Skip to main content
Log in

A post-processing method for true random number generators based on hyperchaos with applications in audio-based generators

  • Research Article
  • Published:
Frontiers of Computer Science Aims and scope Submit manuscript

Abstract

True random number generators (TRNG) are important counterparts to pseudorandom number generators (PRNG), especially for high security applications such as cryptography. They produce unpredictable, non-repeatable random sequences. However, most TRNGs require specialized hardware to extract entropy from physical phenomena and tend to be slower than PRNGs. These generators usually require post-processing algorithms to eliminate biases but in turn, reduces performance. In this paper, a new post-processing method based on hyperchaos is proposed for software-based TRNGs which not only eliminates statistical biases but also provides amplification in order to improve the performance of TRNGs. The proposed method utilizes the inherent characteristics of chaos such as hypersensitivity to input changes, diffusion, and confusion capabilities to achieve these goals. Quantized bits of a physical entropy source are used to perturb the parameters of a hyperchaotic map, which is then iterated to produce a set of random output bits. To depict the feasibility of the proposed post-processing algorithm, it is applied in designing TRNGs based on digital audio. The generators are analyzed to identify statistical defects in addition to forward and backward security. Results indicate that the proposed generators are able to produce secure true random sequences at a high throughput, which in turn reflects on the effectiveness of the proposed post-processing method.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Cret O, Gyorfi T, Suciu A. Implementing true random number generators based on high fanout nets. Romanian Journal of Information Science and Technology, 2012, 15(3): 277–298

    Google Scholar 

  2. Jun B, Kocher P. The intel random number generator. Cryptography Research Inc. White Paper, 1999, 27: 1–8

    Google Scholar 

  3. Cicek I, Pusane A E, Dundar G. An integrated dual entropy core true random number generator. IEEE Transactions on Circuits and Systems II: Express Briefs, 2017, 64(3): 329–333

    Article  Google Scholar 

  4. Karakaya B, Çelik V, Gulten A. Chaotic cellular neural network-based true random number generator. International Journal of Circuit Theory and Applications, 2017, 45(11): 1885–1897

    Article  Google Scholar 

  5. Bonny T, Debsi R A, Majzoub S, Elwakil A S. Hardware optimized FPGA implementations of high-speed true random bit generators based on switching-type chaotic oscillators. Circuits, Systems, and Signal Processing, 2018, 38(3): 1342–1359

    Article  Google Scholar 

  6. Mei F, Zhang L, Gu C, Cao Y, Wang C, Liu W. A highly flexible lightweight and high speed true random number generator on FPGA. In: Proceedings of IEEE Computer Society Annual Symposium on VLSI (ISVLSI). 2018

  7. Nguyen T T N, Kaddoum G, Gagnon F. Implementation of a chaotic true random number generator based on fuzzy modeling. In: Proceedings of the 16th IEEE International New Circuits and Systems Conference. 2018

  8. Kumar D, Nabi K, Misra P K, Goswami M. Modified tent map based design for true random number generator. In: Proceedings of IEEE International Symposium on Smart Electronic Systems. 2018

  9. Alcin M, Koyuncu I, Tuna M, Varan M, Pehlivan I. A novel high speed artificial neural network-based chaotic true random number generator on field programmable gate array. International Journal of Circuit Theory and Applications, 2018, 47(3): 365–378

    Article  Google Scholar 

  10. Hsueh J C, Chen V H C. An ultra-low voltage chaos-based true random number generator for IoT applications. Microelectronics Journal, 2019, 87: 55–64

    Article  Google Scholar 

  11. Gupta R, Pandey A, Baghel R K. FPGA implementation of chaos-based high-speed true random number generator. International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 2019, 32(5): e2604

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Teh J S, Samsudin A, Al-Mazrooie M, Akhavan A. GPUs and chaos: a new true random numbergenerator. Nonlinear Dynamics, 2015, 82(4): 1913–1922

    Article  MathSciNet  Google Scholar 

  14. Davis D, Ihaka R, Fenstermacher P. Cryptographic randomness from air turbulence in disk drives. In: Proceedings of Annual International Cryptology Conference. 1994, 114–120

