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49-410: Many natural phenomena generate low-level, statistically random " noise " signals, including thermal and shot noise, jitter and metastability of electronic circuits, Brownian motion , and atmospheric noise . Researchers also used the photoelectric effect , involving a beam splitter , other quantum phenomena, and even the nuclear decay (due to practical considerations the latter, as well as

98-521: A comparator . 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: The drawbacks of using noise sources for an RNG design are: 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

147-461: A photodiode and sampled by a comparator. The design can be quite small, as all photonics 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 a limited subset of possible output strings. The TRNGs based on

196-484: A coin (thus producing a random bit) dates at least to the times of ancient Rome . The first documented use of a physical random number generator for scientific purposes was by Francis Galton (1890). He devised a way to sample a probability distribution 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). Kendall and Babington-Smith (1938) used

245-514: 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 tables were used for statistical experiments, like PRNG nowadays). On 29 April 1947, the RAND Corporation began generating random digits with an "electronic roulette wheel", consisting of

294-558: A free-running oscillator (FRO) typically utilize one or more ring oscillators (ROs), outputs of which are sampled using yet another oscillator. Since inverters 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. Quantum random number generation technology

343-449: A free-running oscillator-based TRNG can be attacked using a frequency injection . There are mathematical techniques for estimating the entropy 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

392-447: A given degree — very large sequences might contain many rows of a single digit. This might be "random" on the scale of the entire sequence, but in a smaller block it would not be "random" (it would not pass their tests), and would be useless for a number of statistical applications. As random number sets became more and more common, more tests, of increasing sophistication were used. Some modern tests plot random digits as points on

441-573: A globe. This logo was later adopted by McDonnell Douglas in 1967, and became the basis of Boeing 's current logo after their merger in 1997. Douglas Aircraft designed and built a wide variety of aircraft for the U.S. military, including the Navy, Army Air Forces, Marine Corps, Air Force, and Coast Guard. The company initially built torpedo bombers for the U.S. Navy, but it developed a number of different versions of these aircraft, including reconnaissance planes and airmail aircraft. Within five years,

490-638: A government-owned factory in Marietta, Georgia . World War II was a major boost for Douglas. Douglas ranked fifth among United States corporations in the value of wartime production contracts. The company produced almost 30,000 aircraft from 1942 to 1945, and its workforce swelled to 160,000. The company produced a number of aircraft including the C-47 Skytrain, the DB-7 (known as the A-20, Havoc or Boston),

539-513: 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 (" nothing up my sleeve numbers "). Since the early 1950s, research into TRNGs has been highly active, with thousands of research works published and about 2000 patents granted by 2017. A lot of different TRNG designs were proposed over time with

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588-400: A large variety of noise sources and digitization techniques ("harvesting"). However, practical considerations (size, power, cost, performance, robustness) dictate the following desirable traits: Stipčević & Koç in 2014 classified the physical phenomena used to implement TRNG into four groups: Noise-based RNGs generally follow the same outline: the source of a noise generator is fed into

637-424: A pattern is not thereby proved not statistically random. According to principles of Ramsey theory , sufficiently large objects must necessarily contain a given substructure (" complete disorder is impossible "). Legislation concerning gambling imposes certain standards of statistical randomness to slot machines . The first tests for random numbers were published by M.G. Kendall and Bernard Babington Smith in

686-416: A practical TRNG typically includes a few blocks: 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 " seed " for a faster PRNG. DRBG also helps with the noise source "anonymization" (whitening out the noise source identifying characteristics) and entropy extraction . With

735-584: A proper DRBG algorithm selected ( cryptographically secure pseudorandom number generator , CSPRNG), the combination can satisfy the requirements of Federal Information Processing Standards and Common Criteria standards. 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 science and statistical applications: impossibility to re-run

784-444: 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. Douglas Aircraft 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 thyratron tube, when placed in a magnetic field). Twenty of the 32 possible counter values were mapped onto

