阅读说明：本技术 用于生成随机比特样本的方法和系统 (Method and system for generating random bit samples ) 是由 伯特兰·鲁莱特 让-查尔斯·法纳夫 于 2018-12-21 设计创作，主要内容包括：生成随机比特样本的方法涉及量子隧穿势垒。该方法大体上具有：生成跨过所述量子隧穿势垒的电荷的电流,隧穿的电荷的电流具有由于量子隧穿波动而随机改变的瞬时电平并且形成原始信号；从所述原始信号中获取具有第一比特数目n的原始比特样本,所述第一比特数目n是整数；将所述原始比特样本中的随机性提取到随机比特样本中,所述随机比特样本具有小于所述第一比特数目n的第二比特数目m,所述提取是基于校准数据的,所述校准数据至少包括：所述原始比特样本中的所述量子隧穿波动的量子贡献值；和所述原始比特样本中的外部贡献值。(The method of generating random bit samples involves quantum tunneling barriers. The method generally has: generating a current of charge across the quantum tunneling barrier, the current of tunneled charge having a transient level that randomly changes due to quantum tunneling fluctuations and forming an original signal; obtaining original bit samples with a first number n of bits from the original signal, the first number n of bits being an integer; extracting randomness in the original bit samples into random bit samples having a second number of bits m smaller than the first number of bits n, the extracting being based on calibration data comprising at least: a quantum contribution value of the quantum tunneling ripple in the original bit sample; and an external contribution value in the original bit sample.)

1. A method of generating random bit samples using a quantum tunneling barrier comprising an insulator sandwiched between two conductors, the method comprising:

generating a current of charge that tunnels from a first conductor of the two conductors to a second conductor of the two conductors and across the insulator, the current of tunneled charge having a transient level that randomly changes due to quantum tunneling fluctuations and forming an original signal;

obtaining original bit samples with a first number n of bits from the original signal, the first number n of bits being an integer;

extracting randomness in the original bit samples into random bit samples having a second number of bits m smaller than the first number of bits n, the extracting being based on calibration data comprising at least:

a quantum contribution value of the quantum tunneling ripple in the original bit sample; and

an extrinsic contribution value in the original bit sample.

2. The method of claim 1, wherein the second number of bits m is based on a number of bits to be preserved per original bit sample, the second number of bits m being determined based on a minimum entropy of the quantum tunneling fluctuation, the minimum entropy of the quantum fluctuation depending on the quantum contribution value and the extrinsic contribution value.

3. The method of claim 1, wherein the extracting comprises: determining the calibration data from variance data indicative of a variance of raw bit samples taken from the quantum tunneling barrier as a function of a voltage at which the quantum tunneling barrier operates.

4. A method according to claim 3, wherein the variance data is given by a relation equivalent to:

σ²＝A(S_J+S_ext)

wherein σ²Representing said variance data, A representing said effective gain of said acquisition, S_JThe quantum contribution value representing the quantum tunneling fluctuation in the original bit sample, and S_extRepresenting the extrinsic contribution values in the original bit samples.

5. The method of claim 4, wherein the first and second light sources are selected from the group consisting of,wherein the quantum contribution value S_JGiven by a relationship equivalent to:

wherein e represents an electron charge, R represents a resistance of the quantum tunneling barrier, V represents a voltage at which the quantum tunneling barrier operates, and k_BRepresenting the boltzmann constant and representing the temperature at which the quantum tunneling barrier operates.

6. The method of claim 4, wherein σ is determined at least from the variance data at zero voltage²Is at a value greater than a given voltage threshold V_thresVoltage V of_iSaid variance data σ of²To determine the external contribution value S_ext(ii) a The variance data σ at the zero voltage²Is given by a relation equivalent to the following relation:

said voltage being greater than a given voltage threshold V_thresVoltage V of_iSaid variance data σ of²The value of (d) can be given by a relation equivalent to:

wherein e represents an electron charge, R represents a resistance of the quantum tunneling barrier, and V_iRepresents the voltage at which the quantum tunneling barrier operates, k_BRepresents the boltzmann constant, and T represents the temperature at which the quantum tunneling barrier operates.

7. The method of claim 3, further comprising: determining the variance data by varying a voltage at which the quantum tunneling barrier operates and measuring a variance of the raw bit samples as the voltage varies.

8. The method of claim 3, wherein the variance data is received from an accessible memory system.

9. The method of claim 1, wherein the calibration data is received from an accessible memory system.

10. The method of claim 1, wherein the extracting comprises:

comparing previous calibration data indicative of calibration data at a previous time instant with subsequent calibration data indicative of calibration at a subsequent time instant; and

generating an alarm when the difference between the previous calibration data and the subsequent calibration data exceeds a tolerance value.

11. The method of claim 10, wherein the comparing comprises:

determining current calibration data from current variance data obtained by varying the voltage at which the quantum tunneling barrier operates while measuring the variance of the raw bit samples, the current calibration data corresponding to the subsequent calibration data.

12. The method of claim 1, wherein the obtaining comprises: a plurality of source bit samples are obtained and concatenated into the original bit samples.

13. The method of claim 12, further comprising: determining a number of bits to be preserved per source bit sample based on a minimum entropy of the quantum tunneling fluctuation, the original bit sample comprising a given number of concatenated source bit samples, the given number determined such that multiplying by the number of bits to be preserved results in an integer.

14. The method of claim 1, wherein the extracting comprises: multiplying the original bit samples by a random matrix generated using initial seed bit samples to obtain the random bit samples.

