JP5586805B1 - Photon random number generator - Google Patents

Abstract

Provided is a technique capable of making it difficult to reduce the generation efficiency of random numbers even when light used for one trial can include a plurality of photons.
An optical path of light emitted from a light source is branched into n (where n ≧ 3) optical paths having almost the same probability that any photon contained in the light propagates. When it is detected that a photon has propagated through any one of the n optical paths, an n-ary random number value corresponding to the event is output. Further, among the n optical paths, r (where r is a natural number satisfying 1 <r <n satisfying _n C _r ≧ m × n, _where m is a natural number of 1 or more) is a photon. n but also when it is detected that propagated, its events, when belonging to a predetermined subset of the number of elements m × n in the entire set of events _n C _r as in this case, corresponding to the event Outputs a random number value.
[Selection] Figure 1

Description

  The present invention relates to a technique for generating a random number using photons, and particularly to a technique for generating a random number having a radix of 3 or more by utilizing the property of a photon as a Bose particle.

  In principle, it is possible to generate a binary random number sequence by making one photon incident on a beam splitter with a transmittance of 50% and repeating the trial to see if it is transmitted or reflected.

  In Patent Document 1, as an example of development of this binary random number generator, a light source that emits a photon and four optical paths that are substantially equal in the probability that the photon that is emitted from the light source is incident and the photon propagates through it. For each of the four optical paths constructed by this optical system, detection means that can detect whether or not a photon has propagated through the optical path, and photons propagated by this detection means There is disclosed a quaternary random number generator including output means for outputting a quaternary random number value corresponding to a detected optical path.

JP 2003-167729 A JP-T-2001-520839 JP 2005-250714 A

  Patent Document 1 assumes that the light source emits exactly one photon per trial, but it is still difficult to put such a single photon source into practical use.

  For example, it is practical to use a coherent light source as an alternative to a single photon source. However, since the photon number distribution of coherent light follows the Poisson distribution, even if the intensity is attenuated, the probability that the light used in one trial will include multiple photons such as two-photons and three-photons is set to zero. I can't.

  Therefore, when a coherent light source is used for the quaternary random number generator, for example, an event may occur in which photons propagate simultaneously through a plurality of optical paths among the four optical paths in one trial. However, in the method of Patent Document 1, such an event is ignored (see paragraphs 0013 and 0016 of Patent Document 1) and does not contribute to generation of random numbers.

  Japanese Patent Application Laid-Open No. H10-228707 also states that the phenomenon in which photons propagate simultaneously through a plurality of branched optical paths should not be used for generating a random number in consideration of emission of a plurality of photons from a light source.

  For this reason, the use of a coherent light source leads to a reduction in random number generation efficiency. If the coherent light is sufficiently attenuated, it is possible to suppress the probability that the light used for one trial includes a plurality of photons to a negligible level. The probability that the number of photons will be zero will increase, and eventually a decrease in random number generation efficiency is inevitable.

  In Patent Document 3, while using a light source capable of emitting a plurality of photons per trial, two binary random number generators are operated in parallel to alleviate the decrease in random number generation efficiency to some extent. . However, with this method, even if only one of the four configured optical paths is selected, only a binary random value can be output.

  An object of the present invention is to make it difficult to reduce random number generation efficiency even when light used for one trial can include a plurality of photons when generating a random number whose number is equal to the number of optical paths to be configured. Is to provide technology that can

According to one aspect of the present invention, a light source that emits light in a quantum state exhibiting a photon number distribution in which the probability that the number of photons per trial is 1 and the probability that it is plural is not zero, The optical system is configured by n (where n ≧ 3) optical paths that have the same probability of propagation of emitted light and the propagation of photons contained in the light, and the optical system. Further, for each of the n optical paths, a detecting means capable of detecting whether or not a photon has propagated through the optical path, and any one of the n optical paths is converted into a photon by the detecting means. Is detected, the n-ary random number value corresponding to the event is output, and r (where r is a natural number equal to or greater than 1) of the n optical paths, _n C satisfy _r ≧ m × n 1 <a natural number r <n.) of optical When even if a photon is detected to have propagated, its events, which belong to a predetermined subset of the number of elements m × n in the entire set of events _n C _r as in this case, corresponding to the event There is provided a photon random number generator comprising output means for outputting an n-ary random number value.

