On the Entropy of Oscillator-Based True Random Number Generators under Ionizing Radiation
<p>Jitter sampling principle.</p> "> Figure 2
<p>High-frequency oscillators. (<b>a</b>) RO scheme with enable. (<b>b</b>) Self-Timed Ring structure.</p> "> Figure 3
<p>Radiation setup. (<b>a</b>) DUT setup; (<b>b</b>) Irradiator.</p> "> Figure 4
<p>FPGA current (A) vs Total Ionizing Dose [krad(Si)].</p> "> Figure 5
<p>Wold et al. <span class="html-italic">p</span>-value distributions for different accumulated doses.</p> "> Figure 6
<p>Wold et al. % 0’s for different accumulated doses.</p> "> Figure 7
<p>Cherkaoui et al. <span class="html-italic">p</span>-value distributions for different accumulated doses.</p> "> Figure 8
<p>Cherkaoui et al. % 0’s for different accumulated doses.</p> ">
Abstract
:1. Introduction
2. Background
2.1. TRNGs
2.2. Entropy Tests
- Output Statistical Analysis: the most extended way of assessing the TRNG quality is testing the statistical distribution of the output using statistical tests [16]. Traditionally, widely known test suites as NIST or Diehard have been used to obtain an initial evaluation of TRNGs [5,6]. These tests cannot guarantee the entropy of the TRNG because they check the final output (after the post-processing) of the TRNG.
- Entropy Source Statistical Analysis: a new trend in TRNG evaluation was introduced in AIS-31 [17] where not only the final TRNG output is evaluated but also the entropy source. Among the different testing approaches stand out the NIST recommendations about entropy sources that include some statistical tests intended for estimating the min-entropy of a random number generator [18]. Of particular interest are the tests intended for generators that may have dependencies in time and/or state, which are commonly known as non independent and identically distributed (non-IID) number generators. These tests are particularly designed to avoid an overestimation of the entropy of these generators.
- Physical Parameters Analysis: the estimation of entropy must be based on a carefully constructed model of the random number generation process. Once the stochastic model is set, the measurement of some physical parameters (e.g., jitter measurement) can be used to estimate entropy at the output of the generator. In this line, some interesting proposals have been presented [19,20].
2.3. TID on Flash-Based FPGAs
3. Experimental Section
3.1. TRNG Implementations and Tests
3.2. TID Setup
4. Experimental Results
4.1. TRNG-RO Experimental Results
4.2. TRNG-STR Experimental Results
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
- Puig-Suari, J.; Turner, C.; Ahlgren, W. Development of the standard CubeSat deployer and a CubeSat class PicoSatellite. In Proceedings of the 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542), Big Sky, MT, USA, 10–17 March 2001; Volume 1, pp. 1/347–1/353. [Google Scholar]
- Taylor, A.; Bennie, P.; Guyon, F.; Cameron, I.; Glanfield, J.; Emam, O. A proposal for a space flight demonstration of a dynamically reconfigurable programmable module which uses firmware to realise an astrium patented cosmic random number generator for generating secure cryptographic keys. Presented at the DASIA 2013 DAta Systems in Aerospace, Porto, Portugal, 14–16 May 2013; Volume 720, p. 57. [Google Scholar]
- Wieczorek, P.Z. Lightweight TRNG based on multiphase timing of bistables. IEEE Trans. Circuits Syst. I Regul. Pap. 2016, 63, 1043–1054. [Google Scholar] [CrossRef]
- Wieczorek, P.Z.; Gołofit, K. True random number generator based on flip-flop resolve time instability boosted by random chaotic source. IEEE Trans. Circuits Syst. I Regul. Pap. 2018, 65, 1279–1292. [Google Scholar] [CrossRef]
- Rukhin, A.; Soto, J.; Nechvatal, J.; Smid, M.; Barker, E.; Leigh, S.; Levenson, M.; Vangel, M.; Banks, D.; Heckert, A.; et al. A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications; Technical Report; National Institute of Standards and Technology: Boulder, CO, USA, 2001.
- Walker, J. Randomness Battery. 1998. Available online: http://www.fourmilab.ch/random/ (accessed on 28 January 2008).
