A chaos-based image encryption algorithm based on multiresolution singular value decomposition and a symmetric attractor

ABSTRACT

This paper proposes a new image cryptosystem using multiple chaotic maps and multiresolution singular value decomposition (MR-SVD). The encryption process starts with implementing the MR-SVD to decompose the original image into the four fundamental sub-bands, i.e., Approximation (A), Vertical (V), Horizontal (H), Diagonal (D) sub-bands respectively. Since the approximation part gives the most information about the image, this sub-band is selected to perform permutation and diffusion. The permutation of all the four sub-bands is done by deploying the Baker map. The diffusion of pixels in the permuted approximation part is done by our neighbourhood diffusion scheme that uses the numerical solution of the chaotic Thomas' cyclically symmetric attractor. The final cipher is obtained by combining all the four (A, H, V, D) partial ciphers by performing inverse MR-SVD. The experimental results of our proposed scheme on various benchmarks tests indicate that the algorithm is highly secure and can withstand various attacks.

KEYWORDS:

• Baker map
• image encryption
• multiresolution singular value decomposition
• Thomas' cyclically symmetric attractor
• NIST

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes on contributors

Farhan Musanna received his B.sc(H) Mathematics degree from the University of Delhi, India in 2013 and did his Masters in Mathematics with Computer Science from Jamia Millia Islamia, New Delhi, India in 2015. He is currently pursuing his Ph.D. from the Department of Mathematics, Indian Institute of Technology, Roorkee, India. His research interests include multimedia security, privacy,developing encryption algorithms.

Deepak Dangwal is currently pursuing Ph.D. from the Department of Mathematics, Indian Institute of Technology, Roorkee, India. His research interests include multimedia security, privacy, developing encryption algorithms.

Sanjeev Kumar is working as an Associate Professor with Department of Mathematics, Indian Institute of Technology Roorkee since April 2016. Earlier, he worked as an assistant professor with Department of Mathematics, Indian Institute of Technology Roorkee from November 2010 to April 2016. He also worked as a postdoctoral fellow with the Department of Mathematics and Computer Science, University of Udine, Italy from March 2008 to November 2010. He has completed his PhD in Applied Mathematics from IIT Roorkee, India in 2008. His areas of research include image processing, inverse problems and machine learning. He has co-convened the first international conference on computer vision and image processing in 2016, and has served as a reviewer and program committee member of more than 20 international journals and conferences. He conducted two workshops on Image Processing at IIT Roorkee in recent years. He has published more than 58 papers in various international journals and reputed conferences. He has completed a couple of sponsored research projects.

Varun Malik is currently pursuing a B.Tech in Computer Science from Maharaja Surajmal Institute of Technology, New Delhi, India.

ORCID

Sanjeev Kumar http://orcid.org/0000-0001-7728-3668

Additional information

Funding

One of the authors, Farhan Musanna, is thankful to IIT Roorkee and the Ministry of Human Resource Development (MHRD), Government of India, for the financial support for carrying out this work (MHR-01-23-200-428). This work is also supported by the Indian Space Research Organization through its project OGP-150 (RESPOND).