Skip to main content
Log in

Secure exchange of information using artificial intelligence and chaotic system guided neural synchronization

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In this paper, a chaos-based neural synchronization has been proposed for the development of the public-key exchange protocol. A special neural network structure called Tree Parity Machine (TPM) is used for neural synchronization. Two TPMs accept the common input and different weight vector and update the weights using neural learning rule by exchanging their output. In some steps, it results in complete synchronization, and the weights of the two TPMs become identical. These identical weights serve as a secret key. There is, however, hardly some investigation to investigate the randomness of the common input vector used in the synchronization process. In this paper, logistic Chaos system based Tree Parity Machine (CTPM) is proposed. For faster synchronization, this proposed CTPM model uses logistic chaos generated random common input vector. This proposed CTPM model is faster and has better security than TPM with the same input, output, and hidden neurons. This proposed technique has been passed through a series of parametric tests. The results have been compared with some recent techniques. The results of the proposed technique have shown effective and robust potential.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Allam A M, Abbas H M, El-Kharashi M W (2013) Authenticated key exchange protocol using neural cryptography with secret boundaries. In: Proceedings of the 2013 international joint conference on neural networks, IJCNN 2013, pp 1–8

  2. Balasubramaniam P, Muthukumar P (2014) Synchronization of chaotic systems using feedback controller: an application to Diffie–Hellman key exchange protocol and ElGamal public key cryptosystem. J Egypt Math Soc 22(3):365–372. https://doi.org/10.1016/j.joems.2013.10.003

    Article  MathSciNet  Google Scholar 

  3. Bauer F L (2011) Cryptology. Springer, Boston, pp 283–284. https://doi.org/10.1007/978-1-4419-5906-5

    Google Scholar 

  4. Chen H, Shi P, Lim C C (2017) Exponential synchronization for Markovian stochastic coupled neural networks of neutral-type via adaptive feedback control. IEEE Trans Neural Netw Learn Syst 28(7):1618–1632. https://doi.org/10.1109/TNNLS.2016.2546962

    Article  MathSciNet  Google Scholar 

  5. Chen H, Shi P, Lim C C (2019) Cluster synchronization for neutral stochastic delay networks via intermittent adaptive control. IEEE Trans Neural Netw Learn Syst 30(11):3246–3259. https://doi.org/10.1109/tnnls.2018.2890269

    Article  MathSciNet  Google Scholar 

  6. Cover TM, Thomas JA (2006) Elements of information theory. Wiley series in telecommunications and signal processing, 2nd edn, Wiley-Interscience, New York

  7. Desai D R V (2011) Pseudo random number generator using Elman neural network. In: 2011 IEEE recent advances in intelligent computational systems. https://doi.org/10.1109/RAICS.2011.6069312, pp 251–254

  8. Desai V, Patil R T, Deshmukh V, Rao D (2012) Pseudo random number generator using time delay neural network. WJST 2(10):165–169

    Google Scholar 

  9. Diffie W, Hellman M (1976) New directions in cryptography. IEEE Trans Inf Theory 22(6):644–654. https://doi.org/10.1109/tit.1976.1055638

    Article  MathSciNet  Google Scholar 

  10. Dolecki M, Kozera R (2013) Distribution of the tree parity machine synchronization time. Adv Sci Technol– Res J 7(18):20–27. https://doi.org/10.5604/20804075.1049490

    Article  Google Scholar 

  11. Dolecki M, Kozera R (2013) Threshold method of detecting long-time TPM synchronization. In: Computer information systems and industrial management, vol 8104. Springer, pp 241–252

  12. Dolecki M, Kozera R (2015) The impact of the TPM weights distribution on network synchronization time. In: Computer information systems and industrial management, vol 9339. Springer International Publishing, pp 451–460

  13. Dong T, Huang T (2020) Neural cryptography based on complex-valued neural network. IEEE Trans Neural Netw Learn Syst 31(11):4999–5004. https://doi.org/10.1109/TNNLS.2019.2955165

    Article  MathSciNet  Google Scholar 

  14. Dong T, Wang A, Zhu H, Liao X (2018) Event-triggered synchronization for reaction–diffusion complex networks via random sampling. Phys A: Stat Mech Appl 495:454–462. https://doi.org/10.1016/j.physa.2017.12.008

    Article  MathSciNet  Google Scholar 

  15. Eftekhari M (2012) A Diffie–Hellman key exchange protocol using matrices over noncommutative rings. Groups - Complexity - Cryptology 4(1):167–176. https://doi.org/10.1515/gcc-2012-0001

