Invented by Jane Elizabeth Nordholt, Richard John Hughes, Raymond Thorson Newell, Charles Glen Peterson, Triad National Security LLC
The Triad National Security LLC invention works as follows
Random Number Generators” include a thermal-optical source and detector configured for producing random numbers based upon quantum-optical intensity fluctuations. Signals proportional to the optical intensity and a delay optical intensity are then combined. The combined signals may be electrical or optical signals. The optical source must have low coherence within a specified range of delay time. To reduce common mode noise balanced optical detectors may be used. In some cases, optical flux can only be directed at one of two balanced detectors.
Background for Quantum random number generators
Many applications of computer systems need access to random numbers. Cryptography, gaming and statistical analysis are examples of typical applications. Random number generators are based on physical phenomena such as thermal noise from electronic components, radioactive decay and shot noise. Some RNGs use software to generate random numbers based on the timing of computer user movements. RNGs that are well-designed can generate long sequences of numbers. However, the numbers they produce are not statistically random and should be considered pseudo-random. When implemented into an integrated circuit, RNGs based on electrical circuits that use thermal or shot noise may require an excessive amount of wafer space. Alternative approaches to random number generators are required in view of this and the need for random numbers.
The present disclosure is aimed at quantum random numbers generators (QRNG). The QRNGs disclosed in some embodiments are capable of capturing the irreducible unpredictable nature of quantum physics, as manifested in the intensity fluctuations in thermal light. These fluctuations are due to the indistinguishability between photons and the elementary particles of the light. The present disclosure also relates to methods that allow a thermal source’s quantum randomness (entropy), to overpower any classical noise within the QRNG. This allows output random bit streams to not only pass statistical randomness tests but also to have unpredictability traceable back to the quantum properties. In one embodiment, the ‘basic’ QRNG is used. In some embodiments, a?basic? In other embodiments a full quantum entropy, cryptographic version of the QRNG that is compatible with cryptographic true random numbers generator design standards is disclosed. The cryptographic version may include self-testing and fail-safe functions. Both embodiments are capable of operating at high rates (many hundreds of Gbps), with low-cost production, small robust form factors and standard computer interfaces.
As used in the present application and the claims, singular forms are?a? ?an,? The plural forms?an?,? Include the plural form unless the context clearly dictates that it is not. Also, the word ‘includes’ is used. means ?comprises.? The term “coupled” is also used to describe items that are “comprising”. The term “coupled” does not exclude intermediate elements that are present between the items.
The systems, apparatus and methods described in this document should not be construed to be restrictive. The present disclosure is aimed at all novel, non-obvious aspects and features of the disclosed embodiments alone, and in different combinations. The disclosed systems and methods are not restricted to any particular aspect or feature, or any combination thereof. Nor do they require any one or more advantages or problems to be resolved. “Any theories of operation will be used to explain the systems and methods disclosed, but they are not limited by them.
While the operations of certain disclosed methods are described sequentially for convenience, it is important to understand that this description includes rearrangement unless specific language below requires a particular order. In some cases, sequential operations can be rearranged and performed simultaneously. For simplicity’s sake, the figures attached may not depict the many ways that the disclosed systems and methods can be combined with other systems and methods. The description also uses words like “produce” and “provide”. The description of the disclosed methods sometimes uses terms like?produce? To describe the disclosed methods. These terms are abstractions at a high level of the actual operations performed. These terms are high-level abstractions of the actual operations performed.
Random numbers are needed in cryptography to generate public keys using random algorithms. They can also be used as inputs for quantum key distribution systems. Random bits that meet the following criteria are required for cryptographic purposes:
The disclosed quantum random number generation (QRNGs), facilitates all three of these objectives. The QRNGs are based on the inherent unpredictability of quantum phenomena and the entropy they generate. They are particularly useful in adversarial cryptography, where no one can predict or manipulate quantum “noise.” The quantum RNGs have a distinct advantage over other RNGs which only produce pseudorandom. In this respect, the disclosed quantum RNGs are superior to other known RNGs that only produce?pseudorandom? value). These pseudorandom bitstreams can pass statistical tests to prove their randomness. However, they only have the entropy of the bits that were used to seed the pseudorandom RNG. They also exhibit a much lower entropy for each bit than true random bit sequences. One bit of entropy is present in a sequence of 1010 random bits seeded by a single random bit. The quantum RNGs, on the other hand, are true random number generation systems that generate random bitstreams using irreducibly unpredictable quantum phenomena. These bitstreams may have a high degree of entropy and, in certain embodiments, can show a bit per bit of entropy (i.e.?perfect? randomness). The QRNGs have the ability to produce a sequence of bits with 1010 bits full quantum entropy. This means that every bit in the sequence is unpredictable, even if the previous bits were examined. Other true random number generation systems use physical phenomena to generate entropy. However, these systems tend to be classically chaotic rather than inherently unpredictable. The apparent unpredictable nature of these systems is due to a lack in knowledge about the past state of the system and not a fundamental lack determinism. Quantum random number generators are the only ones that can be unpredictable.