15. The method of claim 14, wherein the original bit sample is a first original bit sample and the random bit sample is a first random bit sample, the method further comprising: repeating the obtaining to obtain a second original bit sample; generating another random matrix using at least a portion of the first random bit samples as the initial seed bit samples; and repeating the extracting of the second original bit samples with the other random matrix.

16. The method of claim 1, further comprising: repeating the obtaining to obtain a plurality of consecutive original bit samples, and repeating the extracting for each of the consecutive original bit samples to produce a random bit stream.

17. The method of claim 1, wherein the obtaining comprises sampling the raw signal, including assigning a value to an instantaneous level of the current.

18. The method of claim 17, wherein the raw bit sample corresponds to the value of the instantaneous level of the current.

19. The method of claim 17, wherein the obtaining comprises obtaining a source bit sample from the assignment, the source bit sample corresponding to the value of the instantaneous level of the current, further comprising: the sampling is repeated to obtain a plurality of source bit samples, and the plurality of source bit samples are concatenated into the original bit sample.

20. The method of claim 1, wherein the obtaining comprises identifying a crossover in the instantaneous level of current across a given value as the instantaneous level of current changes, and determining an elapsed time period between two consecutive crossovers comprises assigning a value to the elapsed time period.

21. The method of claim 20, wherein the obtaining comprises obtaining source bit samples from the grant, the source bit samples corresponding to the elapsed time period, further comprising: repeating the identifying and the determining to obtain a plurality of source bit samples, and concatenating the plurality of source bit samples into the original bit sample.

22. The method of claim 1, further comprising: and amplifying the original signal.

23. A system for generating random bit samples, the system comprising:

a quantum tunneling barrier circuit having a quantum tunneling barrier including an insulator sandwiched between two conductors, a current of charge tunneling from a first conductor of the two conductors to a second conductor of the two conductors and across the insulator, the current of tunneled charge having a transient level that randomly changes due to quantum tunneling fluctuations and forming an original signal;

a monitor configured to receive the raw signal and to obtain raw bit samples having a first number n of bits from the raw signal, the first number n of bits being an integer; and

a randomness extractor configured to extract randomness in the original bit samples into random bit samples having a second number of bits m smaller than the first number of bits n, the extraction being based on calibration data comprising at least: a quantum contribution value of the quantum tunneling ripple in the original bit sample; and an external contribution value in the original bit sample.

24. The system of claim 23, wherein the second number of bits m is based on a number of bits to be preserved per original bit sample, the second number of bits m determined based on a minimum entropy of the quantum tunneling fluctuation, the minimum entropy of the quantum fluctuation dependent on the quantum contribution value and the extrinsic contribution value.

25. The system of claim 23, wherein the extracting comprises: determining the calibration data from variance data indicative of a variance of raw bit samples taken from the quantum tunneling barrier as a function of a voltage at which the quantum tunneling barrier operates.

26. The system of claim 25, wherein the variance data is given by a relationship equivalent to:

σ²＝A(S_J+S_ext)

wherein σ²Representing said variance data, A representing said effective gain of said acquisition, S_JThe quantum contribution value representing the quantum tunneling fluctuation in the original bit sample, and S_extRepresenting the extrinsic contribution values in the original bit samples.

27. The system of claim 26, wherein the quantum contribution value S_JGiven by a relationship equivalent to:

wherein e represents an electron charge, R represents a resistance of the quantum tunneling barrier, V represents a voltage at which the quantum tunneling barrier operates, and k_BRepresents the boltzmann constant, in order toAnd represents the temperature at which the quantum tunneling barrier operates.

28. The system of claim 26, wherein σ is based at least on the variance data at zero voltage²Is at a value greater than a given voltage threshold V_thresVoltage V of_iSaid variance data σ of²To determine the external contribution value S_ext(ii) a The variance data σ at the zero voltage²Is given by a relation equivalent to the following relation:

said voltage being greater than a given voltage threshold V_thresVoltage V of_iSaid variance data σ of²The value of (d) can be given by a relation equivalent to:

wherein e represents an electron charge, R represents a resistance of the quantum tunneling barrier, and V_iRepresents the voltage at which the quantum tunneling barrier operates, k_BRepresents the boltzmann constant, and T represents the temperature at which the quantum tunneling barrier operates.

29. The system of claim 25, further comprising: determining the variance data by varying a voltage at which the quantum tunneling barrier operates and measuring a variance of the raw bit samples as the voltage varies.

30. The system of claim 23, further comprising: an amplifier configured to amplify the original signal.

Technical Field

The improvements generally relate to the field of generating random bits (bits) using quantum tunneling of charges.

Background

Random bits have found valuable applications in many fields (e.g., cryptography, games of chance, scientific algorithms, and/or statistical research). In these applications, the randomness of the generated random bits is very important, as the predictability of the random bits will result in insecure communications, e.g., spoofing and/or unreliable scientific results.

In the field of random bit generators, the expression "random" is used in a relatively free manner, since the resulting bit stream is generally known to have a certain level of certainty (i.e., is not purely random). Several methods have been developed in a way to assess the quality of randomness in random bit samples, such as the statistical test suite for random bit generators developed by the National Institute of Standards and Technology (NIST).

Features sought from the random bit generator include the quality of randomness, the ability to generate random bits at a relatively high rate, pricing, footprint (football), etc. Thus, there is still room for improvement in providing suitable apparatus for generating random bit generation.

