Image encryption algorithm with an avalanche effect based on a six-dimensional discrete chaotic system

Article
  • 21 Downloads

Abstract

This paper introduces a six-dimensional discrete chaotic systems (SDDCS) with some simple sine functions and a chaotic pseudorandom number generator (CPRNG) that is designed based on the SDDCS. A encryption scheme with both key avalanche effect and plaintext avalanche effect (SESKPAE) is proposed by using the random sequence generated by the CPRNG. The algorithm has three advantages: First, the initial values of the chaotic system are calculated by using the SHA-256 hash value of the plain image and the given values, there are different initial values for different plain images. Thus, our algorithm can resist against the chosen-plaintext and known-plaintext attacks effectively. Second, the new algorithm adopts ciphertext feedback mechanism to further strengthen the safety. Third, our new algorithm has an “avalanche effect”, in other words, the decrypted ciphertext will become a “white” image with a few “black spots” rather than a random chaotic image as a result of the wrong key. The experimental results and security analysis show that the algorithm has the advantages of large key space, no obvious statistical characteristics of ciphertext, sensitive to plaintext and keys, and able to resist chosen-plaintext attack and active attacks.

Keywords

Image encryption Six dimensional discrete chaotic system Pseudo random number generator Avalanche effect SHA-256 Chosen-plaintext attack 

Notes

Acknowledgements

This work was supported by National Natural Science Foundation of China (No. 61472451), the Open Project of Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing (No. 2016CSOBDP0103), the Shan Dong Province Nature Science Foundation (Grant. ZR2017MEM019) and the Science Research Fund of Liaocheng University (No. 318011606).

