A secure and robust stereo image encryption algorithm based on DCT and Schur decomposition

Document Type : Research Paper


1 Assistant Prof., Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, 248007, India

2 Assistant Professor, Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, 248007, India.

3 Assistant Professor, Department of Mathematics, University of Petroleum and Energy Studies, Dehradun, Uttarakhand, 248007, India

4 Assistant Professor, Department of Mathematics, Graphic Era Deemed to be University, Dehradun, Uttarakhand, 248002, India.

5 Associate Professor, Department of Mathematics, Indian Institute of Technology Jodhpur, Rajasthan, 342037, India.


Security solutions of stereo images are always a major concern during the transmission and communication. In this manuscript, a simple yet efficient framework for encrypting stereo images is formulated using discrete cosine transform (DCT), generalized logistic map, Schur decomposition and magic square method. The framework initiated with the integration of DCT and generalized logistic map to unify both pair of images. This unified image is then encrypted using the Schur decomposition and magic square method. The various experiments and analysis have been done to explore the validity, proficiency and performance of the purport framework.


Agreste S. & Andaloro G. (2008). A new approach to pre-processing digital image for wavelet-based transform. Journal of Computational and Applied Mathematics, 221(2), 274-283.
algorithm with mixed modulation incorporated. Information Sciences, 519, 161-182.
Ali M., Ahn C. W., Pant M., Kumar S., Singh M. K., Saini D. (2020). An optimized digital watermarking scheme based on invariant DC coefficients in spatial domain. Electronics, 9 (9), 14-28.
Alturki F. T., Almutairi A., & Mersereauu R, M. (2007).  Analysis of blind data hiding using discrete cosine transform phase modulation. Signal Processing and Image Communication, 22(4), 347–362.
Amirgholipour S.K. & Naghsh-Nilchi A. R. (2009). Robust digital image watermarking based on joint DWT-DCT. IEEE Transaction on Image Processing, 3(2), 42–54.
based on spatiotemporal chaotic system. Optik, 217, 64884,
based secret image sharing with authentication. Signal Processing, 173, 107571.
Bhat K. V., Sengupta I., & Das A. (2011). A new audio watermarking scheme based on singular value decomposition and quantization. Circuit, System and Signal Processing, 30(5), 915–927.
Bhatnagar G. & Wu Q. M. J. (2012). Selective image encryption based on pixels of interest and singular value decomposition. Digital Signal Processing, 22, 648-663.
Chang C. C., Hwang M. S., & Chen T. S. (2001).  A new encryption algorithm for image cryptosystems. The Journal of System and Software, 58, 83-91.
Chuang T. & Lin J. (1999).  A new multiresolution approach to still image encryption. Pattern Recognition and Image Analysis, 9(3), 431–436.
compressed images.  In:  Advanced Concepts for Intelligent Vision Systems, (pp.  90–97).
Dong H., Lu P., & Ma X. (2011). Image scrambling algorithm based on mixed chaotic systems and extended zigzag transformation. Computer Engineering and Design, 32(4), 1241–1245.
Droogenbroeck M. & Benedett R. (2002). Techniques for a selective encryption of uncompressed and
Guo J.I. & Yen J. C. (2000). A new mirror-like image encryption algorithm and its VLSI architecture. Pattern Recognition and Image Analysis, 10(2), 236–247.
Haq T.U. & Shah T. (2020). 12×12 S-box Design and its Application to RGB Image Encryption. Optik,
Hu H.T., Hsu L. Y., & Chou H. H. (2020).  An improved SVD-based blind color image watermarking
Huijuan X., Shuisheng Q., Chengliang D. , Zhong H. Y., & Ying C. (2007, November).  A composite image encryption scheme using aes and chaotic series.  In: The First International Symposium on Data, Privacy, and E-Commerce (ISDPE), (pp. 277–279).
Images. In Transactions on Data Hiding and Multimedia Security IX, (pp. 25–41).
Knockaert L., Backer B., & Zutter D. (1999). SVD compression, unitary transforms, and computational complexity. IEEE Transaction on Signal Processing, 47(10), 2724-2729.
Kumar S., Bhatnagar G. (2019). SIE: an application to secure stereo images using encryption. In Handbook of Multimedia Information Security: Techniques and Applications, (pp. 37-61).
Kumar S., Bhatnagar G., Raman B., Sukavanam N. (2012). Security of stereo images during communication and transmission. Advanced Science Letters, 6 (1), 173-179.
Lin C., Wu M., Bloom M. J., Cox I. J., Miller M., & Lui Y. (2001). Rotation, scale, and translation resilient watermarking for images. IEEE Transaction on Signal Processing, 10(5), 767-782.
Lin K.T. (2011). Hybrid encoding method by assembling the magic-matrix scrambling method and the binary encoding method in image hiding. Optics Communication, 284, 1778–1784.
Liu X. (2004). Four alternative patterns of the Hilbert curve. Applied Mathematics and Computation, 147(3), 675-685.
Maniccam S.S. & Bourbakis N.G. (2004). Image and video encryption using SCAN patterns. Pattern Recognition, 37(4), 725–737.
Menezes A. J., Oorschot P. C. V., & Vanstone S. (1997). In Handbook of Applied cryptography, Vol. 1. CRC Press.
Mohammad A., Alhaj A., & Shaltaf S. (2008). An improved SVD-based watermarking scheme for protecting rightful ownership. Signal Processing, 88(9), 2158–2180.
Qin Y., Wang H., Wang Z., Gong Q., & Wang D. (2016). Encryption of QR code and grayscale image in interference-based scheme with high quality retrieval and silhouette problem removal. Optics and Lasers in Engineering, 84, 62-73.
Shannon C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379–423.
Singh M. K., Kumar S., Ali M., Saini D. (2020). Application of a novel image moment computation in X-ray and MRI image watermarking. IET Image Processing, 15(3), 666-682.
Singh S. P. & Bhatnagar G. (2018).  A new robust watermarking system in integer DCT domain. Journal of Visual Communication and Image Representation, 53, 86-101.
Stinson D. R. & Paterson M. (2018). In Cryptography: Theory and Practice, Vol. 1.  CRC Press.
Wang X. & Yang J. (2020). A novel image encryption scheme of dynamic S-boxes and random blocks
Xiong L., Zhong X., & Yang C. N. (2020).  DWT-SISA: a secure and effective discrete wavelet transform
Yahya A. & Abdalla A. (2008).  A shuffle image encryption algorithm. Journal of Computer Science,   
Yamaguchi Y. (2014). Extended Visual Cryptography Scheme for Multiple-Secrets Continuous-Tone
Wang X., Liu L., & Zhang Y. (2015).  A novel chaotic block image encryption algorithm based on dynamic random growth technique. Optics and Lasers in Engineering, 66, 10–18.
Li J. (2016). Asymmetric multiple-image encryption based on octomom Fresnel transform and sine logistic modulation map. Journal of the Optical Society of Korea, 20(3), 341–357.
Jithin K. & Sankar S. (2020). Colour image encryption algorithm combining, Arnold map, DNA sequence operation, and a Mandelbrot set. Journal of Information Security and Applications, 50(102428).
Li J., Xiang S., Wang H., Gong J., & Wen A. (2018).  A novel image encryption algorithm based on synchronized random bit generated in cascade-coupled chaotic semiconductor ring lasers. Optics and Lasers in Engineering, 102, 170-180.