Disclosure of Invention

The source of quantum noise exhibits inherently random characteristics and can therefore be used to generate random bits with a high level of randomness quality. For example, the bit samples may be generated based on currents that randomly tunnel charges (negatively charged electrons and/or positively charged holes) through the quantum tunneling barrier. For example, the quantum tunneling barrier may be in the form of an electrical insulator sandwiched between conductors. Due to the inherently random nature of quantum tunneling, the current of the tunneling charge has a randomly changing instantaneous level and thus forms a low level of electrical noise. It will be appreciated that this low level electrical noise is typically filtered, amplified and digitized into raw bit samples from which satisfactory randomness of the bit samples can then be determined.

It may be necessary to process the signal from the quantum tunneling barrier, for example by amplification, in order to be able to provide the original signal that can be used to generate random bits. This process may be partially or fully deterministic in nature and may generate external noise that is inherently entangled with the quantum noise of the original signal and degrades the quality of the randomness of the resulting original bit samples. Thus, even when a true quantum process (e.g., quantum tunneling) is used as the original bit sample generation source, the quality of the randomness may not be ideal and may be hindered during processing.

A method is described herein that can mitigate at least some of the inconveniences associated with the processing of raw signals from a quantum tunneling barrier. This can be achieved by extracting bit samples with a higher randomness quality from the original bit samples using calibration data comprising quantum contribution values of the quantum tunneling barrier and at least extrinsic contribution values caused by the amplifier.

In one aspect, there is provided a method of generating random bit samples using a quantum tunneling barrier comprising an insulator sandwiched between two conductors, the method comprising: generating a current of charge that tunnels from a first conductor of the two conductors to a second conductor of the two conductors and across the insulator, the current of tunneled charge having a transient level that randomly changes due to quantum tunneling fluctuations and forming an original signal; obtaining original bit samples with a first number n of bits from the original signal, the first number n of bits being an integer; extracting randomness in the original bit samples into random bit samples having a second number of bits m smaller than the first number of bits n, the extracting being based on calibration data comprising at least: a quantum contribution value of the quantum tunneling ripple in the original bit sample; and an external contribution value in the original bit sample.

In one aspect, a system for generating random bit samples is provided, the system comprising: a quantum tunneling barrier circuit having a quantum tunneling barrier including an insulator sandwiched between two conductors, a current of charge tunneling from a first conductor of the two conductors to a second conductor of the two conductors and across the insulator, the current of tunneled charge having a transient level that randomly changes due to quantum tunneling fluctuations and forming an original signal; a monitor configured to receive the raw signal and to obtain raw bit samples having a first number n of bits from the raw signal, the first number n of bits being an integer; and a randomness extractor configured to extract randomness in the original bit samples into random bit samples having a second number of bits m smaller than the first number of bits n, the extraction being based on calibration data comprising at least: a quantum contribution value of the quantum tunneling ripple in the original bit sample; and an external contribution value in the original bit sample.

This method can be implemented by a relatively simple electronic assembly and can therefore be easily applied on a common board. Furthermore, the measurement and selection of electronic components may also allow such random bit samples to be generated at a satisfactory rate using very simple electronic components. Furthermore, a random bit generator is provided comprising a board or Printed Circuit Board (PCB) having one or more quantum tunneling barriers mounted thereon and adapted to be connected to a bias source (charge source), which may be incorporated directly on the board or provided separately. Such a random bit generator may also theoretically allow very fast generation and acquisition of random bit samples, since quantum tunneling may involve a large amount of tunneled charges that may tunnel through the quantum tunneling barrier at high speed.

It should be understood that the expression "computer" as used herein should not be construed in a limiting manner. Broadly, it generally refers to a combination of some form of one or more processing units and some form of memory system accessible by the processing unit(s). Similarly, the expression "controller" as used herein should not be construed in a limiting manner, but rather in the broad sense of a device or system having more than one device that performs the function(s) of controlling one or more devices, such as an electronic device or an actuator.

It should be understood that the various functions of the computer or controller may be performed by hardware or by a combination of hardware and software. For example, the hardware may include logic gates included as part of a silicon chip of a processor. The software may be in the form of data such as computer readable instructions stored in a memory system. With respect to a computer, controller, processing unit, or processor chip, the expression "configured to" refers to the presence of hardware or a combination of hardware and software that is operable to perform the associated function.

Many further features and combinations thereof relating to the improvements of the present invention will be apparent to those skilled in the art upon a reading of the present invention.

Drawings

In the drawings, there is shown in the drawings,

fig. 1 is a schematic diagram of an example of a random bit generator comprising a raw bit generator and a randomness extractor, according to an embodiment;

FIG. 2 is a schematic diagram of an example of the raw bit generator of FIG. 1;

FIG. 3 is a graph showing the probability of obtaining a given raw bit sample from the raw bit generator of FIG. 2;

FIG. 4 is a schematic diagram of an example of the randomness extractor of FIG. 1;

FIG. 5 is a graph showing variations of raw bit samples obtained from the raw bit generator of FIG. 2;

FIG. 6 is a schematic diagram of an example of the randomness extractor of FIG. 4, illustrating the generation of an alarm when the difference between the previous calibration data and the subsequent calibration data is greater than a given tolerance value;

FIG. 7 is a schematic diagram of an example of the randomness extractor of FIG. 4 utilizing seed bit samples received by the randomness extractor and iteratively replaced by random bit samples;

FIG. 8 is a front view of an example of an electronic device incorporating the random bit generator of FIG. 1;

fig. 9 is a schematic diagram of an example of the quantum tunneling barrier circuit of fig. 2;

FIG. 10A is a schematic diagram of another example of a raw bit generator with two quantum tunneling barrier circuits;

FIG. 10B is a circuit of the raw bit generator of FIG. 10A; and

fig. 10C is an oblique view of the quantum tunneling barrier of the raw bit generator of fig. 10A.

