31:
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science and statistical applications: impossibility to re-run a series of numbers unless they are stored, reliance on an analog physical entity can obscure the failure of the source. The TRNGs therefore are primarily used in the applications where their unpredictability and the impossibility to re-run the sequence of numbers are crucial to the success of the implementation: in cryptography and gambling machines.
713:
331:). The RAND table was a significant breakthrough in delivering random numbers because such a large and carefully prepared table had never before been available. It has been a useful source for simulations, modeling, and for deriving the arbitrary constants in cryptographic algorithms to demonstrate that the constants had not been selected maliciously ("
149:(due to practical considerations the latter, as well as the atmospheric noise, is not viable). While "classical" (non-quantum) phenomena are not truly random, an unpredictable physical system is usually acceptable as a source of randomness, so the qualifiers "true" and "physical" are used interchangeably.
463:
elements can be integrated on-chip. Stipčević & Koç characterize this technique as "most objectionable", mostly due to the fact that chaotic behavior is usually controlled by a differential equation and no new randomness is introduced, thus there is a possibility of the chaos-based TRNG producing
320:
tube, when placed in a magnetic field). Twenty of the 32 possible counter values were mapped onto the 10 decimal digits and the other 12 counter values were discarded. The results of a long run from the RAND machine, filtered and tested, were converted into a table, which originally existed only as a
857:
of a sequence of symbols. None are so reliable that their estimates can be fully relied upon; there are always assumptions which may be very difficult to confirm. These are useful for determining if there is enough entropy in a seed pool, for example, but they cannot, in general, distinguish between
480:
forming the RO can be thought of as amplifiers with a very large gain, an FRO output exhibits very fast oscillations in phase in frequency domains. The FRO-based TRNGs are very popular due to their use of the standard digital logic despite issues with randomness proofs and chip-to-chip variability.
809:
It is very easy to misconstruct hardware or software devices which attempt to generate random numbers. Also, most 'break' silently, often producing decreasingly random numbers as they degrade. Failure modes in such devices are plentiful and are complicated, slow, and hard to detect. Methods that
662:
The failure of a TRNG can be quite complex and subtle, necessitating validation of not just the results (the output bit stream), but of the unpredictability of the entropy source. Hardware random number generators should be constantly monitored for proper operation to protect against the entropy
303:
Kendall and
Babington-Smith (1938) used a fast-rotating 10-sector disk that was illuminated by periodic bursts of light. The sampling was done by a human who wrote the number under the light beam onto a pad. The device was utilized to produce a 100,000-digit random number table (at the time such
227:
Hardware random number generators can be used in any application that needs randomness. However, in many scientific applications additional cost and complexity of a TRNG (when compared with pseudo random number generators) provide no meaningful benefits. TRNGs have additional drawbacks for data
454:
The idea of chaos-based noise stems from the use of a complex system that is hard to characterize by observing its behavior over time. For example, lasers can be put into (undesirable in other applications) chaos mode with chaotically fluctuating power, with power detected using a
1781:
Turan, Meltem Sönmez; Barker, Elaine; Kelsey, John; McKay, Kerry A; Baish, Mary L; Boyle, Mike (2018). NIST SP800-90B: Recommendation for the entropy sources used for random bit generation (Report). Gaithersburg, MD: National
Institute of Standards and Technology.
346:
A lot of different TRNG designs were proposed over time with a large variety of noise sources and digitization techniques ("harvesting"). However, practical considerations (size, power, cost, performance, robustness) dictate the following desirable traits:
653:
A plurality of quantum random number generators designs are inherently untestable and thus can be manipulated by adversaries. Mannalath et al. call these designs "trusted" in a sense that they can only operate in a fully controlled, trusted environment.
311:
began generating random digits with an "electronic roulette wheel", consisting of a random frequency pulse source of about 100,000 pulses per second gated once per second with a constant frequency pulse and fed into a five-bit binary counter.
813:
Because many entropy sources are often quite fragile, and fail silently, statistical tests on their output should be performed continuously. Many, but not all, such devices incorporate some such tests into the software that reads the device.