- Martin, H.; Korak, T.; San Millan, E.; Hutter, M. Fault attacks on STRNGs: Impact of glitches, temperature, and underpowering on randomness. IEEE Trans. Inf. Forensic Secur. 2015, 10, 266–277. [Google Scholar] [CrossRef]
- Santoro, R.; Sentieys, O.; Roy, S. On-the-fly evaluation of FPGA-based true random number generator. In Proceedings of the 2009 IEEE Computer Society Annual Symposium on VLSI, Tampa, FL, USA, 13–15 May 2009; pp. 55–60. [Google Scholar]
- Rezzak, N.; Wang, J.J.; Huang, C.K.; Nguyen, V.; Bakker, G. Total ionizing dose characterization of 65 nm flash-based FPGA. In Proceedings of the 2014 IEEE Radiation Effects Data Workshop (REDW), Paris, France, 14–18 July 2014; pp. 1–5. [Google Scholar]
- Faccio, F. Radiation effects in the electronics for CMS, CERN Radiation Tutorial. 2006. Available online: http://lhcb-elec.web.cern.ch/lhcb-elec/papers/radiation_tutorial.pdf (accessed on 9 July 2018).
- Wieczorek, P.Z.; Wieczorek, Z. Influence of radiation on metastability-based TRNG. In Proceedings of the Photonics Applications in Astronomy, Communications, Industry, and High Energy Physics Experiments, Wilga, Poland, 28 May 2017; Volume 10445, p. 1044529. [Google Scholar]
- Wold, K.; Tan, C. Analysis and enhancement of random number generator in FPGA based on oscillator rings. Int. J. Reconfig. Comput. 2009, 2009, 4. [Google Scholar] [CrossRef]
- Cherkaoui, A.; Fischer, V.; Fesquet, L.; Aubert, A. A very high speed true random number generator with entropy assessment. In Cryptographic Hardware and Embedded Systems—CHES 2013, Proceedings of the 15th International Workshop, Santa Barbara, CA, USA, 20–23 August 2013; Springer: Berlin/Heidelberg, Germany, 2013; pp. 179–196. [Google Scholar]
- Ortiz-Martin, L.; Picazo-Sanchez, P.; Peris-Lopez, P.; Tapiador, J. Heartbeats do not make good pseudo-random number generators: An analysis of the randomness of inter-pulse intervals. Entropy 2018, 20, 94. [Google Scholar] [CrossRef]
- Chaudhry, M.U.; Lee, J.H. MOTiFS: Monte carlo tree search based feature selection. Entropy 2018, 20, 385. [Google Scholar] [CrossRef]
- Calude, C.S.; Dinneen, M.J.; Dumitrescu, M.; Svozil, K. Experimental evidence of quantum randomness incomputability. Phys. Rev. A 2010, 82, 022102. [Google Scholar] [CrossRef]
- Schindler, W.; Killmann, W. Evaluation criteria for true (physical) random number generators used in cryptographic applications. In Cryptographic Hardware and Embedded Systems—CHES 2002, Proceedings of the 4th International Workshop Redwood Shores, Santa Barbara, CA, USA, 13–15 August 2002; Springer: Berlin/Heidelberg, Germany, 2002; pp. 431–449. [Google Scholar]
- Turan, M.S.; Barker, E.; Kelsey, J.; McKay, K.L.; Baish, M.L.; Boyle, M. NIST Special Publication 800-90B: Recommendation for the Entropy Sources Used for Random Bit Generation; U.S. Department of Commerce, National Institute of Standards and Technology: Gaithersburg, MD, USA, 2018.
