EP4073932A1

EP4073932A1 - Device for generating random numbers

Info

Publication number: EP4073932A1
Application number: EP20824432.7A
Authority: EP
Inventors: Gerhard Humer
Original assignee: AIT Austrian Institute of Technology GmbH
Current assignee: AIT Austrian Institute of Technology GmbH
Priority date: 2019-12-12
Filing date: 2020-12-09
Publication date: 2022-10-19
Also published as: AT523230B1; WO2021113887A1; AT523230A1

Abstract

The invention relates to a method for generating random numbers, wherein a) a source (1) emits energy, in particular in the form of pulses, with a specified distribution at non-predictable points in time, b) a detector (3) which is connected downstream of the source (1) detects the energy emitted by the source (1), in particular in the form of pulses, c) optionally energy emitted by the source (1) is suppressed or attenuated by an attenuator (2) located between the source (1) and the detector (3), and d) the duration between a specified starting time (t0) and the point in time at which a pulse is detected by the detector (3) is ascertained, wherein the result of the time measurement is used as a random number.

Description

Device for generating random numbers

The invention relates to a method and a device for generating random numbers according to patent claims 1 and 7, respectively.

Various methods for generating random numbers are known from the prior art, in which a signal is emitted by means of a generator, which signal is possibly weakened and detected by a receiver. If the receiver detects a relevant signal within a specified time range, the random number generator specifies a related value for this time range, otherwise the random number generator specifies a different value at its output. In this way it is possible to obtain a binary signal that has one of two values within individual time ranges. With such a procedure it is possible to generate a random data stream with one bit per time unit.

This procedure has the major disadvantage that just one bit of random data is generated for each time range. The object of the invention is therefore to generate a random signal based on the present arrangement, which generates a random signal with a higher data rate.

The invention solves this problem in a device of the type mentioned at the beginning with the characterizing features of claim 1.

In order to enable the random distribution to be set easily without the need for subsequent post-processing, it can be provided

- e) that the temporal course of at least one of the following manipulated variables is determined to be variable during the period:

- the distribution of the energy emitted by the source, and / or

- the efficiency of the detector, and / or

- the attenuation caused by the attenuator, and

- f) that the temporal course of the manipulated variable starting from the start time is specified in such a way,

- That the random distribution of the determined time spans corresponds to a predetermined random distribution, and / or

- that in any case a pulse is detected within a predetermined time range. In order to obtain a data signal based on regular intervals or at a constant clock rate, provision can be made for the time measurement to be reset after a predetermined time interval has elapsed and for steps a) to d), in particular a) to f), starting with a further one Start time to be repeated,

- wherein the time interval corresponds in particular to the maximum time span within which a pulse is present in any case, or is greater than this maximum time span.

To further increase the data rate of the random signal, it can be provided that the time measurement is reset immediately after the occurrence of a pulse or at a predetermined time interval from the occurrence of the pulse and steps a) to d), in particular a) to f), starting with repeated at another start time.

It can particularly advantageously be provided that a uniform distribution or Gaussian distribution is specified as the distribution.

The invention also relates to a device for generating random numbers. According to the invention, the following is provided:

- a source that emits energy, in particular in the form of pulses, at unpredictable times with a predetermined distribution,

- a detector which is connected after the source and is designed to detect the energy in the form of pulses,

if necessary, an attenuator located between the source and the detector to suppress the energy or pulses emitted by the source, and

- A time measuring device for determining the time span between a predetermined starting time and the time when a pulse is detected by the detector.

A particularly simple setting of the random distribution can be ensured if

- A control unit is provided which is designed to control the distribution of the energy emitted by the source as a manipulated variable, and / or to specify the efficiency of the detector as a manipulated variable, and / or, if necessary, to specify the attenuation caused by the attenuator as a manipulated variable, the control unit, which changes the temporal course of the manipulated variable starting from the start time in such a way that the random distribution of the determined time spans corresponds to a predetermined random distribution and / or that a pulse is detected within a predetermined time range, and

- the result that is available to the time measurement as a random number.