515:. The entropy harvesting was done using an event counter that was periodically sampled or a time counter that was sampled at the time of the event. Similar designs were utilized in the 1950s to generate random noise in
193:
Hardware random number generators generally produce only a limited number of random bits per second. In order to increase the available output data rate, they are often used to generate the "
688:
checks that the sequences of identical digits are not too long, for a (typical) case of a TRNG that digitizes one bit at a time, this means not having long strings of either 0s or 1s;
285:
in particular have been known for more than 5000 years (found on locations in modern Iraq and Iran), and flipping a coin (thus producing a random bit) dates at least to the times of
300:
using a common gambling dice. In addition to the top digit, Galton also looked at the face of a dice closest to him, thus creating 6*4 = 24 outcomes (about 4.6 bits of randomness).
266:
202:
1859:
327:
95:
189:. TRNGs are mostly used in cryptographical algorithms that get completely broken if the random numbers have low entropy, so the testing functionality is usually included.
730:
2313:
406:. If the voltage is above threshold, the comparator output is 1, otherwise 0. The random bit value is latched using a flip-flop. Sources of noise vary and include:
316:
built the equipment, implementing Cecil
Hasting's suggestion (RAND P-113) for a noise source (most likely the well known behavior of the 6D4 miniature gas
439:
noise levels are typically low, thus the design requires power-hungry amplifiers. The sensitivity of amplifier inputs enables manipulation by an attacker;
338:
Since the early 1950s, research into TRNGs has been highly active, with thousands of research works published and about 2000 patents granted by 2017.
248:
needed to encrypt and sign data. In addition to randomness, there are at least two additional requirements imposed by the cryptographic applications:
206:
1332:
Kendall, M. G., and B. Babington-Smith. 1938. “Randomness and other random sampling numbers”. Journal of the Royal
Statistical Society 101:147–166.
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2066:
1983:
1943:
1911:
1884:
1808:
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1421:
1142:
749:
1391:
197:" for a faster PRNG. DRBG also helps with the noise source "anonymization" (whitening out the noise source identifying characteristics) and
1732:
Markettos, A. Theodore; Moore, Simon W. (2009). "The
Frequency Injection Attack on Ring-Oscillator-Based True Random Number Generators".
835:
The physical processes in HRNG introduce new attack surfaces. For example, a free-running oscillator-based TRNG can be attacked using a
756:
677:
The minimal set of real-time tests mandated by the certification bodies is not large; for example, NIST in SP 800-90B requires just two
255:
guarantees that the knowledge of the past output and internal state of the device should not enable the attacker to predict future data;
2190:
1308:
2375:
1126:
796:
763:
533:, a quantum mechanical noise source found in electronic circuits, while technically a quantum effect, is hard to isolate from the
261:
protects the "opposite direction": knowledge of the output and internal state in the future should not divulge the preceding data.
893:
858:
a true random source and a pseudorandom generator. This problem is avoided by the conservative use of hardware entropy sources.
577:
is a generalization (simplifying the equipment) of the above methods that allows more than one photon in the system at a time;
829:
828:
Just as with other components of a cryptography system, a cryptographic random number generator should be designed to resist
823:
745:
734:
615:
537:, so, with few exceptions, noise sources utilizing it are only partially quantum and are usually classified as "classical";
2380:
2239:
635:
524:
87:
332:
698:). For bit-oriented entropy sources that means that the count of 1s and 0s in the bit stream is approximately the same.
609:
650:
To reduce costs and increase robustness of quantum random number generators, online services have been implemented.
2132:
2078:"A Comprehensive Review of Quantum Random Number Generators: Concepts, Classification and the Origin of Randomness"
1349:
222:
156:"). A physical process usually does not have this property, and a practical TRNG typically includes a few blocks:
2357:, ProtegoST, "Hardware Random Number Generator "Based on quantum physics random number source from a zener diode".
2157:
1825:
410:
2004:
1995:
106:
1853:
297:
71:
770:
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historically was the earliest quantum method used since the 1960s owing its popularity to the availability of
1070:
908:
723:
91:
1993:
Herrero-Collantes, Miguel; Garcia-Escartin, Juan Carlos (2017-02-22). "Quantum random number generators".
1922:
558:
836:
2370:
872:
477:
376:
Stipčević & Koç in 2014 classified the physical phenomena used to implement TRNG into four groups:
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2221:
2018:
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554:
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134:
102:
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245:
79:
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2008:
1300:
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848:
587:
445:
a proof of randomness is near-impossible as multiple interacting physical processes are involved.