- Haddad, P.; Fischer, V.; Bernard, F.; Nicolai, J. A physical approach for stochastic modeling of TERO-based TRNG. In Cryptographic Hardware and Embedded Systems—CHES 2015, Proceedings of the 17th International Workshop, Saint-Malo, France, 13–16 September 2015; Springer: Berlin/Heidelberg, Germany, 2015; pp. 357–372. [Google Scholar]
- Fischer, V.; Lubicz, D. Embedded evaluation of randomness in oscillator based elementary TRNG. In Cryptographic Hardware and Embedded Systems—CHES 2014, Proceedings of the 16th International Workshop, Busan, Korea, 23–26 September 2014; Springer: Berlin/Heidelberg, Germany, 2014; pp. 527–543. [Google Scholar]
- European Space Components Coordination. Total Dose Steady-State Irradiation Test Method, ESCC Basic Specification No. 22900; European Space Agency: Paris, France, 2010. [Google Scholar]
- Morilla, Y.; Muniz, G.; Dominguez, M.; Martin, P.; Jimenez, J.; Praena, J.; Munoz, E.; Sanchez-Angulo, C.I.; Fernandez, G. New gamma-radiation facility for device testing in spain. In Proceedings of the 2014 IEEE Radiation Effects Data Workshop (REDW), Paris, France, 14–18 July 2014; pp. 1–5. [Google Scholar]
- Costantino, A.; Muschitiello, M.; Zadeh, A.; Romero, G.F.; Holgado, P.M.; Morilla, Y.; Muniz, G.; Standaert, L.; Vanhees, J. Dosimetry inter-laboratory comparison between ESTEC, CNA-ALTER/RADLAB, and UCL. In Proceedings of the 2015 15th European Conference on Radiation and Its Effects on Components and Systems, Moscow, Russia, 14–18 September 2015; pp. 1–8. [Google Scholar]
- Allen, G.; McClure, S.; Rezgui, S.; Wang, J.J. Total ionizing dose characterization results of Actel ProAsic3, ProAsic3L, and IGLOO Flash-based FPGA. In Proceedings of the Military and Aerospace Programmable Logic Devices, Annapolis, MD, USA, 15–18 September 2008. [Google Scholar]
- Hagerty, P.; Draper, T. Entropy bounds and statistical tests. In Proceedings of the NIST Random Bit Generation Workshop, Gaithersburg, MD, USA, 5–6 December 2012; pp. 1319–1327. [Google Scholar]
Test | RO-TRNG | STR-TRNG |
---|---|---|
Frequency | 0.911413 | 0.253551 |
Block Frequency | 0.804337 | 0.082177 |
Cumulative Sums | 0.476471 | 0.215914 |
Runs | 0.671779 | 0.804337 |
Longest Run | 0.949602 | 0.991468 |
Rank | 0.253551 | 0.862344 |
FFT | 0.148094 | 0.739918 |
Non-Overlapping Template | 0.462714 | 0.479021 |
Overlapping Template | 0.534146 | 0.299251 |
Universal | 0.253551 | 0.299251 |
Approximate Entropy | 0.066882 | 0.082177 |
Random Excursions | 0.633125 | 0.257812 |
Random Excursions Variant | 0.508011 | 0.135850 |
Serial | 0.789259 | 0.504774 |
Linear Complexity | 0.213309 | 0.122325 |
0 krad(Si) | 5 krad(Si) | 10 krad(Si) | 15 krad(Si) | 20 krad(Si) | 25 krad(Si) | 30 krad(Si) | 35 krad(Si) | 40 krad(Si) | 40.8 krad(Si) | |
---|---|---|---|---|---|---|---|---|---|---|
Most Common Value | 0.99861 | 0.998628 | 0.998306 | 0.998273 | 0.997432 | 0.998117 | 0.998272 | 0.965788 | 0.912059 | 0.75138 |
Collision | 0.944718 | 0.944718 | 0.928538 | 0.944718 | 0.928538 | 0.955606 | 0.955606 | 0.785681 | 0.682587 | 0.447331 |
Markov | 0.998805 | 0.99911 | 0.998105 | 0.998776 | 0.997169 | 0.998986 | 0.998619 | 0.933978 | 0.841065 | 0.605037 |
Compression | 1 | 1 | 0.970713 | 1 | 0.97486 | 1 | 1 | 0.819469 | 0.723149 | 0.527182 |
t-Tuple | 0.933664 | 0.931583 | 0.935803 | 0.935803 | 0.931583 | 0.933664 | 0.933664 | 0.90872 | 0.866229 | 0.60287 |