The disclosed RNGs are capable of generating random numbers at high rates with full quantum entropy. The disclosed quantum RNGs are different from other methods and apparatus because they do not include noise or single-photon detectors. The disclosed QRNGs can generate random numbers up to 44 Gbps in some embodiments. Typical examples of QRNGs with large quantum noise to classical signal ratios are shown. In some cases, differential detection can be used to reduce or eliminate one of the largest sources of classical noise contamination of random numbers. The QRNGs disclosed herein are compact and easy to manufacture.
Below are descriptions of representative embodiments of random numbers generators. These embodiments use light sources to generate random numbers using the large quantum-optical fluctuations that are traceable to quantum physics, where photons behave as identical elementary particles and obey Bose Einstein statistics. This property can be used to create QRNGs. Examples include intensity fluctuations in thermal radiation, such as the black-body spectrum; photon bunching within temporal photon streams and “Hanbury Brown-Twiss” intensity fluctuations produced by combining optical intensity (proportional squared of an optical flux’s amplitude) or electrical signals.
Quantum mechanical effects can cause photons to bunch (intensity fluctuation) from a source of light. This is due to the fact that at the atomic scale, photons emitted by an atom or molecular emit a field of electromagnetic energy. This field becomes ‘high’ when it is high. In a certain optical mode, there is a quantum-mechanical increase in the probability that other emitters also emit in that mode. Photons with the same wavelength and coherence are called bosons. In a mode where there is already one photon, other photons are likely to want to join. More photons in a particular mode will increase the likelihood of more photons being emitted. This results in ‘bunches’. Photons are grouped together to cause fluctuations in the intensity of light sources.
The temporal profile (intensity fluctuations) of quantum mechanical bunching can be random. When photons are not able to remember between units of time, then the presence or absence of intensity fluctuations at one point in time will not influence the probability that an intensity variation will occur at another. Each unit of time is expressed by a “coherence” time. This coherence time can be approximated as the width of the wavelengths produced by the light source divided by the speed light. The random appearance of “bunches”? The random number generators disclosed can generate high-rate random numbers by exploiting the random appearance of?bunches?
The coherence time is the theoretical maximum speed that the random number generators disclosed can generate random numbers. The use of light sources with a larger number of photon modes will allow the random number generators disclosed to generate random bits at a faster pace, but it will also divide the photons generated by the source across a larger number of modes. In general, having a higher number of photons in each optical mode is advantageous to increase the amplitudes of “bunches”. Photons are grouped together to increase the amplitude of?bunches?
The QRNGs disclosed can use quantum-optical intensities based upon optical fluxes large enough to reduce noise effects at least in some cases, unlike randomness generated based on shot noise. Shot noise is more widely recognized because it involves random selections of single photons. Single-photon detectors tend to be slow and expensive. Because the noise-to-signal ratio of shot-noise is inversely related to the square of the number of average photons in the sample, using larger numbers of photos to generate random numbers is not a good idea. If there are 10,000 photons on average per sample, the quantum fluctuations will only be at 1%. This makes it difficult to reject interference from classical noise
However if you use quantum-optical intensity fluctuations, single-photon detectors are not necessary.” In the following examples, optical fluxes between 103 and 108 photons/ns can be convenient and around 106 photons/ns will usually work. Quantum-optical intensity fluctuations have a signal-to noise ratio that is dependent on the number modes. If the mode number remains constant, then the ratio is proportional with the number photons. It is possible to get large signals with a large signal-to noise ratio. As used in this document, optical fluxes are electromagnetic radiations that propagate at wavelengths between 100 nm and 10?m. Although other spectral bands can be used in addition to the ones mentioned above, optical detectors with electrical bandwidths at least of 10 MHz or 100 MHz and 1 GHz are more readily available. Electrical signals that correspond to optical fluxes are associated with voltages, currents or combinations of these produced by one or more photodetectors. These signals are also known as detector signals, and they are proportional with optical intensities. As used in this document, photodetector signal refers to signals that are produced or correspond to the so-called “square law”. detection.