1385:
1118:
571:
use a weak photon source, with the entropy harvested similarly to the case of radioactive decay;
17:
2307:
2062:
2034:
1979:
1949:
1939:
1907:
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1804:
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1046:
695:
619:
500:
Herrero-Collantes & Garcia-Escartin list the following stochastic processes as "quantum":
292:
The first documented use of a physical random number generator for scientific purposes was by
241:
130:
1798:
890:(a hardware random number generator based on movement of the floating material in lava lamps)
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2229:
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1971:
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noise levels are hard to control, they vary with environmental changes and device-to-device;
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308:
277:
Physical devices were used to generate random numbers for thousands of years, primarily for
75:
2180:
1412:
Schneier, Bruce (1995-11-01). "Other Stream
Ciphers and Real Random-Sequence Generators".
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calibration processes needed to ensure a guaranteed amount of entropy are time-consuming;
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circuitry located nearby generates a lot of non-random noise thus lowering the entropy;
355:
293:
152:
A hardware random number generator is expected to output near-perfect random numbers ("
2337:
644:
leading to binary phase state selection in a degenerate optical parametric oscillator;
2364:
1867:
Schindler, Werner (2009). "Random Number
Generators for Cryptographic Applications".
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verifies that any random digit does not occur too frequently in the data stream (low
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504:
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110:
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that implements the physical process producing the entropy. Usually this process is
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153:
832:. Defending against these attacks is difficult without a hardware entropy source.
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Quantum random number generation technology is well established with 8 commercial
2030:
1975:
1746:
1117:
Kollmitzer, Christian; Petscharnig, Stefan; Suda, Martin; Mehic, Miralem (2020).
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The TRNGs based on a free-running oscillator (FRO) typically utilize one or more
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325:, but was later published in 1955 as a book, 50 rows of 50 digits on each page (
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is used to convert the output of the analog source into a binary representation;
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2104:
2077:
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1031:
631:
extract entropy from the interaction of photons with the solid-state materials;
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compact and low-power design. This discourages use of analog components (e.g.,
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530:
456:
403:
114:
2038:
1953:
1935:
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1838:
1824:
Saarinen, Markku-Juhani O.; Newell, G. Richard; Marshall, Ben (2020-11-09).
1788:
1003:
Jacak, Marcin M.; Jóźwiak, Piotr; Niemczuk, Jakub; Jacak, Janusz E. (2021).
460:
366:
317:
39:
1961:
Stipčević, Mario; Koç, Çetin Kaya (2014). "True Random Number
Generators".
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Randomness and
Genuine Random Number Generator With Self-testing Functions
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90:(PRNG, a.k.a. "deterministic random bit generator", DRBG) that utilizes a
887:
867:
667:
278:
1962:
476:(ROs), outputs of which are sampled using yet another oscillator. Since
2122:
1343:
737: in this section. Unsourced material may be challenged and removed.
265:
A typical way to fulfill these requirements is to use a TRNG to seed a
236:
The major use for hardware random number generators is in the field of
142:
2147:
1894:
Sunar, Berk (2009). "True Random Number
Generators for Cryptography".
929:
927:
925:
923:
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Special Publication 800-90B define tests which can be used for this.
2291:
2234:
1930:. 2017 Winter Simulation Conference (WSC). Las Vegas, NV, USA: IEEE.
1295:
903:
118:
98:
that do not include hardware dedicated to generation of entropy.
1741:. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 317–331.
1635:
Huang, Leilei; Zhou, Hongyi; Feng, Kai; Xie, Chongjin (2021-07-07).
398:
Noise-based RNGs generally follow the same outline: the source of a
2094:
2013:
1084:
1064:
Ma, Xiongfeng; Yuan, Xiao; Cao, Zhu; Qi, Bing; Zhang, Zhen (2016).
459:
and sampled by a comparator. The design can be quite small, as all
304:
tables were used for statistical experiments, like PRNG nowadays).
2346:
1483:
1481:
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exclusive use of digital design techniques. This allows an easier
29:
663:
source degradation due to natural causes and deliberate attacks.
557:
randomly takes one of the two paths and sensed by one of the two
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1610:
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1514:
1502:
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372:
mathematical justification of the entropy collection mechanisms.