Detailed Description

Fig. 1 shows an example of a random bit generator. As shown, the random bit generator has a raw bit generator incorporating a quantum tunneling barrier and a randomness extractor. As will be described in detail below with reference to fig. 9, the raw bit generator has quantum tunneling barrier circuitry that incorporates a quantum tunneling barrier having an insulator sandwiched between two conductors.

Returning now to fig. 2, the quantum tunneling barrier circuit is configured to provide an original signal resulting from a charge current tunneling from a first of the two conductors to a second of the two conductors and across the insulator. Since the original signal is an analog signal, the current of the tunneled charge has a randomly changing instantaneous level due to quantum tunneling fluctuation.

As shown, the raw bit generator has a monitor configured to receive the raw signal directly or indirectly from the quantum tunneling barrier. For example, the original signal may be received directly from the quantum tunneling barrier. However, in some other embodiments, such as the one shown, the raw signal provided by the quantum tunneling barrier circuit is suitably amplified with at least one amplifier to provide an amplified raw signal having a satisfactory level. In this case, the original signal is received indirectly from the quantum tunneling barrier via at least one amplifier.

The monitor is also configured to provide one or more digitized raw bit samples from the raw signal. In the illustrated embodiment, the monitor provides raw bit samples from the amplified raw signal received from the amplifier. Each original bit sample has a first number of bits (number) n, where the first number of bits n is an integer. The monitor may be provided in the form of a sampler, as will be described below. However, the sampler is optional, as other detector alternatives may be used to convert the original signal into original bit samples.

In some embodiments, the monitor is provided in the form of a sampler configured to sample an instantaneous level of the raw signal and to impart a value to an instantaneous level of charge current tunneling through the quantum tunneling barrier. In some embodiments, the raw bit samples may correspond to the value of the instantaneous level of current. For example, at a given moment, when the first number of bits n is 4, the sampler may sample the original signal to have a maximum value of 2⁴-1-value 5 in 15, then provides the original bit sample 0101.

In some embodiments, the sampler may sample the instantaneous level of the original signal at different times to provide source bit samples, each source bit sample corresponding to the value of the instantaneous level of current. However, in these embodiments, the source bit samples may be concatenated to each other into raw bit samples using a concatenator (concatenator). For example, at a first time instant, the sampler may sample the original signal to have 2²-1-3, then the first source bit sample 01 provided. Then, at a second time instant, the sampler may sample the original signal to have 2²-1-value 2 in 3, and then provide a second source bit sample 10. In this example, the coupler may couple the first source bit sample and the second source bit sampleThe two source bit samples are concatenated with each other to provide the original bit samples 0110 or 1001. In the described embodiment, the first number of bits n corresponds to the number of source bits per source bit sample multiplied by the number of source bit samples concatenated to each other. It will be appreciated that the coupler may be optional, as the monitor may be configured to convert the raw signal directly into raw bit samples. It can be considered that in embodiments where consecutive source bit samples are uncorrelated with each other, it would not be necessary to concatenate the source bit samples with each other.

It will be appreciated that the raw signal provided by the quantum tunneling barrier circuit can be considered quantum and therefore non-deterministic. However, this is not the case for an amplified original signal or any form of processed original signal. In fact, in this embodiment, the amplification performed by the amplifier adds an external non-quantum and deterministic contribution (contribution) to the signal. Some external contributions may also be added by the monitor (e.g., sampler) or other electronic components of the raw bit generator. Thus, the original signal has a quantum contribution and an external contribution, and so does the original bit sample. As can be appreciated, by having a deterministic external contribution, random bits directly from such original signal can be controlled and/or derived by a third party adversary, which for some applications, such as cryptographic applications, will reduce the trustworthiness of such random bits.

Fig. 3 shows an example of a probability distribution of raw bit samples obtained from a raw bit generator. In this particular example, the first number of bits n corresponds to 3 for simplicity. For example, when the instantaneous value of the original signal when sampled by the sampler is between 0mA and 5mA, the generated original bit sample is 100; when the instantaneous value of the original signal when sampled by the sampler is between 5mA and 10mA, the generated original bit sample is 101, and so on. As shown, the probability of acquiring the original bit samples 100 is greater than the probability of acquiring the original bit samples 101, and so on. The probability distribution shown is composed of the standard deviation σ and the variance σ²And (6) performing characterization.

The inventors propose the variance σ of the raw bit samples generated by the raw bit generator²Can be given by a relation equivalent to:

σ²＝A(S_J+S_ext) (1)

wherein A represents the effective gain of the raw bit generator, S_JQuantum contribution value, S, representing quantum tunneling fluctuation in original bit sample_extRepresenting at least the amplified extrinsic contribution values in the original bit samples. In this example, the effective gain a of the raw bit generator may include the gain and impedance of the amplifier and the detection bandwidth. More specifically, the effective gain a may be represented by the relationship a ═ R²G²Δ f is given, where R represents the resistance of the quantum tunneling barrier, G represents the effective gain of the amplifier, and Δ f represents the bandwidth of the original signal being monitored. In some other embodiments, the effective gain G of the amplifier may be inferred from the specifications of the amplifier used. In an alternative embodiment, the effective gain G of the amplifier may be determined by amplifying a given signal having a known amplitude and by comparing the amplitude of the amplified signal to the known amplitude of the given signal. Otherwise, in the absence of an amplifier, the effective gain of the amplifier corresponds to unity, and the effective gain of the raw bit generator is given by the formula GAA ═ R²Δ f is given.

