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Multiple RGB images encryption algorithm based on elliptic curve, improved Diffie Hellman protocol

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Abstract

For the asymmetric key, the Diffie Hellman Key (DHK) protocol is very efficient, but sometimes it is vulnerable against brute force attacks if the parameters are not chosen carefully. Our study aims to improve the asymmetric key scheme based on the elliptic curve cryptosystem (ECC). The sender and receiver agree on an elliptic curve based on the DHK sharing technique, but generator G is kept secret, and we generate its hash value, which is shared publicly. The authorized members can recover G using the hash value. By keeping G secret, the key protocol becomes much more robust than existing ones. Further, the proposed scheme will be applied to multiple RGB images. In this novel public key algorithm, 4D chaotic sequences are used for the diffusion of image pixels. The pixels’ values are used for permutations of images rather than the chaotic sequences, strengthening the scheme against chosen/known plain text attacks. The simulation and the security analysis of the proposed algorithm show efficiency, potential to endure the varied attacks, and prospects for real-world application.

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References

  1. Abd-El-Hafiz SK, Radwan AG, Haleem SHA, Barakat ML (2014) A fractal-based image encryption system. IET Image Process 8(12):742–752

    Article  Google Scholar 

  2. Bashir Z, Watrobski J, Rashid T, Zafar S, Sałabun W (2017) Chaotic dynamical state variables selection procedure based image encryption scheme. Symmetry 9(12):312

    Article  Google Scholar 

  3. Bashir Z, Iqbal N, Hanif M (2021) A novel grayscale image encryption scheme based on pixels’ swapping operations. Multimed Tools Applic 80(1):1029–1054

    Article  Google Scholar 

  4. Belazi A, El-Latif AAA, Diaconu AV, Rhouma R, Belghith S (2017) Chaos-based partial image encryption scheme based on linear fractional and lifting wavelet transforms. Opt Lasers Eng 88:37–50

    Article  Google Scholar 

  5. Bissell C (2009) Vladimir Aleksandrovich Kotelnikov: pioneer of the sampling theorem, cryptography, optimal detection, planetary mapping [History of Communications]. IEEE Commun Mag 47(10):24–32

    Article  Google Scholar 

  6. Cassels JWS, Silverman JH (1987) The arithmetic of elliptic curves. Bulletin (New Series) of the American Mathematical Society 17(1):148–149

  7. Cokal C, Solak E (2009) Cryptanalysis of a chaos-based image encryption algorithm. Phys Lett A 373(15):1357–1360

    Article  MathSciNet  MATH  Google Scholar 

  8. Das S, Mandal S, Ghoshal N (2015) Multiple-image encryption using genetic algorithm. In: Intelligent computing and applications. Springer, New Delhi, pp 145–153

  9. Dey D, Giri D, Jana B, Maitra T, Mohapatra RN (2018) Linear-feedback shift register-based multi-ant cellular automation and chaotic map-based image encryption. Security and Privacy 1(6):e52

    Article  Google Scholar 

  10. Di H, Kang Y, Liu Y, Zhang X (2016) Multiple image encryption by phase retrieval. Optical Engineering 55(7):073103

    Article  Google Scholar 

  11. Di H, Kang Y, Liu Y, Zhang X (2016) Multiple image encryption by phase retrieval. Opt Eng 55(7):073103

    Article  Google Scholar 

  12. Diffie W, Hellman M (1976) New directions in cryptography. IEEE Trans 22(6):644–654

    MathSciNet  MATH  Google Scholar 

  13. Guesmi R, Farah MAB, Kachouri A, Samet M (2016) A novel chaos-based image encryption using DNA sequence operation and Secure Hash Algorithm SHA-2. Nonlinear Dyn 83(3):1123–1136

    Article  MathSciNet  MATH  Google Scholar 

  14. Hankerson D, Menezes AJ, Vanstone S (2006) Guide to elliptic curve cryptography. Springer Science & Business Media

  15. Huang X, Ye G (2014) An efficient self-adaptive model for chaotic image encryption algorithm. Commun Nonlinear Sci 19(12):4094–4104

    Article  MATH  Google Scholar 

  16. Iqbal N, Abbas S, Khan MA, Alyas T, Fatima A, Ahmad A (2019) An RGB image cipher using chaotic systems, 15-puzzle problem and DNA computing. IEEE Access 7:174051–174071

    Article  Google Scholar 

  17. Karawia AA (2018) Encryption algorithm of multiple-image using mixed image elements and two dimensional chaotic economic map. Entropy 20(10):801

