Image Compression is to shrink insignificance and redundancy of the image data and it is obligatory for efficient transmission and storage of images. Image data are self -descriptive and contains sensitive information, yet partial data will convey more information. Hence robust security mechanisms are required for defending and privacy protection of image data. A robust secured image compression scheme has been proposed in this paper. Methods: In this work two levels of security have been accomplished to improve the robustness of the encryption system. Torus Automorphism and Rubik's cube principle are used for pixel scrambling and shuffling along with adaptive DWT based image compression. Findings: Extracting greatest image quality at a given bit-rate or compression ratio is the main goal of Image Compression. Experimental results have shown that the proposed system of secured image compression offers compression ratio of 97% and a bit rate of 0.25bpp and the scheme is highly robust with respect to the security parameters such as UACI (Unified Average Changing Intensity) and NPCR (Number of Pixels Change Rate). Application: The proposed scheme is highly suitable for small hand held wireless communication gadgets such as mobile phones to upload/download on/from Internet, where fast and efficient on the fly image encryption and transmission are required.