In the following example, the quantum contribution value S_JIs the spectral density of the original signal obtained from the quantum tunneling barrier circuit, and the extrinsic contribution S_extIs the spectral density of the external contribution due at least to the amplification provided by the amplifier.

However, it will be appreciated that in some other embodiments the quantum contribution values may be provided in the form of power values integrated over a given frequency bandwidth with the spectral density of the original signal. Similarly, in these embodiments, the external contribution value may be provided in the form of a power value integrated by the spectral density of the external contribution integrated over a given frequency bandwidth.

Referring now to fig. 4, the randomness extractor is configured to extract randomness in one or more original bit samples into one or more random bit samples having a second number m of bits. As will be understood from the following description, the second number of bits m is smaller than the first number of bits n. Therefore, some bits are lost in the extraction process.

The extraction of randomness is based on including at least a quantum contribution value S_JAnd an external contribution value S_extOf the calibration data of (1).

In some embodiments, the calibration data (e.g., the quantum contribution value S)_JAnd an external contribution value S_ext) Has been determined in advance and is stored in the memory system of the randomness extractor. For example, the calibration data may have been determined during the manufacture of the random bit generator and then stored in the memory system. In this case, the random bit generator may produce satisfactory results when used within certain limits (e.g., some predetermined temperature limit).

In some other embodiments, the variance data σ may be based on²(V) to determine the calibration data (e.g. the quantum contribution value S)_JAnd an external contribution value S_ext) The variance data indicating a variance σ of one or more raw bit samples obtained from a quantum tunneling barrier²How it varies as a function of the voltage V at which the quantum tunneling barrier operates.

For convenience, variance data σ is shown in fig. 5²Examples of (V).

Also, the variance data σ of the quantum tunneling barrier may be determined during the manufacturing of the random bit generator²(V) which is then stored in a memory system to produce satisfactory results as long as the random bit generator is used within certain limits.

However, it is not necessary to determine the variance data σ in advance²(V). Indeed, in some embodiments, the quantum tunneling barrier may be operated at a voltage that is variedTime-measuring the variance of one or more raw bit samples to determine the variance data σ²(V)。

In any case, the quantum contribution value S_JCan be given by the formula equivalent to:

where e represents the electron charge, V represents the voltage at which the quantum tunneling barrier operates, and k_BDenotes the boltzmann constant and T denotes the temperature at which the quantum tunneling barrier operates, as proposed by Spietz, Lafe et al in "Primary electron thermometry using shot noise of a tunnel junction" in Science 300.5627(Science 300.5627) 2003.

The formula (2a) is effective for the frequency f so that hf < k_BT, wherein h represents the Planckian constant. Indeed, at room temperature, equation (2a) may be effective for frequencies where f < 6 THz. Operating at 10GHz may add an exponentially smaller correction.

It is understood that formula (1) is not a linear formula. Thus, the variance σ can be measured at least three voltage values²(V) to derive an external contribution value S of the raw bit generator_extTemperature T and effective gain a. For example, the variance σ for the original bit samples may be determined using ordinary least squares²(V) from which the external contribution S can be derived_extTemperature T and effective gain a. Indeed, in one aspect, two may be selected to be greater than k_BVoltage value of T/e, in this case, the variance σ of the original bit sample²(V) may be linear with the variation of voltage V: the slope of the linear relationship may give an effective gain A, while the y-intercept (y-intercept) yields an external contribution S_ext. Then, in one aspect, the temperature T can be derived by estimating the linear relationship at zero voltage.

As shown in FIG. 5, based on the above formula (1) and formula (2a), in oneIn some other embodiments, the variance data σ of the original bit samples may be based on²(V) to determine the external contribution value S_ext. More specifically, in some embodiments, the variance σ of one or more of the raw bit samples is when the voltage V is zero²(0) Can be given by a relation equivalent to the following relation:

additionally or alternatively, when the voltage V is_iGreater than a given voltage threshold, V_thres＜V_iTime of arrival, variance σ of one or more of the original bit samples²(V_i) Can be given by a relation equivalent to:

in this example, the original bit samples are given and the variance data σ of equations (2a), (3), and (4)²(V) the calibration data, e.g. the quantum contribution value S, may be determined_JAnd an external contribution value S_extSince the external contribution S is known_extDoes not change as a voltage at which the quantum tunneling barrier operates. See, for example, Thibault, Karl et al Physical review letters (Physical review letters)114.23 for "Pauli-Heisenberg oscillations in Electron Quantum transport" (Pauli-heiseng resonances in Electron transport).

Thus, by knowing the quantum contribution value S_JAnd an external contribution value S_extThe relative contribution of each of them with respect to each other, it can be determined how many original bit samples can be associated with quantum contribution values, and how many original bit samples can be associated with external contribution values.