  In this specification, the set X being a subset of the set Y means that the set X is a true subset of the set Y or that the set X is equal to the set Y (X 集合 Y).

  Hereinafter, specific examples corresponding to the present invention will be exemplarily described.

in the case of n = 3, it can take a value of 2 for _r, since it is 3 _C 2 = 3, m is naturally determined 1. At this time, the subset is equal to the entire set, and any of the ₃ C _two kinds of events always belongs to the subset, contributing to the output of ternary random numbers.

When n = 4, the value of r can be at least one of 2 and 3, and ₄ C ₂ = 6 and ₄ C ₃ = 4. Therefore, when r is 2 or 3, m Is automatically set to 1. When r is 2, the subset is a subset of the total set or the subset advance how determined is arbitrary. At this time, when four predetermined events among the six events occur, it contributes to the output of a quaternary random number value. When r is 3, the subset is equal to the entire set, and any ₄ C ₃ events always belong to the subset, contributing to the output of quaternary random numbers.

When n = 5, the value of r can be at least one of 2, 3, and 4. _{Since 5} C ₂ = 10 and ₅ C ₃ = 10, when r is 2 or 3, m is naturally determined to be 1 or 2. It is preferable to take as large a value as possible for m. In other words, when r is 2 or 3, if the value of m is 2, the subset is equal to the entire set, and the occurrence of any of the 10 events can be output to output a quinary random number value. Can contribute. However, when r is 2 or 3, the value of m may be 1. In this case, the subset is a true subset of the entire set, and 5 predetermined patterns out of 10 events. When an event occurs, it contributes to the output of a quinary random number value. _{Since 5} C ₄ = 5, when r is 4, m is automatically determined to be 1. At this time, the subset is equal to the entire set, and all ₅ C ₄ events always belong to the subset. This contributes to the output of quinary random numbers.

In the present invention, when the output means detects that a photon has propagated through the r optical paths among the n optical paths by the detecting means, the event is all of the _n C _r events. when belonging to the complementary set other than the subset of the set, it is preferable to output a _{n C} r _-m × _n-ary random value corresponding to the event. In particular, _{n Cr} −m × n ≠ n may be satisfied.

For example, when n = 4, r = 2, and m = 1, the number of elements in the entire set is ₄ C ₂ = 6, and the number of elements in the subset is 1 × 4. ₄ C ₂ −1 × 4 = 2 ≠ 4. Since the relative appearance probabilities between these two events are substantially equal, they can be used to output binary random numbers.

  Not only the event in which one optical path is selected from among the n optical paths, but also the event in which r optical paths are selected can contribute to the generation of n-ary random numbers, thus reducing the random number generation efficiency. Can be difficult.

1 is a schematic diagram of a photon quaternary random number generator according to an embodiment. FIG. Schematic of a photon quinary random number generator according to an embodiment. 1 is a schematic diagram of a photon ternary random number generator according to an embodiment. FIG. FIG. 4 is a schematic diagram of a photon quaternary random number generator according to another embodiment.

  FIG. 1 shows a schematic diagram of a photon quaternary random number generator according to an embodiment.

  The light source 1 emits coherent light. Coherent light has a Poisson distribution in its photon number distribution. The light source 1 can be constituted by a semiconductor laser, for example.

  The optical attenuator 2 attenuates the intensity of the light emitted from the light source 1. The average number of photons per trial of the light attenuated by the optical attenuator 2 is, for example, 1/100 or more and less than 10.

  The light attenuated by the optical attenuator 2 enters the beam splitter 3. Photons transmitted through the beam splitter 3 enter the beam splitter 4, and photons reflected by the beam splitter 3 enter the beam splitter 5.

  The transmittances of the beam splitters 3 to 5 are all 50%. These beam splitters 3 to 5 constitute four optical paths having almost the same probability that any photon contained in the light emitted from the optical attenuator 2 propagates.

  In this specification, “substantially equal” means to include a case where they are strictly equal, and an ideal value (here, the transmittance / reflectance of the beam splitter) of the branching ratio by means for branching the optical path (here, the beam splitter). In this case, an inevitable error of about several percent from 50/50) is allowed.

  The light transmitted through the beam splitter 4 enters the photon detector A, and the light reflected by the beam splitter 4 enters the photon detector B. The light transmitted through the beam splitter 5 enters the photon detector C, and the light reflected by the beam splitter 5 enters the photon detector D.