A data signal based on regular intervals or with a constant clock rate can advantageously be provided if a control unit is provided which is designed to

- to reset the time measuring device after a specified time interval has elapsed and to set a new starting time for a further determination of a random number,

- wherein the time interval corresponds in particular to the maximum time span within which a pulse is present in any case, or is greater than this maximum time span, and

- by resetting the time measuring device, to cause the control unit again to specify a time profile of the manipulated variable.

The data rate of the random signal can be increased further if a control unit is provided which is designed to

- the time measuring device to set a new starting time for a further determination of a random number immediately after the occurrence of a pulse or at a predetermined time interval from the occurrence of the pulse, and

- With the resetting of the time measuring device, the control unit again controls the temporal course of the manipulated variable starting from the start time in such a way that the random distribution of the determined time spans corresponds to a predetermined random distribution and / or that a pulse is detected within a predetermined time range.

A particularly advantageous device according to the invention in which photons are used to generate random numbers can be provided if

- The source is formed by a laser, the

- An attenuator in the form of a Mach-Zehnder interferometer is connected downstream, and that in turn

- A detector in the form of an optical single photon detector is connected downstream. A particularly advantageous device according to the invention in which a noise signal is used to generate random numbers can be provided if

- the source creates an electrical noise signal, and

- an electronic detector is provided as the detector, which detects a pulse when the electrical noise signal exceeds a predetermined threshold value,

- The manipulated variable is specified by amplifying or weakening the noise signal and by changing the threshold value for the noise signal.

It can particularly advantageously be provided that a manipulated variable is selected by the control unit in such a way that a uniform distribution or a Gaussian distribution results as a random distribution.

Further advantages and embodiments of the invention emerge from the description and the accompanying drawings.

Particularly advantageous, but not limiting, exemplary embodiments of the invention are shown schematically below with reference to the accompanying drawings and are described by way of example with reference to the drawings.

A first embodiment of the invention is shown in more detail in FIG. This embodiment comprises a source 1 in the form of a photon source or a laser. The source 1 emits pulses, in the present case single photons, with a predetermined distribution at unpredictable times.

As an alternative to a laser, it is also possible, for example, to use radioactive sources, sources for quantum fluctuations based on the tunnel effect, a quantum mechanical nondeterministic effect. Alternatively, it is also possible to use electrical noise sources.

1 also shows an attenuator which is connected downstream of the source 1 and is designed to partially suppress or attenuate the pulses or signals emitted by the source 1. In the present case, the attenuator 2 is a Mach-Zehnder interferometer which, due to electro-optical effects, is designed to transmit the laser light emitted by the source 1 to one of two outputs, so that the light emitted at one of the both Outputs of the attenuator 2 is present, has only a predetermined proportion of the total light from the light source. Alternatively, of course, if other sources are used, electrical attenuators or radioactive shielding materials can be used.

The output of the attenuator 2 is followed by a detector 3 which is designed to detect the pulses generated by the source 1 and attenuated by the attenuator 2. In the present exemplary embodiment, this is a single photon detector. Depending on the type of source and attenuator, however, other detectors can also be used which are designed to detect the pulses which are based on correspondingly different physical phenomena. These are, for example, detectors for radioactive decay or electrical or electronic detectors.

In principle, it is not necessary for a device according to the invention to contain an attenuator 2. Rather, it is also possible for the detector 3 to be connected immediately after the source 1.

Furthermore, the embodiment of the invention shown in FIG. 1 shows a time measuring device 5 which is designed to determine the time span between a predetermined starting time T ₀ and time T _{P of} the detection of a pulse by the detector 3. In contrast to the random number generators known from the prior art, it is not the fact that a pulse was detected within a period of time that is used as a random number, but rather the result of the time measurement.