Combining a photodetector response to optical intensity with a delayed version of that same photodetector (i.e. delayed to reduce or eliminate correlations), can improve the randomness of fluctuations. The coherence time (which is usually femtoseconds) of the optical source and the bandwidth (which may be 1-10 GHz) of the electronics can determine the time delay. The delayed signal will be independent from the undelayed one if the delay exceeds these timescales. The delay can be removed to remove undesirable features, such as power supply drifts which slowly alter the overall signal level and biases in electronic designs (e.g. more than 0 s). In the examples disclosed, delays between 10 ns to 10?s can be satisfactory. However, this depends on electronics and source properties. As shown below, these random fluctuations can also be used to generate random numbers. In some cases, it is preferable to avoid the generation of spectral characteristics by coupling optical fluxes from light sources into fibers or other optical components. Optical isolators can be used in some embodiments or with certain light sources. “For example, reflecting an optical flux toward a light source can introduce resonances which increase optical flux coherence that is undesirable for random number generation.
The use of thermal lights is not limited to one type. The term “thermal light source” is used in this context. The term ‘thermal light source’ or ‘thermal light, as used herein, refers to a light that has one or more optical field modes that are populated with photons according to a Bose-Einstein probability distribution of photon number (as opposed chaotic lighting which can have varying distributions). Refers to a light with one or more optical fields that are populated by photons in accordance with a Bose Einstein probability distribution (as compared to chaotic light, which can have a distribution normal of photon numbers). Examples of thermally-distributed optical sources include blackbody radiation from a hot filament (e.g. Incandescent light bulbs, light-emitting Diodes (LEDs), as well as suitable electrically-pumped and optically-pumped semiconductor optic amplifiers are examples of thermally-distributed optical sources.
An ideal source of optical light should possess certain properties.” Ideal optical light sources should have low optical intensity correlation. FIGS. Figures 16A-16D show the spectra of optical intensities for various sources. FIGS. The spectral characteristics of FIGS. 16C indicates that the source associated with it may have unsatisfactory properties of coherence and is unsuitable.
It can be beneficial to use a source of light that emits as many photons per optical mode as possible. It is important to control the number of modes in order to ensure that the bitstream generated has a high level of entropy due to quantum fluctuations. This is because quantum fluctuations are unpredictable and can’t be affected by an opponent. The only labels that are required or possible for light are its spatial, wavelength (spectral) and polarization mode, as well as the number of photons in each mode. Spatial modes are divided into two categories: longitudinal (also called ‘temporal’ modes) and transverse modes. Transverse modes and longitudinal modes are the two types of spatial modes. Transverse modes correspond to directions that are transverse to light propagation. When a thermal source has only one mode (both transverse and longitudinal), quantum fluctuations will affect 100% of its intensity. The thermal nature of light can be confirmed by measuring its second-order temporal coherence. This quantity is known as g(2) ( ) and it is the product of two optical intensities that are offset in time. See, for instance, R. Loudon ‘The Quantum Theory of Light’. 2nd. 2nd. Ed., OUP Oxford 1983. This correlation can be compared to the Hanbury Brown-Twiss correlations in the time domain. It has a value of 2 for thermal light with a single mode (g(2)(0)=2). If a thermal source has several modes (either transverse or longitudinal), each of which fluctuates independently, then any detector that detects the light from this source will see smaller fluctuations around an average. It is therefore advantageous to ensure that the photons are concentrated into as few optical modes possible.
The number of transverse modes can also be influenced by applying a spatial mode filter to the output of a light source, such as a single-mode optical fiber. This will screen out all photons other than those in screened out transverse modes (or filtered set of transverse modes). A spatial mode filter can be applied to the output of an optical fiber or other light source to reduce the number of transverse photons.
However, reducing the number or longitudinal and transverse optical modes by using a space filter to limit the transverse modes can also reduce the optical power of the light source. It can be more difficult to detect fluctuations when the optical power is reduced. This is particularly true when trying to detect high-speed fluctuations, since high-speed detectors require higher optical powers. It is necessary to make a compromise between maintaining high optical power and minimizing the optical modes in order to detect quantum fluctuations at high speeds. Quantum fluctuations are reduced to a small fraction of the fluctuations observed in an optical signal if photons have been spread across too many transverse or longitudinal modes. can dominate. The entropy of the bit stream that results from such a source is no longer dominated by ‘quantum? The origin of the entropy in the resulting bit stream produced from such a light source will no longer be dominantly?quantum? The ideal light source will therefore produce many photons, but in a small number of modes.