  Each of the photon detectors A to D is composed of, for example, an avalanche photodiode, and outputs a detection signal when at least one photon is incident on itself. For each trial, it is detected whether a photon has propagated through each of the four optical paths formed by the beam splitters 3 to 5 depending on which of the photon detectors A to D outputs a detection signal. can do.

  A detection signal output from each of the photon detectors A to D is input to the interface 6. The interface 6 notifies the control device 7 of an event represented by the detection results of the photon detectors A to D for each trial.

  Table 1 shows an example of correspondence between events represented by detection results of the photon detectors A to D and quaternary random values.

  The control device 7 causes the interface 6 to output quaternary random number data RN corresponding to the event represented by the detection results of the photon detectors A to D in accordance with the correspondence relationship in Table 1. Note that this function of the control device 7 can be realized by hardware or software.

  Section (i) represents an event in which none of the photon detectors A to D output a detection signal. The control device 7 ignores such an event. In this case, no random number is output.

The section (ii) represents a set of events in which one of the photon detectors A to D outputs a detection signal. There are ₄ C ₁ = 4 such events, and the relative probability of occurrence among these 4 events is equal. Therefore, quaternary random values can be assigned to these events.

  Specifically, the control device 7 outputs a quaternary random value 0 when only the photon detector A outputs a detection signal, and a quaternary random value 1 when only the photon detector B outputs a detection signal. When only the photon detector C outputs a detection signal, a quaternary random value 2 is output, and when only the photon detector D outputs a detection signal, a quaternary random value 3 is output.

The section (iii) represents a set of events in which two of the photon detectors A to D output detection signals. There are ₄ C ₂ = 6 such events. ₄ C ₂ = 6 is not a multiple of radix 4, but ₄ C ₂ = 6> 4, and the relative appearance probability among these 6 events is equal. Therefore, if attention is paid to only a subset of the number of elements 4 out of the total set of these six events, a quaternary random number value can be assigned to them. Note that how to select a subset is arbitrary.

  In the present embodiment, events belonging to the two-element complement other than the subset are ignored. In Table 1, the random value column of events belonging to the complement is shaded.

  Specifically, the control device 7 outputs a quaternary random value 0 when the photon detectors A and C output detection signals, and outputs a quaternary disturbance when the photon detectors A and D output detection signals. The numerical value 1 is output. When the photon detectors B and C output detection signals, the quaternary random value 2 is output. When the photon detectors B and D output detection signals, the quaternary random value 3 is output. The event that the photon detectors A and B output the detection signal and the event that the photon detectors C and D output the detection signal are ignored.

The section (iv) represents a set of events in which three of the photon detectors A to D output detection signals. There are ₄ C ₃ = 4 such events, and the relative appearance probabilities between these 4 events are equal. Therefore, quaternary random values can be assigned to these events.

  Specifically, the control device 7 outputs a quaternary random number value 0 when the photon detectors A, B, and C output detection signals, and the photon detectors A, B, and D output detection signals. Causes quaternary random value 1 to be output, photon detectors A, C, and D output detection signals, quaternary random value 2 to be output, and photon detectors B, C, and D output detection signals Causes a quaternary random value 3 to be output.

  The section (v) represents an event in which all of the photon detectors A to D output detection signals. The control device 7 ignores such an event. In this case, no random number is output.

  In the present embodiment, one sampling by the photon detectors A to D corresponds to one trial. The light attenuated by the optical attenuator 2 can include a plurality of photons per trial, that is, per sampling period of the photon detectors A to D. However, not only the event in which one of the four optical paths is selected, but also the event in which two optical paths are selected and the event in which three optical paths are selected contribute to the generation of quaternary random numbers. Therefore, it is possible to make it difficult to reduce the random number generation efficiency.

  Consider that the quaternary random numbers 0 to 3 are each represented by 2 bits (two-digit binary number). For example, it may be associated with 0 → 00, 1 → 01, 2 → 10, 3 → 11. In this way, a quaternary random number sequence in which each quaternary random number value is represented by 2 bits can be regarded as a binary random number sequence. Assume that 16 events in Table 1 occur sequentially. According to the present embodiment, a quaternary random number value is output in each of 12 different events, so that a total of 24 bits are output.