    Article  MathSciNet  Google Scholar 

  16. Elashry I F, El-Shafai W, Hasan E S (2020) Efficient chaotic-based image cryptosystem with different modes of operation. Multimed Tools Appl 79:20665–20687. https://doi.org/10.1007/s11042-019-08322-5

    Article  Google Scholar 

  17. Engel A, den Broeck C V (2012) Statistical mechanics of learning. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9781139164542

    MATH  Google Scholar 

  18. Gomez H, Reyes Óscar, Roa E (2017) A 65 nm CMOS key establishment core based on tree parity machines. Integration 58:430–437. https://doi.org/10.1016/j.vlsi.2017.01.010

    Article  Google Scholar 

  19. Jeong Y, Oh K, Cho C, Choi H (2018) Pseudo Random Number Generation Using LSTMs and Irrational Numbers. In: 2018 IEEE International Conference on Big Data and Smart Computing (BigComp), pp 541–544, DOI https://doi.org/10.1109/BigComp.2018.00091, (to appear in print)

  20. Kamrani A, Zenkouar K, Najah S (2020) A new set of image encryption algorithms based on discrete orthogonal moments and Chaos theory. Multimed Tools Appl 79:20263–20279. https://doi.org/10.1007/s11042-020-08879-6

    Article  Google Scholar 

  21. Kanter I, Kinzel W, Kanter E (2002) Secure exchange of information by synchronization of neural networks. Europhys Lett (EPL) 57(1):141–147. https://doi.org/10.1209/epl/i2002-00552-9

    Article  Google Scholar 

  22. Karakaya B, Gülten A, Frasca M (2019) A true random bit generator based on a memristive chaotic circuit: analysis, design and FPGA implementation. Chaos Solitons Fractals 119:143–149

    Article  Google Scholar 

  23. Kinzel W, Kanter I (2002) Interacting neural networks and cryptography. Advances in Solid State Physics, pp 383–391

  24. Klimov A, Mityagin A, Shamir A (2002) Analysis of neural cryptography. In: Proceedings of the international conference on the theory and application of cryptology and information security, pp 288–298

  25. Lakshmanan S, Prakash M, Lim C P, Rakkiyappan R, Balasubramaniam P, Nahavandi S (2018) Synchronization of an inertial neural network with time-varying delays and its application to secure communication. IEEE Trans Neural Netw Learn Syst 29(1):195–207. https://doi.org/10.1109/tnnls.2016.2619345

    Article  MathSciNet  Google Scholar 

  26. Lindell Y, Katz J (2014) Introduction to modern cryptography. Chapman and Hall/CRC

  27. Liu L, Miao S, Hu H, Deng Y (2016) Pseudo-random bit generator based on non-stationary logistic maps. IET Inf Secur 2(10):87–94

    Article  Google Scholar 

  28. Liu P, Zeng Z, Wang J (2019) Global synchronization of coupled fractional-order recurrent neural networks. IEEE Trans Neural Netw Learn Syst 30(8):2358–2368. https://doi.org/10.1109/TNNLS.2018.2884620

    Article  MathSciNet  Google Scholar 

  29. Meneses F, Fuertes W, Sancho J (2016) RSA encryption algorithm optimization to improve performance and security level of network messages. IJCSNS 16(8):55–55

    Google Scholar 

  30. Mu N, Liao X (2013) An approach for designing neural cryptography. In: Gou C, Hou ZG, Zeng Z (eds) Advances in neural networks – ISNN 2013. ISNN 2013. Lecture Notes in Computer Science. https://doi.org/10.1007/978-3-642-39065-4_13, vol 7951. Springer, Berlin, Heidelberg, pp 99–108

  31. Mu N, Liao X, Huang T (2013) Approach to design neural cryptography: a generalized architecture and a heuristic rule. Phys Rev E 87(6). https://doi.org/10.1103/physreve.87.062804

  32. Ni Z, Paul S (2019) A multistage game in smart grid security: a reinforcement learning solution. IEEE Trans Neural Netw Learn Syst 30(9):2684–2695. https://doi.org/10.1109/tnnls.2018.2885530

    Article  MathSciNet  Google Scholar 

  33. Niemiec M (2019) Error correction in quantum cryptography based on artificial neural networks. Quantum Inf Process 174. https://doi.org/10.1007/s11128-019-2296-4

  34. NIST (2020) NIST Statistical Test. http://csrc.nist.gov/groups/ST/toolkit/rng/stats_tests.html

  35. Patidar V, Sud K K, Pareek N K (2009) A pseudo random bit generator based on chaotic logistic map and its statistical testing. Informatica 33:441–452

