In this work, a robust steganography framework to hide a color image into a stereo images is proposed. The embedding algorithm is performed via Discrete Cosine Transform (DCT) and Quantization Index Modulation-Dither Modulation (QIM-DM) hiding the secret data. Additionally, the Arnold’s Cat Map Transform is applied in order to scramble the secret color image, guaranteeing better security and robustness of the proposed system. Novel framework has demonstrated better performance against JPEG compression attacks among other existing approaches. Besides, the proposed algorithm is developed taking into account the parallel paradigm in order to be implemented in multi-core CPU increasing the processing speed. The results obtained by the proposed framework show high values of PSNR and SSIM, which demonstrate imperceptibility and sufficient robustness against JPEG compression attacks.