Chaos-based random number generators. Part II: practical realization
Abstract
This paper and its companion (see ibid., vol. 48, p. 281-88, 2001) are devoted to to the analysis of the application of a chaotic piecewise-linear one-dimensional (PL1D) map as Random Number Generator (RNG). In Part I, me have mathematically analyzed the information generation process of a class of PL1D maps. In this paper, we find optimum parameters that give an RNG with lowest redundancy and maximum margin against parasitic attractors. Further, the map is implemented in a 0.8 /spl mu/m standard CMOS process utilizing switched current techniques. Post-layout circuit simulations of the RNG indicate no periodic attractors over variations in temperature, power supply and process conditions, and maximum redundancy of 0.4%. We estimate that the output bit rate of our RNG is 1 Mbit/s, which is substantially higher than the output bit rate of RNGs available on the market.
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Stojanovski et al. mentioned that chaotic systems exhibit deterministic behavior on the microscopic scale while appearing random on the macroscopic scale; thus the nondeterministic nature of chaotic systems cannot be certified for use as a reliable TRNG.
“Stojanovski et al. mentioned that chaotic systems exhibit deterministic behavior on the microscopic scale, while they appear random on the macroscopic scale18. That is, the nondeterministic nature of chaotic systems cannot be certified for use as a reliable True Random Number Generator (TRNG).”
Cites
Chaos-based random number generators-part I: analysis [cryptography]
Stojanovski, T., & Kocarev, L. (2001) · IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications · doi:10.1109/81.915385 · Cited by 371 · see citing works
Self-citationSecure random number generation using chaotic circuits
Bernstein, G. M., & Lieberman, M. A. (1990) · IEEE Transactions on Circuits and Systems · doi:10.1109/31.57604 · Cited by 125 · see citing works
Nonlinear switched-current CMOS IC for random signal generation
Delgado‐Restituto, M., Medeiro, F., & Rodriguez-Vazquez, A. (1993) · Electronics Letters · doi:10.1049/el:19931471 · Cited by 111 · see citing works
Application of chaotic switched-capacitor circuits for random number generation
Espejo, S., Rodriguez-Vazquez, A., Huertas, J. L., et al. (1989) · European Conference on Circuit Theory and Design · Cited by 7 · see citing works
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Fast physical random number generator using amplified spontaneous emission
Williams, C. R. S., Salevan, J. C., Li, X., Roy, R., & Murphy, T. E. (2010) · Optics Express · doi:10.1364/oe.18.023584 · Cited by 229 · see citing works
Mannalath, V., Mishra, S., & Pathak, A. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04175-y · Cited by 125 · see citing works
“The solution to get a true random number sequence is to exploit the randomness associated with certain natural phenomena such as atmospheric noise [14], cosmic background radiation [15], thermal noises [16], noises in electronic circuits [17], chaotic systems [18], etc.”
A novel design method for discrete time chaos based true random number generators
Cicek, I., Pusane, A. E., & Dundar, G. (2014) · Integration · doi:10.1016/j.vlsi.2013.06.003 · Cited by 101 · see citing works
Drutarovsky, M., & Galajda, P. (2007) · 2007 17th International Conference Radioelektronika · doi:10.1109/radioelek.2007.371423 · Cited by 77 · see citing works
A High Speed IC Truly Random Number Generator Based on Chaotic Sampling of Regular Waveform
ERGÜN, S., GÜLER, Ü., & ASADA, K. (2011) · IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences · doi:10.1587/transfun.e94.a.180 · Cited by 53 · see citing works
True Random Number Generation Via Sampling From Flat Band-Limited Gaussian Processes
Gov, N. C., Mihcak, M. K., & Ergun, S. (2011) · IEEE Transactions on Circuits and Systems I: Regular Papers · doi:10.1109/tcsi.2010.2089561 · Cited by 48 · see citing works
An Offset-Compensated Oscillator-Based Random Bit Source for Security Applications
Bock, H., Bucci, M., & Luzzi, R. (2004) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-28632-5_20 · Cited by 37 · see citing works
Salehi, R., Malik, A. W., Novotny, M. A., & Khan, S. U. (2026) · Scientific Reports · doi:10.1038/s41598-026-51033-9
“Stojanovski et al. mentioned that chaotic systems exhibit deterministic behavior on the microscopic scale, while they appear random on the macroscopic scale 18 .”
- Authors
- Stojanovski, T., Pihl, J., & Kocarev, L.
- Affiliations
- Norwegian University of Science and Technology (NO)
- University of California San Diego (US)
- ORCID
- Kocarev, L.
- Venue
- IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
- Published
- 2001-03
- Volume
- 48
- Issue
- 3
- Pages
- 382-385
- ISSN
- 1057-7122 (ISSN-L)
- OpenAlex
- W2102875151
- Cited by
- 279
- References
- 4
- Citations by year
- 2026: 3 · 2025: 1 · 2024: 3 · 2023: 6 · 2022: 10 · 2021: 7 · 2020: 11 · 2019: 18 · 2018: 11 · 2017: 26 · 2016: 11 · 2015: 22 · 2014: 16 · 2013: 17 · 2012: 12
- FWCI
- 6.91
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Engineering › Biomedical Engineering › Analog and Mixed-Signal Circuit Design
- Keywords
- piecewise linear maps, one-dimensional chaotic maps, redundancy reduction, switched-current circuits, CMOS implementation, physical unclonable functions
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