References

  1. 1.
    Chen XF, Huang XY, Li J (2015) New algorithms for secure outsourcing of large-scale systems of linear equations. IEEE Trans Inf Forensics Secur 10(1):69–78CrossRefGoogle Scholar
  2. 2.
    Chen E, Min LQ, Chen GR (2017) Discrete chaotic systems with one-line equilibria and their application to image encryption. Int J Bifurcation Chaos 27:1750046-1-17MathSciNetMATHGoogle Scholar
  3. 3.
    Feistel H (1973) Cryptography and computer privacy. Sci Amer Mag 228:15–23CrossRefGoogle Scholar
  4. 4.
    Hamza R (2017) A novel pseudo random sequence generator for image-cryptographic applications. J Inf Secur Appl 35:119–127Google Scholar
  5. 5.
    Huang XL, Ye GD (2014) An image encryption algorithm based on hyper-chaos and DNA sequence. Multimedia Tools Appl 72:57–70CrossRefGoogle Scholar
  6. 6.
    Huang ZG, Liu SL, Mao XP (2017) Insight of the protection for data security under selective opening attacks. Inf Sci 412:223–241CrossRefGoogle Scholar
  7. 7.
    Jain A, Rajpal N (2016) A robust image encryption algorithm resistant to attacks using DNA and chaotic logistic maps. Multimedia Tools Appl 75:5455–5472CrossRefGoogle Scholar
  8. 8.
    Lai Q, Chen SM (2016) Research on a new 3D autonomous chaotic system with coexisting attractors. Optik 127:3000–3004CrossRefGoogle Scholar
  9. 9.
    Lambi D (2017) Cryptanalyzing a novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn 89:2255–2257CrossRefGoogle Scholar
  10. 10.
    Li J, Huang XY, Li JW, Chen XF, Xiang Y (2014) Securely outsourcing attribute-based encryption with checkability. IEEE Trans Parallel Distrib Syst 25(8):2201–2210CrossRefGoogle Scholar
  11. 11.
    Li J, Li JW, Chen XF et al (2015) Identity-based encryption with outsourced revocation in cloud computing. IEEE Trans Comput 64(2):425–437MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Li J, Li YK, Chen XF et al (2015) A hybrid cloud approach for secure authorized deduplication. IEEE Trans Parallel Distrib Syst 26(5):1206–1216CrossRefGoogle Scholar
  13. 13.
    Li P, Li J, Huang ZG et al (2017) Multi-key privacy-preserving deep learning in cloud computing. Futur Gener Comput Syst 74:76–85CrossRefGoogle Scholar
  14. 14.
    Liu HJ, Wang XY (2010) Color image encryption based on one-time keys and robust chaotic maps. Comput Math Appl 59:3320–3327MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Liu HJ, Wang XY (2011) Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt Commun 284:3895–3903CrossRefGoogle Scholar
  16. 16.
    Liu L, Zhang Q, Wei XP (2012) A RGB image encryption algorithm based on DNA encoding and chaos map. Comput Electr Eng 38:1240–1248CrossRefGoogle Scholar
  17. 17.
    Liu Y, Tang J, Xie T (2014) Cryptanalyzing a RGB image encryption algorithm based on DNA encoding and chaos map. Opt Lasers Eng 60:1–5Google Scholar
  18. 18.
    Liu Q, Wang GJ, Liu XH, Peng T, Wu J (2017) Achieving reliable and secure services in cloud computing environments. Comput Electr Eng 59:153–164CrossRefGoogle Scholar
  19. 19.
    Min LQ, Chen GR (2013) A novel stream encryption scheme with avalanche effect. Eur Phys J B 86(11):459MathSciNetCrossRefGoogle Scholar
  20. 20.
    Mohammad AA, Fatimah AA, Mahmoud AA (2018) Impact of digital fingerprint image quality on the fingerprint recognition accuracy. Multimed Tools Appl.  https://doi.org/10.1007/s11042-017-5537-5
  21. 21.
    Murillo-Escobar MA, Cruz-Hernández C et al (2017) A novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn 87:407–425MathSciNetCrossRefGoogle Scholar
  22. 22.
    Pang S, Liu Y (2011) A new hyperchaotic system from the Lü system and its control. J Comput Appl Math 235:2775–2789MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Qi GY, Chen GR, van Wyk MA, van Wyk BJ, Zhang YH (2008) A four-wing chaotic attractor generated from a new 3D quadratic autonomous system. Chaos, Solitons Fractrals 38:705–721CrossRefMATHGoogle Scholar
  24. 24.
    Rukhin R, Soto J, Nechvatal J (2001) A statistical test suite for random and pseudorandom numbergenerator for cryptographic applications. NIST Special PublicationGoogle Scholar
  25. 25.
    Shannon CE (1949) Communication theory of security systems. Bell Syst Tech J 28:656–715CrossRefMATHGoogle Scholar
  26. 26.
    Spillman RJ (2005) Classical and contemporary cryptology. Pearson Education INC, Upper Saddle RiverGoogle Scholar
  27. 27.
    Sprott JC (2003) Chaos and time-series analysis. Oxford University Press, OxfordMATHGoogle Scholar
  28. 28.
    Sprott JC, Wang X, Chen GR (2013) Coexistence point, periodic and strange attractors. Int J Bifurcation Chaos 23:1350093MathSciNetCrossRefGoogle Scholar
  29. 29.
    Sun KH, Liu X, Zhu CX, Sprott J (2012) Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system. Nonlinear Dyn 69:1383–1391MathSciNetCrossRefGoogle Scholar
  30. 30.
    Wang X, Teng Y, Qin X (2012) A novel colour image encryption algorithm based on chaos. Signal Process 92:1101–1108CrossRefGoogle Scholar
  31. 31.
    Wu Y, Hua Z, Zhou Y (2015) N-dimensional discrete cat map generation using Laplace expansions. IEEE Trans Cybern 46:2622–2633CrossRefGoogle Scholar
  32. 32.
    Wu X, Zhu B, Hu Y (2017) A novel colour image encryption scheme using rectangular transform-enhanced chaotic tent maps. IEEE Acces 5:6429–6436Google Scholar
  33. 33.
    Yang XP, Min LQ, Wang X (2015) A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption. Chaos 25:053104MathSciNetCrossRefMATHGoogle Scholar
  34. 34.
    Yu S, Wang GJ, Zhou WL (2015) Modeling malicious activities in cyber space. IEEE Netw 29(6):83–87CrossRefGoogle Scholar
  35. 35.
    Yu CY, Li JZ, Li X, Ren XC, Gupta BB (2018) Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram. Multimed Tools Appl 77:4585–4608CrossRefGoogle Scholar
  36. 36.
    Zarei A (2015) Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors. Nonlinear Dyn 81:585–605MathSciNetCrossRefGoogle Scholar
  37. 37.
    Zhang XP, Mao YB, Zhao ZM (2014) An efficient chaotic image encryption based on alternate circular Sboxes. Nonlinear Dyn 78:359–369CrossRefGoogle Scholar
  38. 38.
    Zhang XP, Zhao ZM, Wang JY (2014) Chaotic image encryption based on circular substitution box and key stream buffer. Signal Process Image 29:902–913CrossRefGoogle Scholar
  39. 39.
    Zhu CX (2012) A novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285(1):29–37CrossRefGoogle Scholar
  40. 40.
    Zhu CX, Sun KH (2012) Cryptanalysis and improvement of a class of hyperchaos based image encryption algorithms. Acta Phys Sin 61(12):120503MATHGoogle Scholar
  41. 41.
    Zhu CX, Sun KH (2018) Cryptanalyzing and improving a novel color image encryption algorithm using RT-enhanced chaotic tent maps. IEEE Access 6:18759–18770CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Computer ScienceLiaocheng UniversityLiaochengChina
  2. 2.School of Information Science and EngineeringCentral South UniversityChangshaChina
  3. 3.Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data ProcessingYulin Normal UniversityYulinChina

Personalised recommendations