    MathSciNet  MATH  Google Scholar 

  36. Pu X, Tian X J, Zhang J, Liu C Y, Yin J (2017) Chaotic multimedia stream cipher scheme based on true random sequence combined with tree parity machine. Multimed Tools Appl 76(19):19881–19885. https://doi.org/10.1007/s11042-016-3728-0

    Article  Google Scholar 

  37. Rana S, Mishra D (2020) Secure and ubiquitous authenticated content distribution framework for IoT enabled DRM system. Multimed Tools App. https://doi.org/10.1007/s11042-020-08683-2

  38. Rosen-Zvi M, Kanter I, Kinzel W (2002) Cryptography based on neural networks analytical results. J Phys A: Math Gen 35(47):L707–L713. https://doi.org/10.1088/0305-4470/35/47/104

    Article  MathSciNet  Google Scholar 

  39. Ruttor A (2007) Neural synchronization and cryptography. https://arxiv.org/abs/0711.2411

  40. Ruttor A, Kinzel W, Naeh R, Kanter I (2006) Genetic attack on neural cryptography. Phys Rev E 73(3). https://doi.org/10.1103/physreve.73.036121

  41. Santhanalakshmi S, Sangeeta K, Patra G K (2015) Analysis of neural synchroniz ation using genetic approach for secure key generation. Commun Comput Inf Sci 536:207–216

    Google Scholar 

  42. Steiner M, Tsudik G, Waidner M (1996) Diffie-Hellman key distribution extended to group communication. In: Proceedings of the 3rd ACM conference, pp 31–37

  43. Tirdad A S K (2010a) Hopfield neural networks as pseudo random number generators. https://doi.org/10.1109/NAFIPS.2010.5548182

  44. Tirdad A S K (2010b) Hopfield neural networks as pseudo random number generators. In: 2010 Annual meeting of the North American fuzzy information processing society. https://doi.org/10.1109/NAFIPS.2010.5548182, pp 1–6

  45. Wang A, Dong T, Liao X (2016) Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies. IEEE Trans Neural Netw Learn Syst 74:52–57

    MATH  Google Scholar 

  46. Wang J, Cheng L M, Su T (2018) Multivariate cryptography based on clipped hopfield neural network. IEEE Trans Neural Netw Learn Syst 29 (2):353–363. https://doi.org/10.1109/tnnls.2016.2626466

    Article  MathSciNet  Google Scholar 

  47. Wang J L, Qin Z, Wu H N, Huang T (2019) Passivity and synchronization of coupled uncertain reaction-diffusion neural networks with multiple time delays. IEEE Trans Neural Netw Learn Syst 30(8):2434–2448. https://doi.org/10.1109/TNNLS.2018.2884954

    Article  MathSciNet  Google Scholar 

  48. Xiao Q, Huang T, Zeng Z (2019) Global exponential stability and synchronization for discrete-time inertial neural networks with time delays: a timescale approach. IEEE Trans Neural Netw Learn Syst 30(6):1854–1866. https://doi.org/10.1109/TNNLS.2018.2874982

    Article  MathSciNet  Google Scholar 

  49. Zhang A L Z (2020) Further study on finite-time synchronization for delayed inertial neural networks via inequality skills. Neurocomputing 373:15–23. https://doi.org/10.1016/j.neucom.2019.09.034

    Article  Google Scholar 

  50. Zhang Z, Cao J (2019) Novel finite-time synchronization criteria for inertial neural networks with time delays via integral inequality method. IEEE Trans Neural Netw Learn Syst 30(5):1476–1485. https://doi.org/10.1109/TNNLS.2018.2868800

    Article  MathSciNet  Google Scholar 

  51. Zhang Z, Li A, Yu S (2018) Finite-time synchronization for delayed complex-valued neural networks via integrating inequality method. Neurocomputing 318:248–260. https://doi.org/10.1016/j.neucom.2018.08.063

    Article  Google Scholar 

  52. Zhou X, Tang X (2011) Research and implementation of RSA algorithm for encryption and decryption. In: Proceedings of the 6th international forum on strategic technology. https://doi.org/10.1109/IFOST.2011.6021216. IEEE, pp 1118–1121

Download references

Acknowledgements

The author expressed deep gratitude for the moral and congenial atmosphere support provided by Ramakrishna Mission Vidyamandira, Belur Math, India.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Arindam Sarkar.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sarkar, A. Secure exchange of information using artificial intelligence and chaotic system guided neural synchronization. Multimed Tools Appl 80, 18211–18241 (2021). https://doi.org/10.1007/s11042-021-10554-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-021-10554-3

Keywords

Navigation