359:
282:
1827:
Building a Modern TRNG: An Entropy Source Interface for RISC-V
706:
2354:
2076:
Mannalath, Vaisakh; Mishra, Sandeep; Pathak, Anirban (2023).
1970:. Cham: Springer International Publishing. pp. 275–315.
959:
957:
1416:(Second ed.). John Wiley & Sons, Inc. p. 423.
429:
The drawbacks of using noise sources for an RNG design are:
82:(in other words, the device always has access to a physical
1249:
1247:
1245:
1243:
1241:
205:, CSPRNG), the combination can satisfy the requirements of
618:
generators use spontaneous light emission present in the
944:
942:
351:
use of a commonly available inexpensive silicon process;
2279:
D. Eastlake, 3rd; J. Schiller; S. Crocker (June 2005).
1964:
Open Problems in Mathematics and Computational Science
1719:
1707:
1196:
1184:
933:
267:
cryptographically secure pseudorandom number generator
203:
cryptographically secure pseudorandom number generator
2047:
Quantum Random Number Generation: Theory and Practice
1695:
1683:
1370:
Cobine, Curry (1947), "Electrical Noise Generators",
1157:
1123:
Quantum Random Number Generation: Theory and Practice
974:
972:
853:
There are mathematical techniques for estimating the
810:
combine multiple sources of entropy are more robust.
34:
A USB-pluggable hardware true random number generator
2182:
A Million Random Digits with 100,000 Normal Deviates
877:
328:
A Million Random Digits with 100,000 Normal Deviates
1647:(1). Springer Science and Business Media LLC: 107.
608:that is converted to amplitude using an unbalanced
96:
non-physical nondeterministic random bit generators
2149:Some Tests of the Randomness of a Million Digits
1858:: CS1 maint: bot: original URL status unknown (
183:) that improves the quality of the random bits;
464:a limited subset of possible output strings.
8:
1623:Herrero-Collantes & Garcia-Escartin 2017
1611:Herrero-Collantes & Garcia-Escartin 2017
1599:Herrero-Collantes & Garcia-Escartin 2017
1587:Herrero-Collantes & Garcia-Escartin 2017
1575:Herrero-Collantes & Garcia-Escartin 2017
1563:Herrero-Collantes & Garcia-Escartin 2017
1551:Herrero-Collantes & Garcia-Escartin 2017
1539:Herrero-Collantes & Garcia-Escartin 2017
1527:Herrero-Collantes & Garcia-Escartin 2017
1515:Herrero-Collantes & Garcia-Escartin 2017
1503:Herrero-Collantes & Garcia-Escartin 2017
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1233:Herrero-Collantes & Garcia-Escartin 2017
1221:Herrero-Collantes & Garcia-Escartin 2017
1173:Herrero-Collantes & Garcia-Escartin 2017
991:Herrero-Collantes & Garcia-Escartin 2017
963:
2312:: CS1 maint: numeric names: authors list (
1924:History of uniform random number generation
1898:. Boston, MA: Springer US. pp. 55–73.
101:Many natural phenomena generate low-level,
1871:. Boston, MA: Springer US. pp. 5–23.
1841:. Archived from the original on 2021-03-16
612:. The noise is sampled by a photodetector;
2290:
2233:
2103:
2093:
2012:
1787:
1660:
1294:
1101:
1083:
1040:
1030:
948:
797:Learn how and when to remove this message
342:Physical phenomena with random properties
201:. With a proper DRBG algorithm selected (
207:Federal Information Processing Standards
919:
2305:
1851:
1637:"Quantum random number cloud platform"
1005:"Quantum generators of random numbers"
642:spontaneous parametric down-conversion
60:non-deterministic random bit generator
1436:
1208:
978:
296:(1890). He devised a way to sample a
7:
2282:Randomness Requirements for Security
2261:, Japan: LE Tech RNG, archived from
1197:Saarinen, Newell & Marshall 2020
735:adding citations to reliable sources
1696:Mannalath, Mishra & Pathak 2023
1684:Mannalath, Mishra & Pathak 2023
1158:Mannalath, Mishra & Pathak 2023
358:integration and enables the use of
2210:"Dice for statistical experiments"
2049:. Quantum Science and Technology.
