Advertisement

Performance Analysis of Image Encryption Methods Using Chaotic, Multiple Chaotic and Hyper-Chaotic Maps

  • T. Gopalakrishnan
  • S. Ramakrishnan
Chapter

Abstract

Image Encryption is widely used to construct sensitive hidden information through insecure public networks which could only be accessed by the receiver. The plain image is encrypted using chaotic maps and cipher image is produced thereon. Symmetric keys are used for encrypting and decrypting the image. The challenges involved in the image encryption schemes are one dimensional logistic map having periodic windowing, selection of control parameter values, unsuitable key stream generation, more number of rounds in image encryption and image encryption with limited randomness. These issues are properly addressed and solved by using multiple chaotic maps and multiple hyper-chaotic maps through encryption techniques. Image encryption using multiple chaotic maps enhances correlation and entropy level to establish uniform distribution of histogram and differential attack analysis. The performance analysis metrics such as key space analysis, histogram analysis, correlation coefficient analysis, differential attack analysis information entropy analysis etc., are conducted and compared. The experimental analysis proves that the hyper-chaotic map based encryption method is more resourceful than the chaotic based encryption.

References

  1. 1.
    Blum, L, Blum, M & Shub, M, ‘A simple unpredictable pseudo-random number generator’, SIAM Journal on computing, vol. 15, no. 2, pp. 364-383, 1986.Google Scholar
  2. 2.
    Dachselt, F & Schwarz, W, ‘Chaos and cryptography’, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 12, no. 48, pp. 1498-1509, 2001.Google Scholar
  3. 3.
    Menezes, AJ, Van Oorschot, PC & Vanstone, SA, Handbook of applied cryptography, CRC press, 1996.Google Scholar
  4. 4.
    Palacios, A & Juarez, H, ‘Cryptography with cycling chaos’, Physics Letters A, vol. 303, no. 5, pp. 345-351, 2002.Google Scholar
  5. 5.
    Parker, TS & Chua, LO, ‘Chaos: A tutorial for engineers’, Proceedings of the IEEE, vol. 75, no. 8, pp. 982-1008, 1987.Google Scholar
  6. 6.
    Chen, G, Chen, Y & Liao, X, ‘An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps’, Chaos, solitons & fractals, vol. 31, no. 3, pp. 571-579, 2007.Google Scholar
  7. 7.
    Forouzan, BA & Mukhopadhyay, D, Cryptography and Network Security (Sie), McGraw-Hill Education, 2011.Google Scholar
  8. 8.
    Stallings, W, Cryptography and network security: Principles and practices, 5th edition, Prentice hall, New Delhi, 2011.Google Scholar
  9. 9.
    Zhang, G & Liu, Q, ‘A novel image encryption method based on total shuffling scheme’, Optics Communications, vol. 284, no. 12, pp. 2775-2780, 2011.Google Scholar
  10. 10.
    Zhang. X, Zhao. Z, Wang. J, ‘Chaotic image encryption based on circular substitution box and key stream buffer’, Signal Process.: Image Communication. Vol.29, No.8, pp.902–913, 2014.Google Scholar
  11. 11.
    Schneier, B, ‘A self-study course in block-cipher cryptanalysis’, Cryptologia, vol. 24, no. 1, pp. 18-33, 2000.CrossRefGoogle Scholar
  12. 12.
    Baptista, M 1998, ‘Cryptography with chaos’, Physics Letters A, vol. 240, no. 1, pp. 50-54.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Pecora, LM & Carroll, TL, ‘Synchronization in chaotic systems’, Physical review letters, vol. 64, no. 8, p. 821, 1990.Google Scholar
  14. 14.
    Gligoroski, D, Dimovski, D, Kocarev, L, Urumov, V & Chua, L, ‘A method for encoding messages by time targeting of the trajectories of chaotic systems’, International Journal of Bifurcation and chaos, vol. 6, no. 11, pp. 2119-2125, 1996.Google Scholar
  15. 15.
    Wong, K-W, ‘A combined chaotic cryptographic and hashing scheme’, Physics Letters A, vol. 307, no. 5, pp. 292-298, 2003.MathSciNetCrossRefGoogle Scholar
  16. 16.
    Safwan El Assad, Mousa Farajallah, ‘A new chaos-based image encryption system’, Signal Process.: Image Communication. Vol.41, pp.144-157, 2016.Google Scholar
  17. 17.
    Alvarez, G, Montoya, F, Romera, M & Pastor, G, ‘Cryptanalysis of an ergodic chaotic cipher’, Physics Letters A, vol. 311, no. 2, pp. 172-179, 2003.Google Scholar
  18. 18.