In the above example, the quantum tunneling barrier operates in the linear region, which allows using ohm's law, V ═ RI. Thus, the ratio V/I and the derivative dV/dI will be constant and the resistance R will be obtained. However, in someIn other embodiments, the quantum tunneling barrier may not operate in a linear region, but rather in a nonlinear region, in which case the ratio V/I and derivative dV/dI are not constant. In this context, the quantum contribution value S is such that the transport of charge occurs via quantum tunneling through a quantum tunneling barrier by means of quantum tunneling_jGiven by:

where I represents the current through the quantum tunneling barrier. Herein, the variance σ of one or more of the raw bit samples when the voltage V is zero²(0) And

i is close to zero and when the voltage V is_iGreater than a given voltage threshold, V_thres＜V_iThe variance σ of one or more of the original bit samples²(V_i) Can be given by a relation equivalent to: sigma²(V_i)2 eI. As can be appreciated, the non-linearity of the quantum tunneling barrier can result from, for example, the barrier height of the quantum tunneling barrier being non-infinite and/or the density of states in the electrical contact depending on the energy.

Determining how many bits in the original bit sample are due to quantum contribution involves determining a minimum entropy H of the quantum contribution_∞，Q. According to a definition, the minimum entropy H_∞，QCan be given by a relation equivalent to:

H_∞，Q＝-log₂p_max，Q(5)

wherein p is_max，QRepresenting the maximum probability of acquiring one or other of the values of the instantaneous level of the original signal with only quantum contribution. However, the variance σ of the original bit samples is determined by a relation equivalent to the following relation²Variance with quantum contribution

And (3) correlation:

where γ represents the ratio between the quantum contribution value and the external contribution value. For example, the ratio γ can be given by:

knowing the minimum entropy H of the original bit sample_∞Can be given by a relation equivalent to:

H∞＝-log₂p_max(8)

wherein p is_maxIs the maximum probability of obtaining one of the other original bit samples. For example, referring to FIG. 3, p_maxThere will be a probability of obtaining the original number of bits 011 (or 100). In practice, the processed raw signal may not be distinguishable from the gaussian curve. In this case, if I_maxRepresenting the maximum value of the monitor (e.g. sampler), two consecutive integers correspond to the pass

Two separate currents, where n is the first number of bits and the maximum probability p_maxAnd p_max，QGiven by a relationship equivalent to:

therefore, using equations (5), (6), (8) and (10), it is possible to obtain:

since the minimum entropy H of the original bit samples can be determined as described above_∞The sum ratio γ, and thus the minimum entropy H of the quantum contribution can also be determined_∞，Q. Minimum entropy H of this quantum contribution_∞，QCan be used to determine how many bits in the original bit sample are due to quantum contributions and can therefore be used as input to the randomness extractor.

For example, in a given embodiment, for n-14 bits and I_max3 σ, the minimum entropy H for the original data of 12.7 bits per original bit sample can be obtained_∞. For an amplifier with voltage noise of 1.4 nV/root Hz, the external contribution S_extCan be determined as 2 × 10^-18V²in/Hz. For a quantum tunneling barrier with a resistance of R50 Ohms operating at a voltage of V0.4V, the quantum contribution value S_JCan be determined as 2eVR 6.4 × 10^-18V²A ratio γ of 3.2 can be obtained at/Hz. In this case, the minimum entropy H_∞，QCan be given by 12.5 bits per original bit sample. In this case a security factor of 0.3 bits per original bit sample may be used, which will result in extracting randomness from the original bit samples in order to keep 12.2 bits per original 14 bits original bit sample. In such an embodiment, if the first number of bits n of the original bit sample is 14, the second number of bits m may be floated to 12. By doing so, 0.2 bits per original bit sample, which are generally associated with a satisfactory amount of random properties, will be lost.

Since the throughput of the random bit generator is important in some applications, it would be inconvenient to lose these 0.2 bits per original bit sample. To avoid this, a coupler may be conveniently used. In such an embodiment, the monitor is configured to provide source bit samples having a source bit number of 14, and is based on a minimum entropy of quantum tunneling fluctuation, H_∞，QDetermining that 12.2 bits per source bit sample are to be retained, the concatenator may be used to concatenate a plurality of source bit samples to each other in order to minimize the loss. For example, the number of source bit samples coupled to each other may correspond to the number: the number of bits per original bit sample to be retained may be multiplied to produce an integer. For example, if the number of bits per original bit sample to be retained is 12.2 bits in this particular example, multiplying any multiple of 5, 10, or 5 by 12.2 bits will yield an integer. Thus, it may be preferred that any original bit sample is the result of concatenation of source bit samples of any multiple of 5, 10 or 5 to avoid losing bits associated with a satisfactory amount of random properties.

The randomness extraction may be performed using a variety of different algorithms. Examples of such algorithms may include least significant bit methods, non-universal hash functions, Trevisan extractors, and/or universal hash functions such as Toeplitz hash functions. In some embodiments, the Trevisan extractor and the universal hash function may be preferred because they are considered to be information theoretically provable. See Mansour, Yishay, Noam Nisan, and Praston tiwai for "computational complexity of universal hash" in 2013 theoretical computer science 107.1; ma, xingfeng et al physical comment in 2013 a87.6 "post-processing for quantum random number generators: entropy evaluation and randomness extraction (Postprocessing for quantitative random-number generators: control evaluation and random extraction) "; and Xu, Feihu et al in 2012's optical express (Optics express)20.11, "ultra fast quantum random number generation based on quantum phase fluctuation" in the field of Ultrafast quantum random number generation on quantum phase fluctuations.

In this embodiment, each original bit sample of the Toeplitz random matrix T.n bits of m × n is established to be multiplied by the random matrix T to give a random bit sample of m bits_∞，QSubtracting any final security factor gives m, of course the second number of bits m is less than the minimum entropy H of the original bit sample of n bits_∞. In the extraction processN-m bits are discarded.