In order to now specify the random distribution of the determined time periods, for example to achieve a uniform distribution of the time periods, a control unit 4 is provided which is designed to control the source 1, the detector 3 and the attenuator 2. The control unit 4 regulates the probability of the detection of a pulse in this way and can vary this over time. The control unit 4 specifies each of the partial manipulated variables for the source 1, the detector 3 and the attenuator 2. It is particularly advantageous that the individual effects of the partial manipulated variables l _ϋ , l ₃ , A _q , which are each caused by the source 1, the detector 3 and the attenuator 2, have a multiplicative effect on the overall manipulated variable l. _{The probability q of} the emission of pulses by the source 1 can be specified by the control unit 4 as the first sub-manipulated variable. When using a laser as source 1, this is typically done by specifying the laser current l _L , with a non-linear relationship _q = _q (l _L ). As shown in FIG. 4, the probability l _{h of} the emission of pulses, for example in the form of photons or energy, can be specified by the source by specifying a specific laser current. If the laser current I _L exceeds a predetermined threshold value I _th , the probability of the emission of pulses, photons or energy by the source 1 within a predetermined period of time depends approximately linearly on the increase in the laser current I _L.

The attenuation effect A of the optical attenuator 2 can be specified as the second manipulated variable. To control the optical attenuator 2, a voltage U _{A can be} specified with which a medium with a variable optical length located in a beam path of the Mach-Zehnder interferometer acting as attenuator 2 can be set accordingly. l ₃ = l ₃ (U _A )

The efficiency of the detector (FIG. 6), ie the probability that energy incident on the detector actually leads to a pulse at the output of the detector 3, can also be specified by the control unit 4. In a preferred embodiment of the invention, an avalanche diode located in the beam of the laser is used as the definition. Depending on the design, a bias voltage of 100 V, for example, which is above the breakdown voltage, is applied to the avalanche diode. However, a spontaneous breakdown does not occur until several milliseconds after the voltage has been applied; however, in the case of irradiation, a premature breakdown can be measured. The avalanche diode is operated in Geiger mode, whereby a single photon can trigger the breakdown of the avalanche diode. The higher the voltage U _D at the avalanche diode, the more likely it is that a photon will cause the entire diode to break down. The voltage U _D can be specified within a specified range [U _{D, min} ... U _{D, max} ], in particular a range of a few volts. A SAPD, ie a single photon avalanche photo diode, can preferably be used as the detection.

The detector efficiency QE, ie the probability that a breakthrough will occur due to a photon pulse, can thus be set by specifying a Detector voltage U _{D can be} varied so that the manipulated variable emanating from the detector depends on the detector voltage.

_{Overall, by specifying the laser current I L} and the two voltages U _A , U _D , the control unit 4 can specify the probability value that the pulse is present at the output of the detector 3 within a time segment. It is basically possible that the control unit 4 only regulates one manipulated variable from the set of manipulated variables l ^, l ₃ , l _f namely laser current weakening effect and detector efficiency QE, alternatively the control unit 4 can also control all three of these manipulated variables l ^, l ₃ , regulate and thus the probability that a pulse is applied to the detector within a predetermined time span can be varied. The more different manipulated variables are used, the greater the range of adjustable probabilities that a pulse will be applied to the detector 3 within a predetermined period of time.

In order to now specify a random distribution of the determined time periods, for example to achieve a uniform distribution of the time periods up to the occurrence of the first pulse at the output of the detector within a given time window, one of the following calculation rules can be used.

In the embodiment shown in Fig. 2, the goal is to produce a uniform distribution of the probability of the occurrence of a pulse at the output of the detector 3, the probability that a pulse at the output of the detector 3 within the first nanosecond after the beginning or The start time is 5%. Likewise, the aim is to ensure that the probability of a pulse at the detector output within every further nanosecond from the start time to the twentieth nanosecond is in each case 5%.

If one wants to achieve such a uniform distribution, the manipulated variable, which results as the product of the probability of the release of energy, the efficiency of the detector 3 and the attenuating effect of the attenuator, will have the function curve l (ΐ) shown in FIG. 2. In order to achieve the predetermined function curve, a value is selected in the first time segment Ti, ie within the first nanosecond, which is defined by l ^ Dί = Wi. The manipulated variable for the first nanosecond results according to Wi / At. In order to achieve that the probability of the occurrence of a pulse at the detector output in the second nanosecond again _{corresponds to w 2} = 5%, a manipulated variable li is selected as follows:

(1 -li ^* Dί) ^* l ₂ ^* Dί = w ₂

This means that when calculating the manipulated variable l ₂ during the second time interval, it is taken into account that an event did not already occur during the first nanosecond. The manipulated variable during the second nanosecond or during the second time segment results from conversion to l ₂ = W ₂ / At / (1-VAt).