    Article  Google Scholar 

  18. Kaushik A (2013) Extended Diffie-Hellman algorithm for key exchange and management. Int J Adv Eng Sci Appl Math 3(3)

  19. Koblitz N (1987) Elliptic curve cryptosystems. Math Comput 48(177):203–209

    Article  MathSciNet  MATH  Google Scholar 

  20. Kumar M, Iqbal A, Kumar P (2016) A new RGB image encryption algorithm based on DNA encoding and elliptic curve Diffie-Hellman cryptography. Signal Process 125:187–202

    Article  Google Scholar 

  21. Lai Q, Nestor T, Kengne J, Zhao XW (2018) Coexisting attractors and circuit implementation of a new 4D chaotic system with two equilibria. Chaos Solitons Fractals 107:92–102

    Article  MathSciNet  MATH  Google Scholar 

  22. Laiphrakpam DS, Khumanthem MS (2018) A robust image encryption scheme based on chaotic system and elliptic curve over finite field. Multimed Tools Appl 77(7):8629–8652

    Article  Google Scholar 

  23. Li C, Li S, Lo KT (2011) Breaking a modified substitution–diffusion image cipher based on chaotic standard and logistic maps. Commun Nonlinear Sci 16(2):837–843

    Article  MathSciNet  MATH  Google Scholar 

  24. Li Y, Wang C, Chen H (2017) A hyper-chaos-based image encryption algorithm using pixel-level permutation and bit-level permutation. Opt Lasers Eng 90:238–246

    Article  Google Scholar 

  25. Li CL, Li HM, Li FD, Wei DQ, Yang XB, Zhang J (2018) Multiple-image encryption by using robust chaotic map in wavelet transform domain. Optik 171:277–286

    Article  Google Scholar 

  26. Liu H, Wang X (2012) Image encryption using DNA complementary rule and chaotic maps. Appl Soft Comput 12(5):1457–1466

    Article  Google Scholar 

  27. Liu H, Wang X, Kadir A (2013) Color image encryption using Choquet fuzzy integral and hyperchaotic system. Optik-International Journal for Light and Electron Optics 124(18):3527–3533

    Article  Google Scholar 

  28. Liu W, Xie Z, Liu Z, Zhang Y, Liu S (2015) Multiple-image encryption based on optical asymmetric key cryptosystem. Opt Commun 335:205–211

    Article  Google Scholar 

  29. Luo Y, Ouyang X, Liu J, Cao L (2019) An image encryption method based on elliptic curve elgamal encryption and chaotic systems. IEEE Access 7:38507–38522

    Article  Google Scholar 

  30. Malik MA, Bashir Z, Iqbal N, Imtiaz MA (2020) Color image encryption algorithm based on hyper-chaos and DNA computing. IEEE Access 8:88093–88107

    Article  Google Scholar 

  31. Menzes AJ, Van OPC, Vanstone SA (2001) Handbook of Applied Cryptology [M]

  32. Niyat AY, Moattar MH, Torshiz MN (2017) Color image encryption based on hybrid hyper-chaotic system and cellular automata. Opt Lasers Eng 90:225–237

    Article  Google Scholar 

  33. Norouzi B, Mirzakuchaki S (2014) A fast color image encryption algorithm based on hyper-chaotic systems. Nonlinear Dyn 78(2):995–1015

    Article  Google Scholar 

  34. Noura H, Chehab A, Noura M, Couturier R, Mansour MM (2019) Lightweight, dynamic and efficient image encryption scheme. Multimed Tools Appl 78(12):16527–16561

    Article  MATH  Google Scholar 

  35. Paar C, Pelzl J (2009) Understanding cryptography: a textbook for students and practitioners. Springer Science & Business Media

  36. Sampangi R, Sampalli S (2015) Butterfly encryption scheme for resource-constrained wireless networks. Sensors 15(9):23145–23167

    Article  Google Scholar 

  37. Seyedzade SM, Mirzakuchaki S, Atani RE (2010) A novel image encryption algorithm based on hash function. In: 2010 6th Iranian conference on machine vision and image processing. IEEE, pp 1–6

  38. Shannon CE (1949) Communication theory of secrecy systems. BSTJAN 28(4):656–715

    MathSciNet  MATH  Google Scholar 

  39. Singh LD, Singh KM (2015) Image encryption using elliptic curve cryptography. Procedia Comput Sci 54:472–481

    Article  Google Scholar 

  40. Singh LD, Singh KM (2018) Visually meaningful multi-image encryption scheme. Arab J Sci Eng 43(12):7397–7407

    Article  Google Scholar 

  41. Stallings W (2021) Cryptography and network security: principles and practice 0133354695, 9780133354690

  42. Su Y, Tang C, Gao G, Gu F, Lei Z, Tang S (2017) Optical encryption scheme for multiple color images using complete trinary tree structure. Opt Lasers Eng 98:46–55