For example, let us consider concatenating 100 source bit samples of 14 bits to each other to form a raw number of bits having a first number of bits corresponding to 1400. Minimum entropy H of the source bit samples_∞May be 12.7 bits per source bit sample. Minimum entropy H of quantum signal_∞，QMay be 12.5 bits per original bit sample. Taking a security factor of 0.3 bits per original bit sample, 12.2 bits of the original 14 bits can be kept. Thus, in this example, the second number of bits m corresponds to 1200. It can be noted that the number of source bit samples, i.e. 100, concatenated to each other to form the original number of bits, when multiplied by the number of bits to be maintained, i.e. 12.2 in the present example, results in an integer number and thus avoids the loss of bits associated with a satisfactory amount of random properties. The first number of bits n and the security factor may be selected in dependence on the required bit rate per second and the required security level. The random matrix T may be generated with a random bit seed of n + m-1 random bits, which may be obtained from the original bit samples holding the least significant bits of each original bit sample for a short time, for example. Which may be reinitialized as often as necessary, an example of which will be described below with reference to fig. 7.

A typical quantum tunneling barrier can be assumed to have a bandwidth of about 600 MHz. To avoid unwanted correlation between successive original bit samples, the samples can typically be performed at a sample rate of 1200MS/s if a satisfactory anti-aliasing filter is used. For example, taking a first number of bits with a sample rate of 800MS/s and 14 bits, this may result in a generation rate of 11.2Gb/s of original bit samples, and thus a generation rate of 9.6Gb/s of random bit samples. In the prototype, a sample rate of 125MS/s was used satisfactorily, which resulted in a generation rate of 1.75Gb/s of original bit samples. The limiting feature in this embodiment is typically the rate at which random bit samples can be transferred to the electronic device.

It is conceivable that the amplifier not only adds the voltage fluctuation e (t) to the voltage V it measures_inIt can also be used forThe ripple current i (t) is added to the part connected to its input, thus measuring V at the amplifier output_outThe voltage of (d) can be given by:

V_out＝G(V_in+e+Ri)

where G denotes the effective gain of the amplifier and R denotes the differential resistance R of the quantum tunneling barrier, dV/dI. Thus, the amplifier can pass<e²>+R<ei>+R²<i2>Contributes to the measured voltage noise. First item<e²>Representing voltage noise of the amplifier, the third term R²<i²>Representing current noise entering the amplifier at the node resistance, the second term R<ei>Relates to the correlation (and is generally negligible) between current and voltage noise. This amount depends on the bias current in the node (if R is active). This can be taken into account when fitting the total noise versus bias voltage/current. Thus, the first term is correlated with using an amplifier with low current noise and/or a node with sufficiently low resistance<e²>Compared with the third term R²<i²>Negligible, this may reduce undesirable effects normally associated with current noise of the amplifier.

Fig. 6 is a schematic diagram of the randomness extractor. In this embodiment, the randomness extractor receives previous calibration data and subsequent calibration data, compares the previous calibration data and the subsequent calibration data to each other, and then generates an alarm when a difference between the previous calibration data and the subsequent calibration data exceeds a tolerance value. More specifically, the previous calibration data has been at a first time instant t₁Determining that the subsequent calibration data has been at the second time t₂Determining, the second time t₂At a first time t₁And then. The alarm so generated may therefore provide a diagnostic as to whether the random bit sample generated is authentic.

For example, in one embodiment, the previous calibration data may have been determined and stored in the memory system during manufacture of the random bit generator, may have been previously storedVariance data

To provide the previous calibration data. In this embodiment, the variance may be measured in real time or at

While the subsequent calibration data is determined in real time by varying the voltage at which the quantum tunneling barrier operates, the final variance data may be obtainedTo provide the subsequent calibration data.

It will be appreciated that if the variance data is priorAnd subsequent variance data

A significant difference between them may indicate that the random bit generator is used outside some predetermined limits (e.g., outside a predetermined temperature range). Furthermore, such a difference may also indicate that the random bit generator is being modified/changed by a third party adversary, in which case the alarm so generated may prove that such alarm is correct.

It will be appreciated that the randomness extractor may be configured to repeat such diagnostics at a given frequency or on demand.

Referring now to fig. 7, it is contemplated that the randomness extraction may involve a random bit seed. For example, in this embodiment, the extraction may require a random matrix that is generated using a random bit seed before the randomness is actually extracted from the original bit samples. For example, the original bit samples may be multiplied by a random matrix to provide random bit samples during extraction. Although the initial seed bit samples may only have pseudo-randomness, the resulting random bits may have satisfactory randomness due to shuffling (shuffle) and/or removal of bits during extraction. However, in this embodiment, the randomness extractor generates random bit samples by multiplying the original bit samples by a so-called pseudo-random matrix, after which the random bit seeds used for generating the random matrix may be replaced by the random bit samples thus generated. In this case, the random matrix, which will be pseudo-random first, may quickly become a random matrix, which may produce random bit samples with increased randomness.

Fig. 8 shows an example of an electronic device incorporating a random bit generator. More specifically, the electronic device has a housing in which a random bit generator is mounted. It will be appreciated that the electronic device may be a smart phone, a tablet computer, an electronic credit or debit card, a laptop computer, a television, etc., depending on the application. Further, in some embodiments, the electronic device may be provided in the form of a computer, server, or the like that is accessible via a wired and/or wireless connection over a network, such as the internet.

