Enhancing Image Security during Transmission using Residue Number System and k-shuffle

  • Issah Zabsonre Alhassan Department of Computer Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
  • Edward Danso Ansong Department of Computer Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
  • Gaddafi Abdul-Salaam Department of Computer Science, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
  • Salamudeen Alhassan Department of Mathematics and ICT, Bagabaga College of Education, Tamale, Ghana
Keywords: encryption, decryption, moduli set, k-shuffle, cryptography

Abstract

This paper proposes an algorithm that enhances the speed of transmission and secure images that are transmitted over internet or a network. The proposed cryptosystem uses a modified k-shuffling technique to scramble pixels of images and further decomposes them using Residue Number System. Simulations are done using two moduli sets with the modified k-shuffle technique. Analyses of results showed that both simulations could secure images without any loss of information and also the time taken for a complete encryption/decryption process is dependent on the moduli set. Among the chosen moduli sets, the even moduli set optimizes and completes execution using less time as compared to the traditional moduli set. The proposed scheme also showed resistance to statistical attacks (histogram, ciphertext, correlation attacks) and a significant reduction in the size of cipher images which enhances the speed of transmission over network.

References

A. Roy, A. P. Misra and S. Banerjee, Chaos-based image encryption using vertical-cavity surface-emitting lasers, Optik 176 (2019), 119-131. https://doi.org/10.1016/j.ijleo.2018.09.062

G. Ke, H. Wang, S. Zhou and H. Zhang, Encryption of medical image with most significant bit and high capacity in piecewise linear chaos graphics, Measurement 135 (2019), 385-391. https://doi.org/10.1016/j.measurement.2018.11.074

M. Kumari, S. Gupta and P. Sardana, A survey of image encryption algorithms, 3D Research 8(4) (2017), 37. https://doi.org/10.1007/s13319-017-0148-5

C. Fu et al., A new chaos-based color image encryption scheme with an efficient substitution keystream generation strategy, Security and Communication Networks 2018 (2018), Article ID 2708532, 13 pp. https://doi.org/10.1155/2018/2708532

M. Hazarika, A Review of Chaos Based Image Encryption Techniques, International Journal of Engineering Research & Technology (IJERT) 3(2) (2014), 2209-2212.

S. Alhassan and K. Gbolagade, Enhancement of the Security of a Digital Image using the Moduli Set, International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) 2(7) (2013), 2223-2229.

H. Noura, L. Sleem and R. Couturier, A revision of a new chaos-based image encryption system: Weaknesses and limitations, arXiv preprint arXiv:1701.08371, 2017.

J. Sachs, Digital Image Basics, Digital Light & Color, Cambridge, Massachusetts, 1999.

V. Mishra, S. Kumar and N. Shukla, Image acquisition and techniques to perform image acquisition, A Journal of Physical Sciences, Engineering and Technology 9(1) (2017), 21-24. https://doi.org/10.18090/samriddhi.v9i01.8333

M. Barakat, C. Eder and T. Hanke, An Introduction to Cryptography, Timo Hanke at RWTH Aachen University, 2018.

P. Dixit et al., Traditional and hybrid encryption techniques: A survey, in: Networking Communication and Data Knowledge Engineering, Lecture Notes on Data Engineering and Communications Technologies, vol. 4, Springer, Singapore, 2018, pp. 239-248. https://doi.org/10.1007/978-981-10-4600-1_22

W. Stallings, Cryptography and Network Security, 4/E, Pearson Education India, 2006.

L.-P. Shao et al., 2D triangular mappings and their applications in scrambling rectangle image, Information Technology Journal 7(1) (2008), 40-47. https://doi.org/10.3923/itj.2008.40.47

M. Mishra et al., Image encryption using Fibonacci-Lucas transformation, 2012. arXiv preprint: arXiv:1210.5912. https://doi.org/10.5121/ijcis.2012.2312

K. Shaw, Arnold’s Cat Map, 2006.

K.-L. Chung and L.-C. Chang, Large encrypting binary images with higher security, Pattern Recognition Letters 19(5-6) (1998), 461-468. https://doi.org/10.1016/S0167-8655(98)00017-8

M. Salleh, S. Ibrahim and I. F. Isnin, Image encryption algorithm based on chaotic mapping, Journal Teknologi 39(D) (2003), 1-12. https://doi.org/10.11113/jt.v39.458

L. Zhang, X. Liao and X. Wang, An image encryption approach based on chaotic maps, Chaos, Solitons & Fractals 24(3) (2005), 759-765. https://doi.org/10.1016/j.chaos.2004.09.035

A. Mitra, Y. S. Rao and S. Prasanna, A new image encryption approach using combinational permutation techniques, International Journal of Computer Science 1(2) (2006), 127-131.

