A Framework for Investigating the Performance of Chaotic-Map Truly Random Number Generators
Open accessAbstract
This brief approximates the hidden Markov model of chaotic-map truly random number generators (TRNGs) and describes its fundamental limits based on the approximate entropy rate of the underlying bit-generation process. It is demonstrated that the entropy rate plays a key role in the performance and robustness of chaotic-map TRNGs, which must be taken into account in the circuit design optimization. Finally, the optimality conditions for postprocessing units that extract truly random bits from a raw random number generator are derived.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Chaos is a perfect entropy source for fast TRNGs due to high bandwidth, unpredictability, and insensitivity to disturbance and component tolerances.
“Due to its high bandwidth, unpredictability and insensitive to various disturbance and tolerances of components, chaos is a perfect entropy source for fast TRNGs [14], [76], [77].”
From True Random Number Generators Using Electrical Noise (2019) · cites this paper as [76]
Cites
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2001) · Wiley eBooks · doi:10.1002/0471200611 · Cited by 37,139 · see citing works
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2005) · doi:10.1002/047174882x · Cited by 13,791 · see citing works
Handbook of applied cryptography
(1997) · Choice Reviews Online · doi:10.5860/choice.34-4512 · Cited by 10,357 · see citing works
Introduction to Applied Nonlinear Dynamical Systems and Chaos
Wiggins, S., & Mazel, D. S. (1990) · Computers in Physics · doi:10.1063/1.4822950 · Cited by 3,833 · see citing works
Lasota, A., & Mackey, M. C. (1994) · Applied Mathematical Sciences · doi:10.1007/978-1-4612-4286-4 · Cited by 1,353 · see citing works
Introduction to applied nonlinear dynamical systems and chaos
(1991) · Mathematics and Computers in Simulation · doi:10.1016/0378-4754(91)90060-g · Cited by 812 · see citing works
Ephraim, Y., & Merhav, N. (2002) · IEEE Transactions on Information Theory · doi:10.1109/tit.2002.1003838 · Cited by 782 · see citing works
A noise-based IC random number generator for applications in cryptography
Petrie, C. S., & Connelly, J. A. (2000) · IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications · doi:10.1109/81.847868 · Cited by 487 · see citing works
Bucci, M., Germani, L., Luzzi, R., Trifiletti, A., & Varanonuovo, M. (2003) · IEEE Transactions on Computers · doi:10.1109/tc.2003.1190581 · Cited by 403 · see citing works
Chaotic Electronics in Telecommunications
(2018) · CRC Press eBooks · doi:10.1201/9781482274516 · Cited by 311 · see citing works
Entropy and data compression schemes
Ornstein, D. S., & Weiss, B. (1993) · IEEE Transactions on Information Theory · doi:10.1109/18.179344 · Cited by 288 · see citing works
Callegari, S., Rovatti, R., & Setti, G. (2005) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2004.839924 · Cited by 243 · see citing works
An integrated analog/digital random noise source
Holman, W. T., Connelly, J. A., & Dowlatabadi, A. B. (1997) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/81.586025 · Cited by 190 · see citing works
Callegari, S., Rovatti, R., & Setti, G. (2005) · PORTO Publications Open Repository TOrino (Politecnico di Torino) · doi:10.1109/tsp.2004.839924(410 · Cited by 180 · see citing works
A feedback strategy to improve the entropy of a chaos-based random bit generator
Addabbo, T., Alioto, M., Fort, A., ROCCHI, S., & Vignoli, V. (2006) · IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications · doi:10.1109/tcsi.2005.856670 · Cited by 96 · see citing works
Nejati, H., Beirami, A., & Ali, W. H. (2012) · Analog Integrated Circuits and Signal Processing · doi:10.1007/s10470-012-9893-9 · Cited by 57 · see citing works
Self-citationSwitched-current 3-bit CMOS 4.0-MHz wideband random signal generator
Wang, C., Huang, J., Cheng, H.-C., et al. (2005) · IEEE Journal of Solid-State Circuits · doi:10.1109/jssc.2005.848036 · Cited by 35 · see citing works
A CMOS tailed tent map for the generation of uniformly distributed chaotic sequences
Callegari, S., Setti, G., & Langlois, P. J. (2002) · doi:10.1109/iscas.1997.621829 · Cited by 32 · see citing works
Modeling chaotic systems with hidden Markov models
Myers, C. S., Singer, A. C., Shin, F. B., et al. (1992) · IEEE International Conference on Acoustics Speech and Signal Processing · doi:10.1109/icassp.1992.226385 · Cited by 29 · see citing works
Poli, S., Callegari, S., Rovatti, R., & Setti, G. (2004) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2004.1329071 · Cited by 17 · see citing works
Efficient Post-Processing Module for a Chaos-based Random Bit Generator
Addabbo, T., Alioto, M., Fort, A., et al. (2006) · IEEE International Conference on Electronics, Circuits and Systems (ICECS) · doi:10.1109/icecs.2006.379682 · Cited by 13 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
True Random Number Generators Using Electrical Noise
Gong, L., Zhang, J., Liu, H., Sang, L., & Wang, Y. (2019) · IEEE Access · doi:10.1109/access.2019.2939027 · Cited by 77 · see citing works
“Due to its high bandwidth, unpredictability and insensitive to various disturbance and tolerances of components, chaos is a perfect entropy source for fast TRNGs [14], [76], [77].”
BackgroundWieczorek, P. Z., & Golofit, K. (2018) · IEEE Transactions on Circuits and Systems I: Regular Papers · doi:10.1109/tcsi.2017.2751144 · Cited by 53 · see citing works
- Authors
- Beirami, A., & Nejati, H.
- Affiliations
- Georgia Institute of Technology (US)
- University of Michigan (US)
- ORCID
- Beirami, Ahmad
- Venue
- IEEE Transactions on Circuits and Systems II: Express Briefs
- Published
- 2013-07
- Volume
- 60
- Issue
- 7
- Pages
- 446-450
- ISSN
- 1549-7747 (ISSN-L)
- 1558-3791
- OpenAlex
- W2149404985
- Cited by
- 36
- References
- 21
- Citations by year
- 2025: 1 · 2024: 3 · 2023: 5 · 2022: 2 · 2021: 3 · 2020: 1 · 2019: 6 · 2018: 1 · 2017: 2 · 2016: 4 · 2015: 5 · 2014: 2 · 2013: 1
- FWCI
- 4.50
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- IEEE Transactions on Circuits & Systems II Express Briefs (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Chaos-based Image/Signal Encryption
- Physical Sciences › Computer Science › Hardware and Architecture › Physical Unclonable Functions (PUFs) and Hardware Security
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Keywords
- chaotic maps, hidden Markov models, entropy rate, post-processing, circuit optimization
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