    Alvarez, G, Montoya, F, Romera, M & Pastor, G, ‘Cryptanalysis of dynamic look-up table based chaotic cryptosystems’, Physics Letters-A, vol. 326, no. 3, pp. 211-218, 2004.Google Scholar
  19. 19.
    Rukhin, A, ‘A statistical test suite for random and pseudorandom number generators for cryptographic applications’, NIST special publication, Revision 1a, 2010.Google Scholar
  20. 20.
    Castro, JCH, Sierra, JM, Seznec, A, Izquierdo, A & Ribagorda, A, ‘The strict avalanche criterion randomness test’, Mathematics and Computers in Simulation, vol. 68, no. 1, pp. 1-7, 2005.Google Scholar
  21. 21.
    Forré, R, ‘The strict avalanche criterion: spectral properties of Boolean functions and an extended definition’, in Proceedings on Advances in cryptology, pp. 450-468, 1990.Google Scholar
  22. 22.
    Wang, Y, Wong, K-W, Liao, X & Chen, G, ‘A new chaos-based fast image encryption algorithm’, Applied soft computing, vol. 11, no. 1, pp. 514-522, 2011.Google Scholar
  23. 23.
    Ye, R, ‘A novel chaos-based image encryption scheme with an efficient permutation-diffusion mechanism’, Optics Communications, vol. 284, no. 22, pp. 5290-5298, 2011.Google Scholar
  24. 24.
    Zeghid, M, Machhout, M, Khriji, L, Baganne, A & Tourki, R, ‘A modified AES based algorithm for image encryption’, International Journal of Computer Science and Engineering, vol. 1, no. 1, pp. 70-75, 2007.Google Scholar
  25. 25.
    Wong, K-W, ‘A fast chaotic cryptographic scheme with dynamic look-up table’, Physics Letters A, vol. 298, no. 4, pp. 238-242, 2002.MathSciNetCrossRefGoogle Scholar
  26. 26.
    Kwok, H & Tang, WK, ‘A fast image encryption system based on chaotic maps with finite precision representation’, Chaos, solitons & fractals, vol. 32, no. 4, pp. 1518-1529, 2007.Google Scholar
  27. 27.
    Patidar, V, Pareek, N, Purohit, G & Sud, K, ‘A robust and secure chaotic standard map based pseudorandom permutation-substitution scheme for image encryption’, Optics Communications, vol. 284, no. 19, pp. 4331-4339, 2011.Google Scholar
  28. 28.
    Yang, H, Wong, K-W, Liao, X, Zhang, W & Wei, P, ‘A fast image encryption and authentication scheme based on chaotic maps’, Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 11, pp. 3507-3517, 2010.Google Scholar
  29. 29.
    Wong, K-W & Yuen, C-H, ‘Embedding compression in chaos-based cryptography’, IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 55, no. 11, pp. 1193-1197, 2008.Google Scholar
  30. 30.
    Dong, Ce, ‘Color image encryption using one-time keys and coupled chaotic systems’, Signal Processing: Image Communication, vol. 29, no. 5, pp. 628-640, 2014.Google Scholar
  31. 31.
    Yuen, C-H & Wong, K-W, ‘A chaos-based joint image compression and encryption scheme using DCT and SHA-1’, Applied soft computing, vol. 11, no. 8, pp. 5092-5098, 2011.Google Scholar
  32. 32.
    Singh, N & Sinha, A, ‘Chaos based multiple image encryption using multiple canonical transforms’, Optics & Laser Technology, vol. 42, no. 5, pp. 724-731, 2010.Google Scholar
  33. 33.
    Tang, Z, Song, J, Zhang, X & Sun, R, ‘Multiple-image encryption with bit-plane decomposition and chaotic maps’, Optics and Lasers in Engineering, vol. 80, pp. 1-11, 2016.Google Scholar
  34. 34.
    Lian, S, Sun, J & Wang, Z, ‘A block cipher based on a suitable use of the chaotic standard map’, Chaos, solitons & fractals, vol. 26, no. 1, pp. 117-129, 2005.Google Scholar
  35. 35.
    François, M, Grosges, T, Barchiesi, D, Erra, R, ‘A new image encryption scheme based on a chaotic function’, Signal Processing: Image Communication, vol. 27, no. 3, pp. 249-259, 2012.zbMATHGoogle Scholar
  36. 36.
    Ahmad, J, Hwang, SO, ‘Chaos-based diffusion for highly autocorrelated data in encryption algorithms’, Nonlinear Dynamics, vol. 82, no. 4, pp. 1839-1850, 2015.MathSciNetCrossRefGoogle Scholar
  37. 37.
    Wong, K-W, Kwok, BS-H & Law, W-S, ‘A fast image encryption scheme based on chaotic standard map’, Physics Letters A, vol. 372, no. 15, pp. 2645-2652, 2008.Google Scholar
  38. 38.
    Liu, H & Wang, X 2011, ‘Color image encryption using spatial bit-level permutation and high-dimension chaotic system’, Optics Communications, vol. 284, no. 16, pp. 3895-3903.Google Scholar
  39. 39.
    Norouzi, B, Seyedzadeh, SM, Mirzakuchaki, S & Mosavi, MR, ‘A novel image encryption based on row-column, masking and main diffusion processes with hyper chaos’, Multimedia Tools and Applications, vol. 74, no. 3, pp. 781-811, 2015.Google Scholar