833-591: A sense that they can only operate in a fully controlled, trusted environment. 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 source degradation due to natural causes and deliberate attacks. FIPS Pub 140-2 and NIST Special Publication 800-90B define tests which can be used for this. The minimal set of real-time tests mandated by

882-411: 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. The major use for hardware random number generators

931-584: A three-dimensional plane, which can then be rotated to look for hidden patterns. In 1995, the statistician George Marsaglia created a set of tests known as the diehard tests , which he distributes with a CD-ROM of 5 billion pseudorandom numbers. In 2015, Yongge Wang distributed a Java software package for statistically distance based randomness testing. Pseudorandom number generators require tests as exclusive verifications for their "randomness," as they are decidedly not produced by "truly random" processes, but rather by deterministic algorithms. Over

980-514: A true random source and a pseudorandom generator. This problem is avoided by the conservative use of hardware entropy sources. Statistically random A numeric sequence is said to be statistically random when it contains no recognizable patterns or regularities; sequences such as the results of an ideal dice roll or the digits of π exhibit statistical randomness. Statistical randomness does not necessarily imply "true" randomness , i.e., objective unpredictability . Pseudorandomness

1029-529: A wholly owned subsidiary of McDonnell Douglas, with Douglas' son, Donald Wills Douglas Jr. , as president. Later, former McDonnell president David S. Lewis became chairman of Douglas Aircraft. His successful turnaround of the division allowed him to become president of McDonnell Douglas in 1969. Meanwhile, Douglas' space and missiles division became part of a new subsidiary called McDonnell Douglas Astronautics Company. McDonnell Douglas later merged with its rival Boeing in 1997. Boeing merged Douglas Aircraft into

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1078-608: Is in the field of data encryption , for example to create random cryptographic keys and nonces needed to encrypt and sign data. In addition to randomness, there are at least two additional requirements imposed by the cryptographic applications: A typical way to fulfill these requirements is to use a TRNG to seed a cryptographically secure pseudorandom number generator . Physical devices were used to generate random numbers for thousands of years, primarily for gambling . Dice in particular have been known for more than 5000 years (found on locations in modern Iraq and Iran), and flipping

1127-562: Is probable there would be long sequences of nothing but repeating numbers, though on the whole the sequence might be random. Local randomness refers to the idea that there can be minimum sequence lengths in which random distributions are approximated. Long stretches of the same numbers, even those generated by "truly" random processes, would diminish the "local randomness" of a sample (it might only be locally random for sequences of 10,000 numbers; taking sequences of less than 1,000 might not appear random at all, for example). A sequence exhibiting

1176-433: Is sufficient for many uses, such as statistics, hence the name statistical randomness. Global randomness and local randomness are different. Most philosophical conceptions of randomness are global—because they are based on the idea that "in the long run" a sequence looks truly random, even if certain sub-sequences would not look random. In a "truly" random sequence of numbers of sufficient length, for example, it

1225-501: Is well established with 8 commercial quantum random number generator ( QRNG ) products offered before 2017. Herrero-Collantes & Garcia-Escartin list the following stochastic processes as "quantum": To reduce costs and increase robustness of quantum random number generators, online services have been implemented. 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

1274-612: The Journal of the Royal Statistical Society in 1938. They were built on statistical tools such as Pearson's chi-squared test that were developed to distinguish whether experimental phenomena matched their theoretical probabilities. Pearson developed his test originally by showing that a number of dice experiments by W.F.R. Weldon did not display "random" behavior. Kendall and Smith's original four tests were hypothesis tests , which took as their null hypothesis

1323-852: The Boeing Commercial Airplanes division, and retired the Douglas Aircraft name after 76 years. The last Long Beach -built commercial aircraft, the Boeing 717 (third generation version of the Douglas DC-9), ceased production in May 2006. By 2011, the Boeing C-17 Globemaster III was the last aircraft being assembled at the Long Beach facility; the final C-17 was assembled in late 2015. However,