  As a comparative example, in the random number generator of Patent Document 3, when the 16 events shown in Table 1 occur sequentially, only a total of 16 bits are output. From this, it can be seen that the present embodiment is superior to the technique of Patent Document 3 in terms of random number generation efficiency.

  Further, in the above embodiment, the events AB and CD in the section (iii) in Table 1 are ignored, but since the relative appearance probabilities between these two events are equal, binary random values can be assigned to these events. it can. For example, when the photon detectors A and B output a detection signal, the control device 7 outputs a binary random value 0, and when the photon detectors C and D output a detection signal, a binary random value 1 is output. When outputting, when the 16 events in Table 1 occur in sequence, a total of 26 bits are output. As a result, the random number generation efficiency can be further reduced.

  FIG. 2 is a schematic diagram of a photon quinary random number generator according to another embodiment.

  The coherent light emitted from the light source 8 is attenuated by the optical attenuator 9. The beam splitters 10 to 13 form five optical paths that have almost the same probability of propagation of photons contained in the attenuated light.

  Specifically, the transmittance of the beam splitter 10 is 2/5 (reflectance is 3/5), the transmittance of the beam splitter 11 is 1/2 (the reflectivity is also 1/2), and the transmittance of the beam splitter 12 is 1/3 (reflectance is 2/3) and the transmittance of the beam splitter 13 is 1/2 (reflectance is also 1/2).

  The photon detectors A to E can detect whether or not a photon has propagated through each of the five optical paths. A detection signal output from each of the photon detectors A to E is input to the interface 14.

  Table 2 shows an example of correspondence between events represented by detection results of the photon detectors A to E and quinary random numbers.

  The control device 15 causes the interface 14 to output the ternary random number data RN corresponding to the event represented by the detection results of the photon detectors A to E according to the correspondence relationship in Table 2.

  The category (i) represents an event in which none of the photon detectors A to E output a detection signal. Ignore such events.

The section (ii) represents a set of events in which one of the photon detectors A to E outputs a detection signal. There are ₅ C ₁ = 5 such events, and the relative probability of occurrence among these five events is equal. Therefore, quinary random values can be assigned to these events.

The section (iii) represents a set of events in which four of the photon detectors A to E output detection signals. There are ₅ C ₄ = 5 such events, and the relative probability of occurrence among these 4 events is equal. Therefore, quinary random values can be assigned to these events.

  The section (iv) represents an event in which all of the photon detectors A to E output detection signals. Ignore such events.

The section (v) represents a set of events in which two of the photon detectors A to E output detection signals. There are ₅ C ₂ = 10 such events. This is a multiple of radix 5 ( ₅ C ₂ = 5 × 2), and the relative appearance probabilities among these 10 events are equal. Therefore, among all the ten events, a quinary random number value can be assigned to a subset of 5 elements, and a quinary random value can also be assigned to a complement of the remaining 5 elements.

The section (vi) represents a set of events in which three of the photon detectors A to E output detection signals. There are ₅ C ₃ = 10 such events. This is a multiple of radix 5 ( ₅ C ₂ = 5 × 2), and the relative appearance probabilities among these 10 events are equal. Therefore, among all the ten events, a quinary random number value can be assigned to a subset of 5 elements, and a quinary random value can also be assigned to a complement of the remaining 5 elements.

  FIG. 3 is a schematic diagram of a photon ternary random number generator according to still another embodiment.

  The coherent light emitted from the light source 16 is attenuated by the optical attenuator 17. The beam splitters 18 and 19 form three optical paths that have almost the same probability of propagation of photons contained in the attenuated light.

  Specifically, the transmittance of the beam splitter 18 is 2/3 (reflectance is 1/3), and the transmittance of the beam splitter 19 is 1/2 (reflectance is also 1/2).

  The photon detectors A to C can detect whether or not a photon has propagated through each of the three optical paths. A detection signal output from each of the photon detectors A to C is input to the interface 20.

  Table 3 shows an example of correspondence between events represented by the detection results of the photon detectors A to C and ternary random values.

  The control device 21 causes the interface 20 to output ternary random number data RN corresponding to the event represented by the detection results of the photon detectors A to C in accordance with the correspondence relationship in Table 3.

  The section (i) represents an event in which none of the photon detectors A to C output a detection signal. Ignore such events.

