A public and private key image encryption by modified approach of Vigener cipher and the chaotic maps

ABSTRACT

The article presents a real-time image encryption using a modified approach of Vigenère cipher and the chaotic maps with an efficient key management. The modification is provided to Vigenère cipher through the key expansion procedure. The proposed encryption chooses four random keys of 8-tuples to expand into the $8\times 8$ initial key block. Thereafter, the Vigenère cipher encrypts the pixels blocks using the initial key block and the next blocks through key updation using the XOR operation and the Arnold transform. Later, the partially encrypted image is further scrambled through the Baker map to increase the randomness and unpredictability of the data. The chosen secret key parameters are exchanged publicly through the Diffie–Hellman key exchange agreement. Simulation results and comparison analysis of some extant systems ensure that the proposed algorithm is secure against cryptanalytic attacks and efficient in real-time image processing. Further, the average execution time for encryption and decryption of an image with size $256\times 256$ is 0.4926 which is very efficient than a typical and recent encryption scheme.

KEYWORDS:

• Vigenère cipher
• Arnold transform
• Diffie–Hellman key exchange
• Baker map
• Public and private key
• Baker map

Additional information

Funding

The fourth author is thankful to the National Board for Higher Mathematics [grant number 02011/10/2020 NBHM(R.P.)/R&D II/7025], Department of Atomic Energy, India for providing financial support.

Notes on contributors

Umar Hussain Mir

Umar Hussain Mir, is a Ph.D. student in the Department of Mathematics Central University of Jammu, India. He obtained his Masters in Mathematics from University of Kashmir in 2014. His current areas of interests include image encryption algorithms, cryptography and image processing.

Parveiz Nazir Lone

Parveiz Nazir lone, is a Ph.D. student in the Department of Mathematics Central University of Jammu, India. He obtained his Bachelors and Masters from University of Kashmir in 2013 and 2015 respectively. His current research of interests include, algebraic cryptography, multimedia security, chaos based cryptography and image processing.

Deep Singh

Deep Singh, is presently an Associate Professor and Head of the Department of Mathematics and Statistics at Central University of Punjab, India, and has done his Ph.D. from Indian Institute of Technology, Roorkee, India. He has published more than 20 research articles in reputed journals. His areas of interest includes image processing, information security, boolean functions and their generalization, cryptology and cryptography.

D. C. Mishra

D. C. Mishra, is presently working as a Assistant Professor and Head of the Department of Mathematics at Govt. P. G. College Jaiharikhal, Uttarakhand, India, and has done his Ph.D. from Indian Institute of Technology, Delhi, India. He has published more than 50 research papers in international journals and is actively working in several area of applied cryptography, network security, and image security.