue. In the TPE-ASPEC scheme, all block pixels go through two rounds of permutation and substitution (PSP) phases to encrypt the image. This effectively addresses the issue of inadequate encryption efficiency and significantly enhances encryption speed. The experiments indicate that the cipher image is suitable for managing cloud-based medical data because it balances usability and security well.