The section (ii) represents a set of events in which one of the photon detectors A to C outputs a detection signal. There are ₃ C ₁ = 3 such events, and the relative probability of occurrence among these three events is equal. Therefore, ternary random values can be assigned to these events.

The section (iii) represents a set of events in which two of the photon detectors A to C output detection signals. There are ₃ C ₂ = 3 such events, and the relative probability of occurrence among these three events is equal. Therefore, ternary random values can be assigned to these events.

  The section (iv) represents an event in which all of the photon detectors A to C output detection signals. Ignore such events.

  FIG. 4 shows a schematic diagram of a photon quaternary random number generator according to another embodiment.

  The light source 22 emits pulse laser light, which is linearly polarized light, one after another in synchronization with the pulse timing signal given from the time measuring device 29. The light source 22 can be configured using, for example, a pulsed semiconductor laser.

  The optical attenuator 23 attenuates the intensity of the pulse laser beam. The average number of photons per pulse of the attenuated pulse laser beam is, for example, 1/100 or more and less than 10.

  Pulse laser light enters the polarization beam splitters 24 to 27. These polarization beam splitters 24 to 27 are arranged in such a direction that the linear polarization direction of the pulsed laser light is an oblique linear polarization direction in which P-polarized light and S-polarized light are superposed with equal weight on itself.

  For this reason, the probability that the photons contained in the pulsed laser light are transmitted through the polarization beam splitter 24 and reflected is equal to 50%. The P-polarized photon that has passed through the polarizing beam splitter 24 is also P-polarized with respect to the polarizing beam splitter 25, and thus passes through the polarizing beam splitter 25. The S-polarized photon reflected by the polarizing beam splitter 24 is also reflected by the polarizing beam splitter 25 because it is also S-polarized by the polarizing beam splitter 25.

  P-polarized photons transmitted through the polarizing beam splitter 25 or S-polarized photons reflected by the polarizing beam splitter 25 are incident on the quarter-wave plate QWP. The quarter-wave plate QWP is disposed with its own fast phase axis and slow axis tilted by 45 ° with respect to the P polarization direction and the S polarization direction. For this reason, the quarter wave plate QWP converts P-polarized light into clockwise circularly polarized light and converts S-polarized light into counterclockwise circularly polarized light.

  A clockwise circularly polarized photon or a counterclockwise circularly polarized photon is incident on the polarization beam splitter 26. Since both the right-handed circularly polarized light and the left-handed circularly polarized light contain the P-polarized light component and the S-polarized light component equally, the probability that the photon incident on the polarizing beam splitter 26 will be transmitted through the polarized beam splitter 26 and reflected will be equal. 50%.

  The P-polarized photon that has passed through the polarization beam splitter 26 is also P-polarized light with respect to the polarization beam splitter 27, and therefore passes through the polarization beam splitter 27. The photon reflected by the polarization beam splitter 26 is also S-polarized by the polarization beam splitter 27 and is reflected by the polarization beam splitter 27.

  Photons included in one pulse of the pulsed laser light emitted from the light source 22 are transmitted through the first optical path, the polarized beam splitters 24 and 25, which pass through all of the polarized beam splitters 24 to 27, and the polarized beam splitters 26 and 27. Any of the second optical path reflected by the polarizing beam splitters 24 and 25, the third optical path reflected by the polarizing beam splitters 26 and 27, and the fourth optical path reflected by all the polarizing beam splitters 24-27. Probability of propagating is almost equal. However, the optical path lengths of these four optical paths are different from each other.

  Photons emitted from the polarization beam splitter 27 are incident on the photon detector 28. The photon detector 28 is composed of, for example, an avalanche photodiode, and outputs a detection signal each time at least one photon is incident on itself.

  Data representing the relative time with respect to the time at which the pulse signal is given, at the time when the timing device 29 obtains the detection signal from the photon detector 28 every time the pulse timing signal is given to the light source 22. To the interface 30.

  Since the optical path lengths of the first to fourth optical paths are different from each other, the timing device 29 may acquire a detection signal from the photon detector 28 at each of four different relative times. Since the optical path and the relative time correspond to 1: 1, it is possible to detect which optical path is selected based on the relative time.

  If these four relative times are represented by A, B, C, and D, the control device 31 can cause the interface 30 to output a random number RN using the correspondence relationship in Table 1.