  40. 40.
    Xu, L, Li, Z, Li, J & Hua, W, ‘A novel bit-level image encryption algorithm based on chaotic maps’, Optics and Lasers in Engineering, vol. 78, pp. 17-25, 2016.Google Scholar
  41. 41.
    Abd-El-Hafiz, SK, Abd-El-Haleem, SH & Radwan, AG 2016, ‘Novel permutation measures for image encryption algorithms’, Optics and Lasers in Engineering, vol. 85, pp. 72-83, 2016.Google Scholar
  42. 42.
    Zhang, Y-Q, Wang, X-Y, Liu, J & Chi, Z-L, ‘An image encryption scheme based on the MLNCML system using DNA sequences’, Optics and Lasers in Engineering, vol. 82, pp. 95-103, 2016.Google Scholar
  43. 43.
    Li Shujun, LI, Qi, LI, Wenmin 2001, ‘Statistical properties of digital piecewise linear chaotic maps and their roles in cryptography and pseudo-random coding’, Lecture notes in computer science, vol.2260, pp.205-221, 2001.Google Scholar
  44. 44.
    Li Shujun, Guanrong Chen, Xuanqin Mou, ‘On the dynamic degradation of digital piecewise linear chaotic maps’, International Journal of Bifurcation and Chaos, vol.15, no.10, pp.3119-3151, 2005.MathSciNetCrossRefGoogle Scholar
  45. 45.
    Lozi, Rene, ‘Emergence of randomness from chaos’, International Journal of Bifurcation and Chaos, vol.22, no.2, pp.3119-3151, 2012.MathSciNetCrossRefGoogle Scholar
  46. 46.
    Gopalakrishnan, T., Ramakrishnan, S., Dhivya, N.: ‘An Image Encryption-Compression Algorithm Based on Hyper-Chaos and Number theory’, Proceedings of National Conference RTCSP-2014, Amrita Vishwa Vidyapeetham, Coimbatore, pp 88-91, 2014.Google Scholar
  47. 47.
    Gang-Quan, Si., Cao Hui., Zhang Yan-Bin, ‘A new four dimensional hyperchaotic Lorenz system and its adaptive control’, Chinese Phys.B, 20(1), pp 1-9, 2011.Google Scholar
  48. 48.
    Sriti Thakur, Amit Kumar Singh, Satya Prakash Ghrera, Mohamed Elhoseny, ‘Multi-layer security of medical data through watermarking and chaotic encryption for tele-health applications’, Multimedia Tools and Applications, first online, pp 1-14, Jun 2018.CrossRefGoogle Scholar
  49. 49.
    Wai-Kit Wong, Lap-piu, & Wong, K-w, ‘A modified chaotic cryptographic method’, Computer Physics Communications, vol.138, no.3, pp. 234-236, 2001.Google Scholar
  50. 50.
    Zhou, Y, Bao, L & Chen, CP, ‘Image encryption using a new parametric switching chaotic system’, Signal Processing, vol. 93, no. 11, pp. 3039-3052, 2013.Google Scholar
  51. 51.
    Zhou, Y, Bao, L & Chen, CP, ‘A new 1D chaotic system for image encryption’, Signal Processing, vol. 97, pp. 172-182, 2014.Google Scholar
  52. 52.
    Wang, X-Y, Yang, L, Liu, R & Kadir, A, ‘A chaotic image encryption algorithm based on perceptron model’, Nonlinear Dynamics, vol. 62, no. 3, pp. 615-621, 2010.Google Scholar
  53. 53.
    Bigdeli, N, Farid, Y & Afshar, K, ‘A robust hybrid method for image encryption based on Hopfield neural network’, Computers & Electrical Engineering, vol. 38, no. 2, pp. 356-369, 2012.Google Scholar
  54. 54.
    Zhu, H, Zhao, C & Zhang, X, ‘A novel image encryption–compression scheme using hyper-chaos and Chinese remainder theorem’, Signal Processing: Image Communication, vol. 28, no. 6, pp. 670-680, 2013.Google Scholar
  55. 55.
    Gopalakrishnan, T & Ramakrishnan, S, ‘Image Encryption in Bit Wise and Key Generation using Multiple Chaotic Maps’, Australian Journal of Basic and Applied Sciences, ISSN: 1991-8178, vol. 9, no. 27, pp. 200-208, Aug 2015.Google Scholar
  56. 56.
    Gopalakrishnan, T., Ramakrishnan, S, ‘Chaotic image encryption with Hash keying as key generator’, IETE Journal of Research, 63(2), pp 172-187, 2017.CrossRefGoogle Scholar
  57. 57.
    Gao, T & Chen, Z, ‘A new image encryption algorithm based on hyper-chaos’, Physics Letters A, vol. 372, no. 4, pp. 394-400, 2008.Google Scholar
  58. 58.
    Tedmori, S & Al-Najdawi, N, ‘Image cryptographic algorithm based on the Haar wavelet transform’, Information Sciences, vol. 269, pp. 21-34, 2014.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • T. Gopalakrishnan
    • 1
  • S. Ramakrishnan
    • 2
  1. 1.Department of Electrical and Electronics EngineeringKarpagam College of EngineeringCoimbatoreIndia
  2. 2.Department of Information TechnologyDr. Mahalingam College of Engineering and TechnologyPollachiIndia

Personalised recommendations