1800:Simulation for Data Science with R
1390:, Rand Corporation, January 2001,
1268:"Dice for statistical experiments"
1119:"Quantum Random Number Generation"
1066:"Quantum random number generation"
746:"Hardware random number generator"
468:Free-running oscillators-based RNG
25:
2339:The Intel Random Number Generator
1735:Lecture Notes in Computer Science
1342:Brown, George W. (January 1949),
1314:from the original on 4 March 2016
1127:Springer International Publishing
2124:History of Rand's Million Digits
894:List of random number generators
711:
497:) products offered before 2017.
68:physical random number generator
44:hardware random number generator
18:Hardware random-number generator
2242:from the original on 2004-04-04
2193:from the original on 2002-12-16
2160:from the original on 2007-06-05
2146:Brown, Bernice (October 1948),
2135:from the original on 2007-06-05
1394:from the original on 2018-04-15
1352:from the original on 2007-06-05
722:needs additional citations for
491:quantum random number generator
240:, for example to create random
2082:Quantum Information Processing
824:Random number generator attack
616:amplified spontaneous emission
1:
2121:Brown, George W (June 1949),
636:optical parametric oscillator
561:thus generating a random bit;
523:concerns, low bit rates, and
88:pseudorandom number generator
2031:10.1103/revmodphys.89.015004
1976:10.1007/978-3-319-10683-0_12
1747:10.1007/978-3-642-04138-9_23
1348:, Papers, Rand Corporation,
598:laser phase noise generators
590:to probe the changes in the
333:nothing up my sleeve numbers
133:. Researchers also used the
52:true random number generator
2173:Electron Tube Data handbook
1904:10.1007/978-0-387-71817-0_4
1877:10.1007/978-0-387-71817-0_2
1135:10.1007/978-3-319-72596-3_2
610:Mach-Zehnder interferometer
575:attenuated pulse generators
519:. The major drawbacks were
2397:
2105:10.1007/s11128-023-04175-y
1833:. New York, NY, USA: ACM.
1662:10.1038/s41534-021-00442-x
1032:10.1038/s41598-021-95388-7
846:
821:
394:Electrical noise-based RNG
223:Applications of randomness
220:
2059:10.1007/978-3-319-72596-3
2005:American Physical Society
1996:Reviews of Modern Physics
1921:L'Ecuyer, Pierre (2017).
1896:Cryptographic Engineering
1869:Cryptographic Engineering
1372:Proceedings of the I.R.E.
606:single spatial mode laser
569:photon counting generator
565:time of arrival generator
383:free-running oscillators;
2376:Random number generation
1936:10.1109/wsc.2017.8247790
1488:Stipčević & Koç 2014
1473:Stipčević & Koç 2014
1461:Stipčević & Koç 2014
1449:Stipčević & Koç 2014
1266:Galton, Francis (1890).
964:Stipčević & Koç 2014
692:adaptive proportion test
553:so that a photon from a
547:branching path generator
525:non-uniform distribution
298:probability distribution
145:phenomena, and even the
125:of electronic circuits,
72:generates random numbers
1839:10.1145/3411504.3421212
1789:10.6028/nist.sp.800-90b
1641:npj Quantum Information
1374:(September 1947): 875–9
1071:npj Quantum Information
909:Trusted Platform Module
679:continuous health tests
559:single-photon detectors
92:deterministic algorithm
307:On 29 April 1947, the
35:
2319:Best Common Practice.
1103:10.1038/npjqi.2016.21
873:Bell test experiments
686:repetition count test
622:as a source of noise;
411:Johnson–Nyquist noise
109:" signals, including
78:capable of producing
33:
2381:Computer peripherals
1803:. Packt Publishing.
1414:Applied Cryptography
731:improve this article
555:single-photon source
181:randomness extractor
135:photoelectric effect
103:statistically random
27:Cryptographic device
2321:Obsoletes RFC
2226:1890Natur..42...13G
2023:2017RvMP...89a5004H
1653:2021npjQI...7..107H
1490:, pp. 288–289.
1451:, pp. 279–280.
1287:1890Natur..42...13G
1094:2016npjQI...216021M
1023:2021NatSR..1116108J
837:frequency injection
604:on the output of a
582:vacuum fluctuations
423:avalanche breakdown
2114:General references
1797:Templ, M. (2016).