  It should be noted that the relative time interval is longer than the dead time of the photon detector 28, that is, the time from when a certain photon is detected until the next photon can be detected. The optical path length difference is set. The optical path length difference can be adjusted not only by the spatial distance but also by the refractive index.

  In this embodiment, emission of one pulse of pulsed laser light from the light source 22 corresponds to one trial. The light attenuated by the optical attenuator 2 can include a plurality of photons per trial, that is, per pulse. However, not only the event in which one of the four optical paths is selected, but also the event in which two optical paths are selected and the event in which three optical paths are selected contribute to the generation of quaternary random numbers. Therefore, it is possible to make it difficult to reduce the random number generation efficiency.

  As mentioned above, although this invention was demonstrated along the Example, this invention is not limited to this.

  In the above embodiment, a semiconductor laser is used as a light source. However, as a laser light source that emits laser light, for example, a solid-state laser such as a YAG laser or a titanium sapphire laser, a gas laser, or a quantum dot laser can be used. . Furthermore, the quantum state of the light emitted from the light source is not limited to the coherent state, and may be a pure state that is a superposition state of a plurality of photon states, a mixed state of a plurality of photon states, or a stochastic mixture thereof. May be. In short, it is only necessary that the light is in a quantum state showing a photon number distribution in which the probability that the number of photons per trial is 1 and the probability that they are plural are not zero. As the light source, for example, a light emitting diode, a halogen lamp, a discharge lamp, or other light sources that emit light in a heat state may be used. The light emitted from the light source may be CW light or pulsed light.

  In the above embodiment, an avalanche photodiode is used as the photon detector. However, the photon detector is not limited to a semiconductor, and for example, a photon detector using superconductivity, a photomultiplier tube, or the like can be used.

  In the above embodiment, a beam splitter or a polarization beam splitter is used for branching the optical path, but an optical fiber coupler may be used. Shielding means for preventing light from other than the light source and other electromagnetic waves from entering the photon detector may be used. The photon random number generator of the present invention can be miniaturized by realizing at least a part thereof as an optical integrated circuit. It will be apparent to those skilled in the art that various modifications, improvements, combinations, and the like can be made.

  The random number generator of the present invention can be used for, for example, simulation, numerical calculation, encryption, one-time password generation, game, and the like.

1 ... light source,
2 ... optical attenuator,
3-5 ... Beam splitter,
6 ... interface,
7 ... Control device,
8 ... light source,
9: Optical attenuator,
10-13 ... Beam splitter,
14 ... interface,
15 ... Control device,
16 ... light source,
17 ... optical attenuator,
18, 19 ... Beam splitter,
20 ... interface,
21 ... Control device,
22 ... Light source,
23. Optical attenuator,
24-27 ... Polarizing beam splitter,
28: Photon detector,
29 ... Timing device,
30 ... interface,
31 ... Control device,
QWP: 1/4 wavelength plate,
A, B, C, D, E: Photon detector.

Claims (3)

A light source that emits light in a quantum state exhibiting a photon number distribution such that the probability that the number of photons per trial is 1 and the probability that it is plural is not zero;
An optical system that constitutes n (where n ≧ 3) optical paths, in which light emitted from the light source is incident and the probability of propagation of photons contained in the light is substantially equal;
Detection means capable of detecting whether or not a photon has propagated through each of the n optical paths configured by the optical system;
When it is detected by the detection means that a photon has propagated through any one of the n optical paths, an n-ary random number value corresponding to the event is output, and the n optical paths Of these, r (where r is a natural number satisfying 1 <r <n satisfying _n C _r ≧ m × n, _where m is a natural number of 1 or more) is detected that a photon has propagated through one optical path. Even in this case, when the event belongs to a predetermined subset of the number of elements m × n in the entire set of _n C _r events in this case, an output that outputs an n-ary random number value corresponding to the event And a photon random number generator. When the output means detects that the photon has propagated through the r optical paths among the n optical paths by the detecting means, the event is the subset of the total set of the _n C _r events. 2. The photon random number generator according to claim 1, wherein, when belonging to a complementary set other than, outputs an _n C _r −m × n-ary random number value corresponding to the event.   A program for causing a computer to function as the output means in the photon random number detector according to claim 1.