LRS | 0.98132 | 0.973757 | 1 | 0.999913 | 0.999368 | 0.981764 | 0.912897 | 0.991443 | 0.932321 | 0.832981 |
MultiMCW Prediction | 0.999113 | 0.998501 | 0.999401 | 0.998223 | 0.998953 | 0.999325 | 0.999181 | 0.971087 | 0.912829 | 0.736576 |
Lag Prediction | 0.998727 | 0.99869 | 0.998496 | 0.998613 | 0.997539 | 0.999286 | 0.999181 | 0.963841 | 0.912324 | 0.751094 |
MultiMMC Prediction | 0.998784 | 0.999426 | 0.998903 | 0.998675 | 0.998834 | 0.998969 | 0.998536 | 0.962938 | 0.882302 | 0.586627 |
LZ78Y Prediction | 0.99864 | 0.99906 | 0.998615 | 0.998359 | 0.997974 | 0.999135 | 0.998135 | 0.96379 | 0.912679 | 0.751365 |
min-entropy | 0.933664 | 0.931583 | 0.928538 | 0.935803 | 0.928538 | 0.933664 | 0.912897 | 0.785681 | 0.682587 | 0.447331 |
0 krad(Si) | 5 krad(Si) | 10 krad(Si) | 15 krad(Si) | 20 krad(Si) | 25 krad(Si) | 30 krad(Si) | 35 krad(Si) | 40 krad(Si) | 40.8 krad(Si) | |
---|---|---|---|---|---|---|---|---|---|---|
Most Common Value | 0.996126 | 0.997298 | 0.99782 | 0.979399 | 0.997371 | 0.990443 | 0.987387 | 0.962743 | 0.908064 | 0.750457 |
Collision | 0.944718 | 0.928538 | 0.939304 | 1 | 0.933911 | 0.944718 | 0.944718 | 0.782042 | 0.682587 | 0.446371 |
Markov | 0.996467 | 0.996604 | 0.99818 | 0.982565 | 0.997971 | 0.990434 | 0.987576 | 0.930175 | 0.83738 | 0.604465 |
Compression | 0.931584 | 0.933664 | 0.927586 | 0.933664 | 0.935803 | 0.931584 | 0.935803 | 0.856409 | 0.863284 | 0.629717 |
t-Tuple | 0.931584 | 0.933664 | 0.927586 | 0.933664 | 0.935803 | 0.931584 | 0.935803 | 0.856409 | 0.863284 | 0.629717 |
LRS | 0.952589 | 0.994943 | 0.932321 | 0.99972 | 0.996622 | 0.998976 | 0.999929 | 0.987735 | 0.932321 | 0.839317 |
MultiMCW Prediction | 0.998189 | 0.998657 | 0.998235 | 0.987077 | 0.999218 | 0.996626 | 0.996279 | 0.962677 | 0.908805 | 0.680523 |
Lag Prediction | 0.975427 | 0.998682 | 0.997838 | 0.997586 | 0.999067 | 0.997723 | 0.998898 | 0.962677 | 0.911805 | 0.69826 |
MultiMMC Prediction | 0.996487 | 0.998412 | 0.998411 | 0.979472 | 0.998083 | 0.990706 | 0.987457 | 0.96084 | 0.880258 | 0.586456 |
LZ78Y Prediction | 0.996362 | 0.997591 | 0.998346 | 0.97946 | 0.997859 | 0.990483 | 0.987461 | 0.962788 | 0.908079 | 0.680523 |
min-entropy | 0.931584 | 0.928538 | 0.927586 | 0.933664 | 0.933911 | 0.931584 | 0.935803 | 0.782042 | 0.682587 | 0.446371 |
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Martin, H.; Martin-Holgado, P.; Peris-Lopez, P.; Morilla, Y.; Entrena, L. On the Entropy of Oscillator-Based True Random Number Generators under Ionizing Radiation. Entropy 2018, 20, 513. https://doi.org/10.3390/e20070513
Martin H, Martin-Holgado P, Peris-Lopez P, Morilla Y, Entrena L. On the Entropy of Oscillator-Based True Random Number Generators under Ionizing Radiation. Entropy. 2018; 20(7):513. https://doi.org/10.3390/e20070513
Chicago/Turabian StyleMartin, Honorio, Pedro Martin-Holgado, Pedro Peris-Lopez, Yolanda Morilla, and Luis Entrena. 2018. "On the Entropy of Oscillator-Based True Random Number Generators under Ionizing Radiation" Entropy 20, no. 7: 513. https://doi.org/10.3390/e20070513
APA StyleMartin, H., Martin-Holgado, P., Peris-Lopez, P., Morilla, Y., & Entrena, L. (2018). On the Entropy of Oscillator-Based True Random Number Generators under Ionizing Radiation. Entropy, 20(7), 513. https://doi.org/10.3390/e20070513