1129:. pp. 11–34.
1010:Scientific Reports
849:Entropy estimation
843:Estimating entropy
620:optical amplifiers
588:homodyne detection
413:("thermal noise");
242:cryptographic keys
199:entropy extraction
36:
2171:"Tube type 6D4",
2068:978-3-319-72596-3
1985:978-3-319-10682-3
1945:978-1-5386-3428-8
1913:978-0-387-71816-3
1886:978-0-387-71816-3
1810:978-1-78588-587-7
1756:978-3-642-04137-2
1722:, pp. 25–27.
1720:Turan et al. 2018
1708:Turan et al. 2018
1625:, pp. 27–28.
1613:, pp. 24–25.
1601:, pp. 23–24.
1589:, pp. 21–22.
1577:, pp. 20–21.
1529:, pp. 13–14.
1517:, pp. 10–13.
1423:978-0-471-11709-4
1185:Turan et al. 2018
1144:978-3-319-72596-3
934:Turan et al. 2018
807:
806:
799:
781:
513:radiation sources
485:Quantum-based RNG
380:electrical noise;
131:atmospheric noise
70:is a device that
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2187:RAND Corporation
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2175:, Sylvania, 1957
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1387:Monograph report
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952:
946:
937:
931:
802:
795:
791:
788:
782:
780:
739:
715:
707:
658:Performance test
627:Raman scattering
521:radiation safety
517:analog computers
474:ring oscillators
389:quantum effects.
314:Douglas Aircraft
309:RAND Corporation
259:backward secrecy
76:physical process
21:
2396:
2395:
2391:
2390:
2389:
2387:
2386:
2385:
2361:
2360:
2355:ProtegoST SG100
2349:, 22 April 1999
2342:
2336:
2333:
2328:
2304:
2295:. BCP 106.
2278:
2271:
2269:
2265:
2258:
2252:
2245:
2243:
2206:Galton, Francis
2204:
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2007:(APS): 015004.
1992:
1986:
1967:
1960:
1946:
1927:
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1854:cite conference
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1281:(1070): 13–14.
1270:
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1111:
1063:
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1058:
1002:
1001:
997:
989:
985:
977:
970:
962:
955:
947:
940:
932:
921:
917:
899:Lottery machine
864:
851:
845:
830:certain attacks
826:
820:
803:
792:
786:
783:
740:
738:
728:
716:
705:
660:
511:and calibrated
509:Geiger counters
487:
470:
452:
450:Chaos-based RNG
400:noise generator
396:
344:
275:
253:forward secrecy
238:data encryption
234:
225:
219:
211:Common Criteria
127:Brownian motion
28:
23:
22:
15:
12:
11:
5:
2394:
2392:
2384:
2383:
2378:
2373:
2363:
2362:
2359:
2358:
2352:
2332:
2331:External links
2329:
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2250:
2220:(1070): 13–4,
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1492:
1477:
1475:, p. 286.
1465:
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1453:
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983:
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953:
949:Schindler 2009
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911:
906:
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822:Main article:
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787:September 2023
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541:quantum optics
538:
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469:
466:
451:
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440:
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427:
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402:is fed into a
395:
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363:
356:system-on-chip
352:
343:
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294:Francis Galton
274:
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262:
256:
233:
230:
218:
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191:
190:
184:
173:
137:, involving a
86:), unlike the
84:entropy source
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
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2284:
2283:
2277:
2268:on 2018-03-01
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2056:
2052:
2051:Springer Cham
2048:
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2028:
2024:
2020:
2015:
2010:
2006:
2002:
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1973:
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1965:
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1607:
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1600:
1595:
1592:
1588:
1583:
1580:
1576:
1571:
1568:
1565:, p. 20.
1564:
1559:
1556:
1553:, p. 17.
1552:
1547:
1544:
1541:, p. 15.
1540:
1535:
1532:
1528:
1523:
1520:
1516:
1511:
1508:
1504:
1499:
1497:
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1482:
1478:
1474:
1469:
1466:
1462:
1457:
1454:
1450:
1445:
1442:
1439:, p. 57.