  15. Hu Y, Liao X, Wo Wong K, Zhou Q. A true random number generator based on mouse movement and chaotic cryptography. Chaos, Solitons & Fractals, 2009, 40(5): 2286–2293

    Article  Google Scholar 

  16. Xingyuan W, Xue Q, Lin T. A novel true random number generator based on mouse movement and a one-dimensional chaotic map. Mathematical Problems in Engineering, 2012

  17. Yeoh W Z, Teh J S, Chern H R. A parallelizable chaos-based true random numbergenerator based on mobile device cameras for the android platform. Multimedia Tools and Applications, 2019, 78(12): 15929–15949

    Article  Google Scholar 

  18. Nikolic S, Veinovic M. Advancement of true random number generators based on sound cards through utilization of a new post-processing method. Wireless Personal Communications, 2016, 91(2): 603–622

    Article  Google Scholar 

  19. Davies R B. Exclusive OR (XOR) and hardware random number generators. see Wikipedia, 2002

  20. Von Neumann J. Various techniques used in connection with random digits. National Bureau of Standards Applied Mathematical Series, 1951, 12(36–38): 5

    Google Scholar 

  21. Lacharme P. Post-processing functions for a biased physical random number generator. In: Proceedings of International Workshop on Fast Software Encryption. 2008, 334–342

  22. Avaroglu E, Tuncer T, Ozer A, Ergen B, Turk M. A novel chaos-based post-processing for TRNG. Nonlinear Dynamics, 2015, 81(1–2): 189–199

    Article  MathSciNet  Google Scholar 

  23. Schindler W, Killmann W. Evaluation criteria for true (physical) random number generators used in cryptographic applications. In: Proceedings of International Workshop on Cryptographic Hardware and Embedded Systems. 2002, 431–449

  24. Sunar B, Martin W J, Stinson D R. A provably secure true random number generator with built-in tolerance to active attacks. IEEE Transactions on Computers, 2007, 56(1): 109–119

    Article  MathSciNet  Google Scholar 

  25. Kwok S H, Ee Y L, Chew G, Zheng K, Khoo K, Tan C H. A comparison of post-processing techniques for biased random number generators. In: Proceedings of IFIP International Workshop on Information Security Theory and Practices. 2011, 175–190

  26. Ahmad M, Khurana S, Singh S, AlSharari H D. A simple secure hash function schemeusing multiple chaotic maps. 3D Research, 2017, 8(2): 13

    Article  Google Scholar 

  27. Li Y, Ge G. Cryptographic and parallel hash function based on cross coupled map lattices suitable for multimedia communication security. Multimedia Tools and Applications, 2019, 78(13): 17973–17994

    Article  MathSciNet  Google Scholar 

  28. ur Rehman A, Liao X. A novel robust dual diffusion/confusion encryption technique for color image based on chaos, DNA and SHA-2. Multimedia Tools and Applications, 2018, 78(2): 2105–2133

    Article  Google Scholar 

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

    Article  Google Scholar 

  30. Garcia-Bosque M, Perez-Resa A, Sanchez-Azqueta C, Aldea C, Celma S. Chaos-based bitwise dynamical pseudorandom numbergeneratoron FPGA. IEEE Transactions on Instrumentation and Measurement, 2019, 68(1): 291–293

    Article  Google Scholar 

  31. Rukhin A, Soto J, Nechvatal J. A statistical test suite for random and pseudorandom number generators for cryptographic applications. National Institute of Standards, NIST Special Publication 800–22, 2010

  32. Marsaglia G. DIEHARD: a battery of tests of Randomness. 1996

  33. Walker J. ENT Program. 2008

  34. Teh J S, Teng W, Samsudin A. A true random number generator based on hyperchaos and digital sound. In: Proceedings of the 3rd International Conference on Computer and Information Sciences. 2016, 264–269

