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

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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.

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References

  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):69–78

    Article  Google Scholar 

  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 27:1750046-1-17

    MathSciNet  MATH  Google Scholar 

  3. Feistel H (1973) Cryptography and computer privacy. Sci Amer Mag 228:15–23

    Article  Google Scholar 

  4. Hamza R (2017) A novel pseudo random sequence generator for image-cryptographic applications. J Inf Secur Appl 35:119–127

    Google Scholar 

  5. Huang XL, Ye GD (2014) An image encryption algorithm based on hyper-chaos and DNA sequence. Multimedia Tools Appl 72:57–70

    Article  Google Scholar 

  6. Huang ZG, Liu SL, Mao XP (2017) Insight of the protection for data security under selective opening attacks. Inf Sci 412:223–241

    Article  Google Scholar 

  7. Jain A, Rajpal N (2016) A robust image encryption algorithm resistant to attacks using DNA and chaotic logistic maps. Multimedia Tools Appl 75:5455–5472

    Article  Google Scholar 

  8. Lai Q, Chen SM (2016) Research on a new 3D autonomous chaotic system with coexisting attractors. Optik 127:3000–3004

    Article  Google Scholar 

  9. Lambi D (2017) Cryptanalyzing a novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn 89:2255–2257

    Article  Google Scholar 

  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):2201–2210

    Article  Google Scholar 

  11. Li J, Li JW, Chen XF et al (2015) Identity-based encryption with outsourced revocation in cloud computing. IEEE Trans Comput 64(2):425–437

    Article  MathSciNet  Google Scholar 

  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):1206–1216

    Article  Google Scholar 

  13. Li P, Li J, Huang ZG et al (2017) Multi-key privacy-preserving deep learning in cloud computing. Futur Gener Comput Syst 74:76–85

    Article  Google Scholar 

  14. Liu HJ, Wang XY (2010) Color image encryption based on one-time keys and robust chaotic maps. Comput Math Appl 59:3320–3327

    Article  MathSciNet  Google Scholar 

  15. Liu HJ, Wang XY (2011) Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt Commun 284:3895–3903

    Article  Google Scholar 

  16. Liu L, Zhang Q, Wei XP (2012) A RGB image encryption algorithm based on DNA encoding and chaos map. Comput Electr Eng 38:1240–1248

    Article  Google Scholar 

  17. Liu Y, Tang J, Xie T (2014) Cryptanalyzing a RGB image encryption algorithm based on DNA encoding and chaos map. Opt Lasers Eng 60:1–5

    Google Scholar 

  18. Liu Q, Wang GJ, Liu XH, Peng T, Wu J (2017) Achieving reliable and secure services in cloud computing environments. Comput Electr Eng 59:153–164

    Article  Google Scholar 

  19. Min LQ, Chen GR (2013) A novel stream encryption scheme with avalanche effect. Eur Phys J B 86(11):459

    Article  MathSciNet  Google Scholar 

  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. Murillo-Escobar MA, Cruz-Hernández C et al (2017) A novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn 87:407–425

    Article  MathSciNet  Google Scholar 

  22. Pang S, Liu Y (2011) A new hyperchaotic system from the Lü system and its control. J Comput Appl Math 235:2775–2789

    Article  MathSciNet  Google Scholar 

  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 38:705–721

    Article  Google Scholar 

  24. Rukhin R, Soto J, Nechvatal J (2001) A statistical test suite for random and pseudorandom numbergenerator for cryptographic applications. NIST Special Publication

  25. Shannon CE (1949) Communication theory of security systems. Bell Syst Tech J 28:656–715

    Article  Google Scholar 

  26. Spillman RJ (2005) Classical and contemporary cryptology. Pearson Education INC, Upper Saddle River

    Google Scholar 

  27. Sprott JC (2003) Chaos and time-series analysis. Oxford University Press, Oxford

    MATH  Google Scholar 

  28. Sprott JC, Wang X, Chen GR (2013) Coexistence point, periodic and strange attractors. Int J Bifurcation Chaos 23:1350093

    Article  MathSciNet  Google Scholar 

  29. Sun KH, Liu X, Zhu CX, Sprott J (2012) Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system. Nonlinear Dyn 69:1383–1391

    Article  MathSciNet  Google Scholar 

  30. Wang X, Teng Y, Qin X (2012) A novel colour image encryption algorithm based on chaos. Signal Process 92:1101–1108

    Article  Google Scholar 

  31. Wu Y, Hua Z, Zhou Y (2015) N-dimensional discrete cat map generation using Laplace expansions. IEEE Trans Cybern 46:2622–2633

    Article  Google Scholar 

  32. Wu X, Zhu B, Hu Y (2017) A novel colour image encryption scheme using rectangular transform-enhanced chaotic tent maps. IEEE Acces 5:6429–6436

    Google Scholar 

  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 25:053104

    Article  MathSciNet  Google Scholar 

  34. Yu S, Wang GJ, Zhou WL (2015) Modeling malicious activities in cyber space. IEEE Netw 29(6):83–87

    Article  Google Scholar 

  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 77:4585–4608

    Article  Google Scholar 

  36. Zarei A (2015) Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors. Nonlinear Dyn 81:585–605

    Article  MathSciNet  Google Scholar 

  37. Zhang XP, Mao YB, Zhao ZM (2014) An efficient chaotic image encryption based on alternate circular Sboxes. Nonlinear Dyn 78:359–369

    Article  Google Scholar 

  38. Zhang XP, Zhao ZM, Wang JY (2014) Chaotic image encryption based on circular substitution box and key stream buffer. Signal Process Image 29:902–913

    Article  Google Scholar 

  39. Zhu CX (2012) A novel image encryption scheme based on improved hyperchaotic sequences. Opt Commun 285(1):29–37

    Article  Google Scholar 

  40. Zhu CX, Sun KH (2012) Cryptanalysis and improvement of a class of hyperchaos based image encryption algorithms. Acta Phys Sin 61(12):120503

    MATH  Google Scholar 

  41. Zhu CX, Sun KH (2018) Cryptanalyzing and improving a novel color image encryption algorithm using RT-enhanced chaotic tent maps. IEEE Access 6:18759–18770

    Article  Google Scholar 

Download references

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).

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Authors and Affiliations

  1. School of Computer Science, Liaocheng University, Liaocheng, 252059, China

    Shuqin Zhu

  2. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Congxu Zhu

  3. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin, 537000, China

    Congxu Zhu

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  1. Shuqin Zhu
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  2. Congxu Zhu
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Correspondence to Congxu Zhu.

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Zhu, S., Zhu, C. Image encryption algorithm with an avalanche effect based on a six-dimensional discrete chaotic system. Multimed Tools Appl 77, 29119–29142 (2018). https://doi.org/10.1007/s11042-018-6078-2

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  • DOI: https://doi.org/10.1007/s11042-018-6078-2

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