1438:
1433:
1430:
1425:
1419:
1415:
1408:
1405:
1393:
1389:
1388:
1381:
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1347:
1346:
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1302:
1297:
1292:
1288:
1284:
1280:
1276:
1269:
1262:
1259:
1255:
1254:L'Ecuyer 2017
1250:
1248:
1246:
1244:
1242:
1238:
1234:
1229:
1226:
1222:
1217:
1214:
1211:, p. 90.
1210:
1205:
1202:
1198:
1193:
1190:
1186:
1181:
1178:
1174:
1169:
1167:
1163:
1159:
1154:
1151:
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1140:
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1132:
1128:
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1120:
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1110:
1104:
1099:
1095:
1091:
1086:
1081:
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1073:
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1067:
1060:
1057:
1052:
1048:
1043:
1038:
1033:
1028:
1024:
1020:
1016:
1012:
1011:
1006:
999:
996:
992:
987:
984:
981:, p. 56.
980:
975:
973:
969:
965:
960:
958:
954:
950:
945:
943:
939:
936:, p. 64.
935:
930:
928:
926:
924:
920:
914:
910:
907:
905:
902:
900:
897:
895:
892:
889:
886:
884:
881:
879:
876:
874:
871:
869:
866:
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859:
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850:
842:
840:
838:
833:
831:
825:
817:
815:
811:
801:
798:
790:
779:
776:
772:
769:
765:
762:
758:
755:
751:
748: –
747:
743:
742:Find sources:
736:
732:
726:
725:
720:This section
718:
714:
709:
708:
702:
697:
693:
690:
687:
684:
683:
682:
680:
675:
673:
669:
666:
657:
655:
651:
643:
639:
637:
633:
630:
628:
624:
621:
617:
614:
611:
607:
603:
599:
596:
593:
589:
585:
583:
579:
576:
573:
570:
566:
563:
560:
556:
552:
548:
545:
544:
542:
539:
536:
535:thermal noise
532:
529:
526:
522:
518:
514:
510:
506:
505:nuclear decay
503:
502:
501:
498:
496:
492:
484:
482:
479:
475:
467:
465:
462:
458:
449:
444:
441:
438:
435:
432:
431:
430:
424:
421:
418:
415:
412:
409:
408:
407:
405:
401:
393:
388:
385:
382:
379:
378:
377:
371:
368:
364:
361:
357:
353:
350:
349:
348:
341:
339:
336:
334:
330:
329:
324:
323:punched cards
319:
315:
310:
305:
301:
299:
295:
290:
288:
284:
280:
272:
270:
268:
260:
257:
254:
251:
250:
249:
247:
243:
239:
231:
229:
224:
216:
214:
212:
208:
204:
200:
196:
188:
185:
182:
178:
174:
171:
167:
163:
159:
158:
157:
155:
150:
148:
147:nuclear decay
144:
140:
139:beam splitter
136:
132:
128:
124:
123:metastability
120:
116:
112:
108:
104:
99:
97:
93:
89:
85:
81:
77:
73:
69:
65:
61:
57:
53:
49:
45:
41:
32:
19:
2371:Cryptography
2338:
2318:
2281:
2270:, retrieved
2263:the original
2254:
2244:, retrieved
2217:
2213:
2195:, retrieved
2181:
2172:
2162:, retrieved
2148:
2137:, retrieved
2123:
2085:
2081:
2046:
2000:
1994:
1963:
1923:
1895:
1868:
1843:. Retrieved
1826:
1814:. Retrieved
1799:
1734:
1727:
1715:
1703:
1698:, p. 9.
1691:
1686:, p. 4.
1679:
1644:
1640:
1630:
1618:
1606:
1594:
1582:
1570:
1558:
1546:
1534:
1522:
1510:
1505:, p. 2.
1468:
1456:
1444:
1432:
1413:
1407:
1396:, retrieved
1386:
1380:
1371:
1365:
1354:, retrieved
1344:
1337:
1328:
1316:. Retrieved
1278:
1274:
1261:
1235:, p. 7.
1228:
1223:, p. 6.
1216:
1204:
1192:
1187:, p. 6.
1180:
1175:, p. 4.
1153:
1122:
1112:
1078:(1): 16021.
1075:
1069:
1059:
1017:(1): 16108.
1014:
1008:
998:
993:, p. 8.
986:
951:, p. 7.