M. A. B. Younes, and A. Jantan, Image encryption using block-based transformation algorithm, IAENG International Journal of Computer Science 35(1) (2008).

K. Struss, A Chaotic Image Encryption, Mathematics Senior Seminar, University Minnesota, USA, 2009, pp. 1-19.

M. Ahmad and M. S. Alam, A new algorithm of encryption and decryption of images using chaotic mapping, International Journal on Computer Science and Engineering 2(1) (2009), 46-50.

D. Chattopadhyay, M. Mandal and D. Nandi, Symmetric key chaotic image encryption using circle map, Indian Journal of Science and Technology 4(5) (2011), 593-599.

P. V. N. Reddy and R. Karumuri, Image encryption and decryption in RNS domain based on {2n, 22n+1-1, 2n+1, 2n-1} moduli set, 2016 International Conference on Communication and Electronics Systems (ICCES), Coimbatore, 2016, pp. 1-5. https://doi.org/10.1109/CESYS.2016.7889984

D. G. Amalarethinam and J. S. Geetha. Image encryption and decryption in public key cryptography based on MR, 2015 International Conference on Computing and Communications Technologies (ICCCT), Chennai, 2015, pp. 133-138. https://doi.org/10.1109/ICCCT2.2015.7292733

S. Chakraborty et al., A novel lossless image encryption method using DNA substitution and chaotic Logistic map, International Journal of Security and Its Applications 10(2) (2016), 205-216. https://doi.org/10.14257/ijsia.2016.10.2.19

J. Ferdush, M. Begum and A. Mahmood, A new image encryption technique combining the idea of one time pad with RGB value, International Journal of Computer Applications 178(5) (2017), 12-15. https://doi.org/10.5120/ijca2017915823

P. Deshmukh, An image encryption and decryption using AES algorithm, International Journal of Scientific & Engineering Research 7(2) (2016), 2229-5518.

V. K. P. Kalubandi et al., A novel image encryption algorithm using AES and visual cryptography, 2016 2nd International Conference on Next Generation Computing Technologies (NGCT), Dehradun, 2016, pp. 808-813. https://doi.org/10.1109/NGCT.2016.7877521

G. Ye et al., A chaotic image encryption algorithm based on information entropy, International Journal of Bifurcation and Chaos 28(01) (2018), 1850010. https://doi.org/10.1142/S0218127418500104

C. Yu et al., Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram, Multimedia Tools and Applications 77(4) (2018), 4585-4608. https://doi.org/10.1007/s11042-017-4637-6

B. Liu et al. Experimental realizing image encryption based on optical chaos, Proc. SPIE 11052, Third International Conference on Photonics and Optical Engineering, 1105219, 24 January 2019. https://doi.org/10.1117/12.2522014

N. Singh, An overview of Residue Number System, National Seminar on Devices, Circuits & Communication, November 06th – 07th, 2008, Organized by Department of ECE, B.I.T, Mesra, Ranchi, 2008.

K. Isupov and V. Knyazkov, Interval estimation of relative values in residue number system, Journal of Circuits, Systems and Computers 27(01) (2018), 1850004. https://doi.org/10.1142/S0218126618500044

P. Diaconis, R. Graham and W. M. Kantor, The mathematics of perfect shuffles, Advances in Applied Mathematics 4(2) (1983), 175-196. https://doi.org/10.1016/0196-8858(83)90009-X

E. S. Packard, The Order of a Perfect k-shuffle, Texas Tech University, 1990.

S. Ramnath and D. Scully, Moving card i to position j with perfect shuffles, Mathematics Magazine 69(5) (1996), 361-365. https://doi.org/10.1080/0025570X.1996.11996475

A. Madain et al., Audio scrambling technique based on cellular automata, Multimedia Tools and Applications 71(3) (2014), 1803-1822. https://doi.org/10.1007/s11042-012-1306-7

S. Goel, Analysis of top to bottom-k shuffles, Annals of Applied Probability 16(1) (2006), 30-55. https://doi.org/10.1214/10505160500000062

K. A. Gbolagade and S. D. Cotofana, A residue to binary converter for the {2n + 2, 2n + 1, 2n} moduli set, 2008 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, 2008, pp. 1785-1789. https://doi.org/10.1109/ACSSC.2008.5074734

Published
2020-07-07
How to Cite
Alhassan, I. Z., Ansong, E. D., Abdul-Salaam, G., & Alhassan, S. (2020). Enhancing Image Security during Transmission using Residue Number System and k-shuffle. Earthline Journal of Mathematical Sciences, 4(2), 399-424. https://doi.org/10.34198/ejms.4220.399424
Section
Articles