If the fact that a corresponding detector event did not occur during the first two time intervals is taken into account for the third time interval, the following relationship results when determining the manipulated variable during the third time interval:

(1 -li ^* At) ^* (1 -l ₂ ^* Dί) ^* l ₃ ^* Dί = w ₃

Correspondingly, through transformation one obtains l ₃ = w ₃ / At / (1 -li ^* At) / (1 -l ₂ ^* Dί).

In the event that a uniform distribution is desired, i.e. Wi = w ₂ = w ₃ = ... = w _c , the manipulated variable during the third time interval can correspond to l ₃ = w _c / At / (1 -3 ^* At) be simplified.

In the general case, manipulated variable l _p can be determined for the further time intervals as follows:

[n _{i = i ... n} _i (1-l _ί ^* DI)] ^* l _p ^* Dί = w _n

Accordingly it results l _p = w _n / At / [Il _{i = 1 ... P-Ί} (1 -l _ί ^* Dΐ)].

If a uniform distribution of the probability is desired, _{the following value results for the manipulated variable l p} : lp = w / At / [1-n ^ ₀ ^* At]

In order to achieve in the present exemplary embodiment that a pulse occurs at the latest at the end of the predefined time period, in the present case after 20 nanoseconds, a very large manipulated variable is predefined during the last time interval. According to the given formula, if h ^* l ₀ ^* Dί results in exactly the value 1, a manipulated variable l _p that has a very large or infinite effect is obtained. In this case, the largest possible manipulated variable that can be output by the system should be used.

As already stated above, the present embodiment of the invention is in no way restricted to the specification of a uniform distribution. Rather, of course, there is also the possibility of specifying deviating distributions, for example a Gaussian distribution.

As shown in FIG. 3, the probability values, ie the probabilities that a pulse occurs for the first time in the last time segment T o, are determined by specifying deviating probability values w _1; ..., w _n given. The individual manipulated variables can also be specified in accordance with the formulas presented above.

In order to make available a large number of random numbers generated in the same way continuously, ie within a certain period of time, different procedures can be used in order to repeat the method described above.

In a particularly preferred embodiment of the invention, the specifications presented above are carried out at constant time intervals, ie each random number formation takes the same length of time. The control unit 4 in each case emits a reset pulse to the time measuring unit 5 and, if necessary, also to the detector 3 and sets the control values in accordance with the predetermined, previously numerically determined time curve. Even if the pulse has already occurred after one of the time intervals, a period of time is awaited which corresponds to the maximum duration up to or time span for the occurrence of a pulse; in the exemplary embodiment shown in FIG. 2, this takes 20 ns. The advantage of this procedure is that the random numbers occur regularly, ie it can be determined in advance how many random numbers occur in one second - in the present exemplary embodiment 50 million random numbers.

Alternatively, there is also the option of starting the reset immediately after the occurrence of a pulse, ie not waiting for the maximum duration or time span. In this case, the random numbers do not appear regularly; however, the occurrence of random numbers can in principle be determined on the basis of the given distribution. Basically, in order to have enough time to save the data, a minimum time for the generation of a random number or a minimum time interval until the time measuring device 5 is reset or a fixed waiting time between the occurrence of a pulse on the detector and the resetting of the time measuring device 5 can be specified become.

If the manipulated variables are kept constant over time, the result is a probability distribution of the times in the form of an exponential distribution. If such an exponential distribution is desired or post-processing of the

If probability values are made, the manipulated variables cannot be changed over time.

Claims

1. A method for generating random numbers, wherein a) a source (1) which emits energy, in particular in the form of pulses, at unpredictable times with a predetermined distribution, b) a detector (3) which the source (1) is connected downstream, and which detects the energy emitted by the source (1), in particular in the form of pulses, in the form of pulses, c) optionally emitted by the source (1) energy from an energy between the source (1) and the detector (3) located attenuator (2) is suppressed or weakened, d) the time span between a predetermined starting time (t ₀ ) and the time of the detection of a pulse by the detector (3) is determined, characterized in that the result of the time measurement is used as a random number.