852:
834:
827:
812:
808:
793:
784:
774:
767:
760:
753:
741:
729:Please help
724:verification
721:
691:
685:
678:
676:
661:
652:
649:
634:
625:
597:
592:vacuum state
586:use a laser
580:
574:
568:
564:
551:beamsplitter
546:
499:
494:
490:
488:
471:
453:
428:
397:
375:
345:
337:
326:
306:
302:
291:
287:ancient Rome
276:
264:
235:
232:Cryptography
226:
192:
187:health tests
186:
176:
169:
162:noise source
161:
154:full entropy
151:
100:
83:
67:
63:
59:
55:
51:
47:
43:
37:
2088:(12): 439.
878:/dev/random
602:phase noise
417:Zener noise
213:standards.
177:conditioner
2365:Categories
2272:2015-04-20
2246:2004-03-28
2197:2002-12-22
2164:2009-05-10
2152:, Papers,
2139:2009-05-10
2127:, papers,
2095:2203.00261
2014:1604.03304
1845:2023-09-09
1816:2023-08-07
1437:Sunar 2009
1398:2009-01-29
1356:2009-05-10
1209:Templ 2016
1085:1510.08957
979:Sunar 2009
915:References
847:See also:
757:newspapers
629:generators
584:generators
531:shot noise
457:photodiode
404:comparator
367:amplifiers
221:See also:
2039:0034-6861
1954:1558-4305
1765:0302-9743
1671:2056-6387
668:Pub 140-2
640:uses the
638:generator
478:inverters
461:photonics
318:thyratron
170:digitizer
40:computing
2308:citation
2240:archived
2208:(1890),
2191:archived
2158:archived
2133:archived
2053:. 2020.
1392:archived
1350:archived
1309:Archived
1051:34373502
888:Lavarand
868:AN/CYZ-9
862:See also
703:Problems
600:use the
549:using a
321:deck of
279:gambling
141:, other
2222:Bibcode
2019:Bibcode
1775:Sources
1649:Bibcode
1305:4038609
1283:Bibcode
1090:Bibcode
1042:8352985
1019:Bibcode
855:entropy
818:Attacks
771:scholar
273:History
168:, so a
143:quantum
117:noise,
111:thermal
80:entropy
74:from a
2214:Nature
2065:
2037:
1982:
1952:
1942:
1910:
1883:
1807:
1763:
1753:
1669:
1420:
1318:14 May
1303:
1275:Nature
1141:
1049:
1039:
904:RDRAND
773:
766:
759:
752:
744:
386:chaos;
246:nonces
166:analog
119:jitter
66:), or
2347:Intel
2343:(PDF)
2266:(PDF)
2259:(PDF)
2090:arXiv
2009:arXiv
2003:(1).
1968:(PDF)
1928:(PDF)
1831:(PDF)
1739:(PDF)
1345:P-113
1312:(PDF)
1301:S2CID
1271:(PDF)
1080:arXiv
883:ERNIE
778:JSTOR
764:books
360:FPGAs
335:").
107:noise
2323:1750
2314:link
2300:4086
2063:ISBN
2035:ISSN
1980:ISBN
1950:ISSN
1940:ISBN
1908:ISBN
1881:ISBN
1860:link
1805:ISBN
1761:ISSN
1751:ISBN
1667:ISSN
1418:ISBN
1320:2014
1139:ISBN
1047:PMID
750:news
696:bias
672:NIST
670:and
665:FIPS
567:and
495:QRNG
283:Dice
244:and
217:Uses
209:and
195:seed
121:and
115:shot
113:and
94:and
64:NRBG
56:TRNG
48:HRNG
42:, a
2297:RFC
2287:doi
2230:doi
2100:doi
2055:doi
2027:doi
1972:doi
1932:doi
1900:doi
1873:doi
1835:doi
1784:doi
1743:doi
1657:doi
1291:doi
1131:doi
1098:doi
1037:PMC
1027:doi
733:by
58:),
50:),
38:In
2367::
2345:,
2310:}}
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2084:.
2080:.
2061:.
2033:.
2025:.
2017:.
2001:89
1999:.
1978:.
1948:.
1938:.
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1856:}}
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1759:.
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1665:.
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281:.
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175:a
160:a
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2029::
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2011::
1988:.
1974::
1956:.
1934::
1916:.
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1786::
1767:.
1745::
1710:.
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1659::
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