1372-478: The Douglas DC-2 , followed by the famous DC-3 in 1936. The wide range of aircraft produced by Douglas included airliners , light and medium bombers , fighter aircraft , transports, reconnaissance aircraft, and experimental aircraft. The company is most famous for the "DC" (Douglas Commercial) series of commercial aircraft, including what is often regarded as the most significant transport aircraft ever made:

1421-779: The Douglas DC-3 , which was also produced as a military transport known as the C-47 Skytrain or "Dakota" in British service. Many Douglas aircraft have long service lives. During World War II , Douglas joined the BVD ( Boeing - Vega -Douglas) consortium to produce the B-17 Flying Fortress . After the war, Douglas built another Boeing design under license, the B-47 Stratojet turbojet -powered bomber, using

1470-610: The SBD Dauntless dive bomber , and the A-26 Invader . Douglas Aircraft suffered cutbacks at the end of the war, with an end to government aircraft orders and a surplus of aircraft. It was necessary to cut heavily into its workforce, letting go of nearly 100,000 workers. The United States Army Air Forces established 'Project RAND' (Research ANd Development) with the objective of looking into long-range planning of future weapons. In March 1946, Douglas Aircraft Company

1519-625: The U.S. Navy . The DTs were taken from the assembly lines at the company's manufacturing plants in Rock Island, Illinois , and Dayton, Ohio , to be modified. The modified aircraft known as the Douglas World Cruiser (DWC), also was the first major project for Jack Northrop who designed the fuel system for the series. After the prototype was delivered in November 1923, upon the successful completion of tests on 19 November,

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1568-504: 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 deck of punched cards , but was later published in 1955 as a book, 50 rows of 50 digits on each page ( A Million Random Digits with 100,000 Normal Deviates ). The RAND table was a significant breakthrough in delivering random numbers because such

1617-620: The 1950s. Douglas moved from producing air-to-air rockets and missiles to entire missile systems under the 1956 Nike missile program and became the main contractor for the Skybolt air-launched ballistic missile program and the Thor ballistic missile program. Douglas also earned contracts from NASA, most notably for designing the S-IVB stage of the Saturn IB and Saturn V rockets. In 1967,

1666-652: The Army commissioned Douglas to build four production series aircraft. Due to the demanding expedition ahead, spare parts, including 15 extra Liberty L-12 engines, 14 extra sets of pontoons, and enough replacement airframe parts for two more aircraft were chosen. These were sent to airports along the route. The last of these aircraft was delivered to the U.S. Army on March 11, 1924. The four aircraft left Seattle , Washington, on April 6, 1924, flying west, and two of these returned there on 28 September to great acclaim, while one plane had been lost under fog conditions, and another

1715-652: The Davis-Douglas Company. An early claim to fame was the first circumnavigation of the world by air in Douglas airplanes in 1924. In 1923, the U.S. Army Air Service was interested in carrying out a mission to circumnavigate the Earth for the first time by aircraft , a program called "World Flight". Donald Douglas proposed a modified Douglas DT to meet the Army's needs. The two-place, open cockpit DT biplane torpedo bomber had previously been produced for

1764-419: 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. A hardware random number generator is expected to output near-perfect random numbers (" full entropy "). A physical process usually does not have this property, and

1813-517: The certification bodies is not large; for example, NIST in SP 800-90B requires just two continuous health tests : Just as with other components of a cryptography system, a cryptographic random number generator should be designed to resist certain attacks . Defending against these attacks is difficult without a hardware entropy source. The physical processes in HRNG introduce new attack surfaces. For example,

1862-489: The company was building about 100 aircraft annually. Among the early employees at Douglas were Ed Heinemann , "Dutch" Kindelberger , Carl Cover , and Jack Northrop , who later founded the Northrop Corporation . The company retained its military market and expanded into amphibian airplanes in the late 1920s, also moving its facilities to Clover Field at Santa Monica, California . The Santa Monica complex