2. The method according to claim 1, characterized in that e) that the time course of at least one of the following manipulated variables is set to be variable during the time period:

- The distribution of the energy emitted by the source (1), and / or

- the efficiency of the detector (3), and / or

- the attenuation caused by the attenuator (2), and f) that the temporal course of the manipulated variable starting from the start time (t ₀ ) is specified in such a way,

- That the random distribution (w) of the determined time spans corresponds to a predetermined random distribution, and / or

- That a pulse is detected within a predetermined time range (T _max ) in any case.

3. The method according to claim 1 or 2, characterized in that the time measurement is reset after a predetermined time interval has elapsed and steps a) to d), in particular a) to f), are repeated _{starting with a further starting time (t 0),}

- wherein the time interval corresponds in particular to the maximum time span (T _max ) within which a pulse is present in any case, or is greater than this maximum time span

(T max)

4. The method according to claim 1 or 2, characterized in that the time measurement is reset immediately after the occurrence of a pulse or at a predetermined time interval to the occurrence of the pulse and steps a) to d), in particular a) to f), beginning be repeated with a further start time (t ₀ ).

5. The method according to any one of claims 2 to 4, characterized in that the control unit (4) supplies a manipulated variable such that a uniform distribution results as a random distribution.

6. The method according to any one of claims 2 to 4, characterized in that the control unit (4) supplies a manipulated variable such that a Gaussian distribution results as a random distribution.

7. Apparatus for generating random numbers, comprising

- a source (1) which emits energy, in particular in the form of pulses, at unpredictable times with a predetermined distribution,

- a detector (3) which is connected downstream of the source and is designed to detect the energy in the form of pulses,

- optionally an attenuator (2) located between the source (1) and the detector (3) for suppressing the energy or pulses emitted by the source (1), and

- A time measuring device (5) for determining the time span between a predetermined starting time (t ₀ ) and the time when a pulse is detected by the detector (3).

8. Apparatus according to claim 7, characterized by

- A control unit (4) which is designed to control the distribution of the energy emitted by the source (1) as a manipulated variable, and / or to specify the efficiency of the detector (3) as a manipulated variable, and / or, if applicable, that of the attenuator (2) to specify the weakening effect as a manipulated variable,

- the control unit (4), which changes the temporal course of the manipulated variable starting from the start time in such a way that the random distribution of the determined time spans corresponds to a predetermined random distribution, and / or that in any case a pulse is detected within a predetermined time range, and

- the result that is available to the time measurement as a random number.

9. Apparatus according to claim 7 or 8, characterized in that a control unit (4) is provided which is designed to

- to reset the time measuring device (5) after a predetermined time interval (T _max ) has elapsed and to set a new starting time for a further determination of a random number,

- by resetting the timing device (5) to cause the control unit (4) again to specify a time profile of the manipulated variable.

10. The device according to claim 7 or 8, characterized in that a control unit (4) is provided which is designed to

_{- the time measuring device (5) to set a new starting time (t 0} ) for a further determination of a random number immediately after the occurrence of a pulse or at a predetermined time interval from the occurrence of the pulse, and

- With the resetting of the time measuring device (5), the control unit (4) again _{controls the temporal course of the manipulated variable starting from the start time (t 0} ) in such a way that the random distribution of the determined time spans corresponds to a predetermined random distribution, and / or that within a predetermined time range in any case a pulse is detected.

11. Device according to one of claims 7 to 10, characterized in that

- The source (1) is formed by a laser, the

- An attenuator (2) in the form of a Mach-Zehnder interferometer is connected downstream, and that in turn

- A detector (3) in the form of an optical single photon detector is connected downstream.

12. Device according to one of claims 7 to 11, characterized in that

- The source (1) creates an electrical noise signal, and - An electronic detector is provided as the detector (3) which detects a pulse when the electrical noise signal exceeds a predetermined threshold value,

13. Device according to one of the preceding claims 7 to 12, characterized in that a manipulated variable is selected by the control unit (4) such that a uniform distribution results as a random distribution.

14. Device according to one of the preceding claims 7 to 12, characterized in that a manipulated variable is selected by the control unit (4) such that a Gaussian distribution results as the random distribution.