As shown in this embodiment, the electronic device has a processing unit and a memory system that are separate and communicatively coupled (e.g., wired and/or wireless communication) to the random bit generator. In some other embodiments, the processing unit and the memory system of the electronic device may act as a randomness extractor, in which case the raw bit generator is communicatively coupled to the processing unit and/or the memory system of the electronic device.

Fig. 9 shows an example of a raw bit generator. The raw bit generator generally includes a board (not shown) on which the quantum tunneling barrier circuit is mounted. As shown, the quantum tunneling barrier circuit of the raw bit generator may include a quantum tunneling barrier, one or more capacitors, one or more inductors, and one or more resistors. A bias source is provided for varying the voltage at which the quantum tunneling barrier operates. In this example, the original signal from the quantum tunneling barrier circuit is amplified with an amplifier. The original bit sample stream is acquired by means of a monitor, which is provided in this example in the form of a sampler that samples the amplified original signal from the amplifier. It will be appreciated that the quantum tunneling barrier circuit, bias source, amplifier and monitor may be mounted on the board. For example, the board may be a Printed Circuit Board (PCB) that mechanically supports the components and electrically connects the components to each other via conductive traces etched from a copper sheet laminated onto a non-conductive substrate.

As described above, the quantum tunneling barrier may be provided in the form of a quantum tunneling member having a quantum tunneling barrier in the form of one or more insulating layers sandwiched between conductive layers serving as conductors. It should be noted that the conductive layer may be made of, for example, a metallic material or a semiconductor material, and the insulating layer may be made of any material that satisfactorily inhibits free conduction of electrons (or holes) thereon by classical reflection. The insulating layer has two externally opposed faces, each face being in contact with a respective one of the two conductive layers, and the two conductive layers may be connected to the first and second terminals of the bias source. It will be appreciated that the bias source may be mounted on the plate and fixedly connected to the conductive layer of the quantum tunneling barrier, or provided separately.

In this embodiment, the bias source may be used to perform the step of varying the voltage at which the quantum tunneling barrier operates. The amplifier may be adapted to perform the step of amplifying an original signal provided by the quantum tunneling barrier circuit. The sampler may be adapted to perform the step of sampling the original signal and the filter may be adapted to perform the step of filtering the original signal. The filter may be connected to the quantum tunneling barrier, which is in turn connected to an amplifier and then to a sampler. When operatively connected to each other, the raw bit generator may monitor the raw signal to obtain raw bit samples. Further, the bias source may cure the potential difference applied to the quantum tunneling barrier. The bias source may also be varied to allow on-board measurement of the variance σ (V) of the original bit samples.

Fig. 10A shows another example of a raw bit generator according to another embodiment. It will be appreciated that to reduce the effects of extraneous contributions, a differential circuit having two quantum tunneling barrier circuits may be advantageously used in some embodiments. As shown, the raw bit generator has a differential amplifier configured to amplify a difference between first and second raw signals provided by first and second quantum tunneling barrier circuits, respectively. More specifically, in this example, the first and second quantum tunneling barriers are biased by a common bias source. In this embodiment, the bias source is used to apply a DC current or voltage to the first quantum tunneling barrier circuit and the second quantum tunneling barrier circuit. In this embodiment, a high-pass filter may be included in each quantum tunneling barrier circuit to remove low-frequency components in the first original signal and the second original signal. In practice, the high-pass filter is used to separate DC from fluctuations at finite frequencies, which are the original signals intended for isolation and detection. Still in this example, an analog-to-digital monitor is provided to monitor the output of the differential amplifier and provide raw bit samples. With this configuration, the common external contribution can be suppressed.

The circuitry of such a raw bit generator is shown in fig. 10B. As shown, the bias source generates a voltage V for biasing the first and second quantum tunneling barrier circuits₀. The resistor R is used to limit the current of tunneling charges generated by the first and second quantum tunneling barriers. Inductors and/or capacitors separate the DC component from the AC fluctuations of the original signal. In this example, the capacitor acts as a high pass filter. In this embodiment, the voltage V₀The possible noise on the ends has no influence on the measurement on the ends, because the two branches of the raw bit generator are symmetrical to each other. They may thus cancel each other out.

Fig. 10C shows an image of a pair of quantum tunneling barriers of the raw bit generator of fig. 10A. As shown, the pair of quantum tunneling barriers can be fabricated using a common contact using photolithography techniques. In the example shown, a first layer of aluminium (approximately 200nm thick) is deposited on the substrate to form a common contact GND connected to circuit ground. The first layer is oxidized using pure oxygen to form a quantum tunneling barrier about 1nm thick. A second aluminum layer (about 300nm thick) was deposited to form contact C1 and contact C2. Each of contact 1 and contact 2 overlaps the first layer, and the overlap defines quantum tunneling barriers J1 and J2.

It will be appreciated that the above and illustrated examples are exemplary only. In some embodiments, the monitor may be configured to identify a crossover in the instantaneous level of current across a given value as the instantaneous level of current changes, and to determine the time period elapsed between two successive crossovers. In these embodiments, values are assigned to the elapsed time periods and the original bit samples are formed. For example, the monitor may identify that the instantaneous level of current crosses a zero value at a first time and then crosses back with a zero value at a second time. Thus, the value assigned to the original bit sample will be the difference between the first time instant and the second time instant and vice versa. Similarly, when using a sampler, a source bit sample can be obtained by identifying the path of the instantaneous value at a given value and determining the time period elapsed between two successive paths of the instantaneous level of the current at the given value. In these embodiments, a concatenator may also be used to concatenate the source bit samples to each other to provide the raw bit samples. The scope being indicated by the appended claims.