1911-569: The company was struggling to expand production to meet demand for DC-8 and DC-9 airliners and the A-4 Skyhawk military attack aircraft. The company was also struggling with quality and cash flow problems and DC-10 development costs, as well as shortages due to the Vietnam War . Under the circumstances, Douglas was very receptive to an offer from McDonnell Aircraft Corporation . On April 28, 1967, after almost four years of merger talks,

1960-541: The history of random number generation, many sources of numbers thought to appear "random" under testing have later been discovered to be very non-random when subjected to certain types of tests. The notion of quasi-random numbers was developed to circumvent some of these problems, though pseudorandom number generators are still extensively used in many applications (even ones known to be extremely "non-random"), as they are "good enough" for most applications. Other tests: Douglas Aircraft The Douglas Aircraft Company

2009-518: The idea that each number in a given random sequence had an equal chance of occurring, and that various other patterns in the data should be also distributed equiprobably. If a given sequence was able to pass all of these tests within a given degree of significance (generally 5%), then it was judged to be, in their words "locally random". Kendall and Smith differentiated "local randomness" from "true randomness" in that many sequences generated with truly random methods might not display "local randomness" to

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2058-472: The more "jet age" style F4D Skyray in 1951. Douglas also made commercial jets, producing the Douglas DC-8 in 1958 to compete with the new Boeing 707 . Douglas was a pioneer in related fields, such as ejection seats , air-to-air missiles , surface-to-air missiles , and air-to-surface missiles , launch rockets, bombs, and bomb racks. The company was ready to enter the new missile business during

2107-626: The motto "First Around the World – First the World Around". Douglas initially used a logo that combined two letter Ds with two wings extended outwards, and two Ds placed back to back to form a heart as a reference to the Clan Douglas . After the success of the DWC, the company adopted a logo that showed three airplanes circling a globe. The logo eventually evolved into an aircraft, a missile, and

2156-403: The two companies merged as McDonnell Douglas Corporation . The two companies seemed to be a good match for each other. McDonnell was a major defense contractor, but had almost no civilian business. Douglas' commercial contracts would allow McDonnell to withstand any downturns in procurement. Conversely, McDonnell had enough revenue to help solve Douglas' financial problems; soon after the merger

2205-630: Was an American aerospace and defense company based in Southern California . Founded in 1921 by Donald Wills Douglas Sr. , it merged with McDonnell Aircraft in 1967 to form McDonnell Douglas , where it operated as a division. McDonnell Douglas merged with Boeing in 1997. The company was founded as the Douglas Company by Donald Wills Douglas Sr. on July 22, 1921, in Santa Monica, California , following dissolution of

2254-460: Was announced, McDonnell bought 1.5 million shares of Douglas stock to help Douglas meet "immediate financial requirements". The merged company was based at McDonnell's facility in St. Louis, Missouri . It adopted a modified version of Douglas' logo. Donald Wills Douglas Sr. became honorary chairman of the merged company, a post he would hold until his death in 1981. Douglas Aircraft Company continued as

2303-670: Was forced down over the Atlantic and sank (the DWC prototype was then rechristened, and joined the other two in completing the North American leg of the flight). After the success of this flight, the Army Air Service ordered six similar aircraft as observation aircraft. The success of the DWC established the Douglas Aircraft Company among the major aircraft companies of the world and led it to adopt

2352-495: Was granted the contract to research on intercontinental warfare. Project RAND later become the RAND Corporation . Douglas continued to develop new aircraft, including the successful four-engined Douglas DC-6 (1946) and its last propeller-driven commercial aircraft, the Douglas DC-7 (1953). The company had moved into jet propulsion, producing its first for the U.S. Navy — the straight-winged F3D Skyknight in 1948 and then

2401-430: Was so large, the mail girls used roller skates to deliver the intracompany mail. By the end of World War II, Douglas had facilities at Santa Monica, El Segundo , Long Beach , and Torrance, California , Tulsa and Midwest City , Oklahoma, and Chicago, Illinois . On November 30, 1928, the company was reorganized as the Douglas Aircraft Company. In 1934, Douglas produced a commercial twin-engined transport plane ,

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