<p>To address the escalating need for secure and efficient multimedia transmission and optimized data storage, this paper proposes a robust double-phase image encryption and compression framework that integrates decomposition techniques within the Gyrator transform domain. In the proposed scheme, input images are converted into phase images and QZ synthesis is then utilized to fuse these images, generating highly secure, independent key components. These synthesized components are mapped into the Gyrator domain, whose additional rotational degree of freedom and strong parameter sensitivity provide improved security and encoding flexibility over conventional Fourier and fractional Fourier transform-based methods. To achieve efficient data handling, the transformed data undergoes truncated singular value decomposition. This step extracts structured components that facilitate concurrent encryption and compression, ensuring that the ciphertext is secure and compact. Upon decryption the input images are recovered with high accuracy as evidenced by the statistical metrics: MSE, PSNR, CC and SSIM. The truncated parameter k provides flexibility to control the trade-off between compression efficiency and reconstruction quality. The integration of these multi-domain operations results in a significantly enlarged key space and enhances resistance against brute-force, statistical, differential and basic cryptographic attacks. Numerical simulation results confirm that the proposed scheme maintains high compression efficiency without compromising the reconstruction fidelity. Robustness of the scheme is also evident from its endurance of noise and occlusion attacks.</p>