    Article  Google Scholar 

  43. Suri S, Vijay R (2017) An AES-CHAOS-Based Hybrid approach to encrypt multiple images. In: Recent developments in intelligent computing, communication and devices. Springer, Singapore, pp 37–43

  44. Tang Z, Song J, Zhang X, Sun R (2016) Multiple-image encryption with bit-plane decomposition and chaotic maps. Opt Lasers Eng 80:1–11

    Article  Google Scholar 

  45. Toughi S, Fathi MH, Sekhavat YA (2017) An image encryption scheme based on elliptic curve pseudo-random and advanced encryption system. Signal Process 141:217–227

    Article  Google Scholar 

  46. Wei X, Guo L, Zhang Q, Zhang J, Lian S (2012) A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system. J Syst Softw 85(2):290–299

    Article  Google Scholar 

  47. Wu Y, Zhou Y, Noonan JP, Agaian S (2014) Design of image cipher using Latin squares. Inf Sci 264:317–339

    Article  MathSciNet  MATH  Google Scholar 

  48. Xiong Z, Wu Y, Ye C, Zhang X, Xu F (2019) Color image chaos encryption algorithm combining CRC and nine palace map. Multimed Tools Appl 78(22):31035–31055

    Article  Google Scholar 

  49. Xu M, Tian Z (2019) A novel image cipher based on 3D bit matrix and Latin cubes. Inf Sci 478:1–14

    Article  Google Scholar 

  50. Yuan S, Liu X, Zhou X, Li Z (2016) Multiple-image encryption scheme with a single-pixel detector. J Mod Opt 63(15):1457–1465

    Article  Google Scholar 

  51. Zhang X, Wang X (2017) Multiple-image encryption algorithm based on mixed image element and chaos. Comput Electr Eng 62:401–413

    Article  Google Scholar 

  52. Zhang X, Wang X (2017) Multiple-image encryption algorithm based on mixed image element and permutation. Opt Lasers Eng 92:6–16

    Article  Google Scholar 

  53. Zhang X, Wang X (2018) Digital Image Encryption Algorithm Based on Elliptic Curve Public Cryptosystem. IEEE Access 6:70025–70034

    Article  Google Scholar 

  54. Zhang X, Wang X (2018) Multiple-image encryption algorithm based on the 3D permutation model and chaotic system. Symmetry 10(11):660

    Article  Google Scholar 

  55. Zhang X, Wang X (2019) Multiple-image encryption algorithm based on DNA encoding and chaotic system. Multimed Tools Appl 78(6):7841–7869

    Article  Google Scholar 

  56. Zhang L, Zhou Y, Huo D, Li J, Zhou X (2018) Multiple-image encryption based on double random phase encoding and compressive sensing by using a measurement array preprocessed with orthogonal-basis matrices. Opt Laser Technol 105:162–170

    Article  Google Scholar 

  57. Zhao Z, Zhang X (2013) ECC-based image encryption using code computing. In: Proceedings of the 2012 international conference on communication, electronics and automation engineering. Springer, Berlin, pp 859–865

  58. Zhou Y, Panetta K, Agaian S, Chen CP (2012) Image encryption using P-Fibonacci transform and decomposition. Opt Commun 285(5):594–608

    Article  Google Scholar 

  59. Zhou N, Zhang A, Wu J, Pei D, Yang Y (2014) Novel hybrid image compression-encryption algorithm based on compressive sensing. Optik-International Journal for Light and Electron Optics 125(18):5075–5080

    Article  Google Scholar 

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

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, 45320, Pakistan

    Zia Bashir & Muhammad Hussain

  2. School of Business and ICT, Universal College of Learning, Palmerston North, 4442, New Zealand

    M. G. Abbas Malik

  3. Department of Computer Science & IT, University of Lahore, Lahore, Pakistan

    Nadeem Iqbal

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  1. Zia Bashir
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  2. M. G. Abbas Malik
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  3. Muhammad Hussain
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  4. Nadeem Iqbal
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Bashir, Z., Malik, M.G.A., Hussain, M. et al. Multiple RGB images encryption algorithm based on elliptic curve, improved Diffie Hellman protocol. Multimed Tools Appl 81, 3867–3897 (2022). https://doi.org/10.1007/s11042-021-11687-1

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  • DOI: https://doi.org/10.1007/s11042-021-11687-1

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