  35. Dodis Y, Pointcheval D, Ruhault S, Vergniaud D, Wichs D. Security analysis of pseudo-random number generators with input: /dev/random is not robust. In: Proceedings of the 2013 ACM SIGSAC Conference on Computer & Communications Security. 2013, 647–658

  36. Coron J S. On the security of random sources. In: Proceedings of International Workshop on Public Key Cryptography. 1999, 29–42

  37. Benítez R, Bolós V, Ramírez M. A wavelet-based tool for studying non-periodicity. Computers & Mathematics with Applications, 2010, 60(3): 634–641

    Article  MathSciNet  Google Scholar 

  38. Ritter T. The efficient generation of cryptographic confusion sequences. Cryptologia, 1991, 15(2): 81–139

    Article  MathSciNet  Google Scholar 

  39. Golomb S W. Shift register sequences. World Scientific. 2014

  40. Massey J. Shift-register synthesis and BCH decoding. IEEE Transactions on Information Theory, 1969, 15(1): 122–127

    Article  MathSciNet  Google Scholar 

  41. Menezes A J, van Oorschot P C, Vanstone S A. Handbook of Applied Cryptography. CRC Press, 2018

  42. Bardis N G, Markovskyi A P, Doukas N, Karadimas N V. True random number generation based on environmental noise measurements for military applications. In: Proceedings of the 8th WSEAS International Conference on Signal Processing, Robotics and Automation. 2009, 68–73

Download references

Acknowledgements

This work was supported in part by the Ministry of Education Malaysia under the Fundamental Research Grant Scheme (FRGS/1/2019/ICT05/USM/02/1), Universiti Sains Malaysia (304/PKOMP/6315190) and the National Natural Science Foundation of China (Grant No. 61702212).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Je Sen Teh.

Additional information

Je Sen Teh received the BEng degree (Hons.) majoring in Electronics from Multimedia University, Malaysia in 2011, then received his MSc and PhD in Computer Science from Universiti Sains Malaysia in 2013 and 2017, respectively. He is currently working as a Senior Lecturer in Universiti Sains Malaysia under the School of Computer Sciences. His research interests include symmetric cryptography, cryptanalysis, random number generation and chaos theory.

Weijian Teng graduated from Multimedia University, Malaysia with a BEng (hons) in Electronics Engineering in 2011. He subsequently pursued his MSc in Acoustics and Music Technology from the University of Edinburgh, UK in 2012. Since then, he has been working as a lecturer in private institutions of higher learning and is now attached to INTI International College Penang, Malaysia. His areas of interest include areas of applied mathematics and sciences like audio and digital signal processing as well as heuristics and algorithms.

Azman Samsudin is a Professor at the School of Computer Science, Universiti Sains Malaysia (USM), Malaysia. He earned his BSc in Computer Science from University of Rochester, USA in 1989. Later, he received his MSc and PhD in Computer Science, in 1993 and 1998, respectively, both from the University of Denver, USA. His research interests include Cryptography, Switching Networks and Parallel Computing. He has published more than 100 articles over a series of books, professional journals and conference proceedings.

Jiageng Chen received the BS degree from the School of Compuer Science and Technology, Huazhong University of Science and Technology (HUST), China in 2004 and recieved his MS and PhD of computer science from the School of Information Science, Japan Advanced Institute of Science and Technology (JAIST), Japan in 2007 and 2012, respectively. He was working as an Assistant Professor in School of Information Science, Japan Advanced Institute of Science and Technology, Japan from 2012 to 2015. And currently, he is an Associate Professor at the Computer School of Central China Normal University, China. His research areas include cryptography, especially in the areas of algorithms, cryptanalysis, secure designs and so on.

Electronic Supplementary Material

11704_2019_9120_MOESM1_ESM.pdf

A post-processing method for true random number generators based on hyperchaos with applications in audio-based generators

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Teh, J.S., Teng, W., Samsudin, A. et al. A post-processing method for true random number generators based on hyperchaos with applications in audio-based generators. Front. Comput. Sci. 14, 146405 (2020). https://doi.org/10.1007/s11704-019-9120-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11704-019-9120-2

Keywords