Randomness evaluation method and system for continuous variable source independent quantum random number generator based on limited sampling interval

Abstract

The invention provides a randomness evaluation method and system for a continuous variable source independent quantum random number generator based on a limited sampling interval, and relates to the technical field of quantum information communication. In the existing security analysis of the source-independent quantum random number generator based on randomized local oscillator light, the security problem introduced by the limited sampling interval of the ADC is not considered, while in the randomness evaluation method and system provided by the invention, the limited sampling interval of the actual ADC is considered, and the measurement saturation probability of the ADC is introduced, so that the security of the source-independent quantum random number generator is evaluated. According to the method, the randomness evaluation formula is corrected, the problem of security vulnerabilities introduced by ADC saturation measurement can be solved, ADC sampling interval parameters can be optimized, the optimal ADC sampling interval is given, the actual security and performance of the system are further improved, and the security of output random numbers is ensured.

Description

Technical Field

[0001] The present invention relates to the field of quantum information communication technology, and in particular to a randomness evaluation method and system for a continuous variable source-independent quantum random number generator based on a finite sampling interval. Background Art

[0002] As an important randomness resource, random numbers have a wide range of application needs in numerical simulation, information security, cryptography and other fields. Quantum random number generators designed based on the principle of intrinsic randomness in quantum mechanics can theoretically generate quantum random numbers with true randomness, providing important guarantees for fields with high requirements for randomness, such as quantum secure communications. However, the physical implementation of quantum random number generators often faces security vulnerabilities caused by the non-ideal characteristics of actual devices, and even potential risks of being controlled by hackers, which causes errors in quantum entropy evaluation and affects the security of the final output random numbers. Therefore, accurate entropy evaluation of the output of the quantum random number generator is an important condition to ensure the security of the output random numbers.

[0003] According to the degree of trust in physical devices, quantum random number generators can be divided into device-trusted quantum random number generators, semi-device-independent quantum random number generators, and device-independent quantum random number generators. Among them, semi-device-independent quantum random number generators can achieve a relatively high random number generation rate by trusting some devices, and at the same time have a certain ideal security. In particular, source-independent quantum random number generators that do not require any assumptions about the quantum entropy source have attracted widespread attention from researchers due to their advantages such as high rate and easy implementation. Among source-independent quantum random number generators, source-independent quantum random number generators based on continuous variables have higher bandwidth systems and random number generation rates than discrete variable source-independent quantum random number generators, and are more practical.

[0004] Generally speaking, the continuous variable source-independent quantum random number generator is mainly implemented based on the vacuum fluctuation noise scheme, using homodyne detection technology or heterodyne detection technology to measure the two regular components of the unknown quantum state of the input, the measurement result of one component is used to generate the original random number, and the measurement result of the other component is used to estimate the quantum entropy content, and then the lower bound of the extractable random number content is accurately estimated by using the entropy uncertainty relationship or Gaussian state extreme value theorem and other security analysis methods. In the source-independent quantum random number generator scheme based on homodyne detection technology, it is also necessary to add an additional phase modulator to change the phase of the local oscillator light to achieve the measurement of a specific regular component of the quantum state. In order to further simplify the continuous variable source-independent quantum random number generator device, Smith et al. proposed a source-independent quantum random number generator scheme based on phase randomized local oscillator light. The scheme uses the light pulse output by the gain switching laser as the local oscillator light. Since the output light pulse has a random phase, it is possible to measure any regular component of the input unknown quantum state without adding an additional phase modulator, thereby realizing a source-independent quantum random number generator.

[0005] In the continuous variable source-independent quantum random number generator, the quantum signal measured by the balanced zero-beat detector is a continuous signal. In order to further evaluate the extractable random number content and data processing, a data acquisition quantization device, an analog-to-digital converter (ADC), is usually used to collect and discretize the continuous electrical signal, output a binary digital sequence, and obtain the original quantum random number. Therefore, ADC, as a key device for signal acquisition quantization, plays a vital role in the continuous variable source-independent quantum random number generator.

[0006] For an actual ADC, its characteristics are described by sampling rate, sampling precision and sampling interval. For example, if the sampling precision is n and the sampling interval is [-N-δ ADC / 2,N-δ ADC / 2], where δ ADC =N / 2 n-1 The width of the minimum resolvable quantization interval of the ADC. The ADC will discretize the sampling interval into 2 n The limited sampling interval will lead to saturation of the measured signal, that is, when the input electrical signal exceeds the ADC sampling interval, the corresponding signal will be accumulated in the first or last discretized ADC quantization interval, causing saturation in the first and last intervals.

[0007] In the existing security analysis of source-independent quantum random number generators based on phase randomized local oscillator light, the security issues introduced by the limited sampling interval of the ADC are not considered. Instead, it is assumed that the ADC has infinite sampling accuracy and sampling interval, and all measurement information can be fully characterized by the ADC without losing any information. However, in actual systems, once the measured signal exceeds the limited sampling interval of the ADC, it will cause the signal to be saturated during the measurement process, resulting in the inability of legitimate users to obtain specific information about the signal beyond the sampling range. If the eavesdropper has a strong attack capability and conducts an eavesdropping attack by obtaining the side information of the saturated signal, the security of the generated random number will inevitably be destroyed. Therefore, under the condition of the limited sampling interval of the ADC, it is crucial to provide a security analysis method for the continuous variable source-independent quantum random number generator. Summary of the invention

[0008] In order to accurately evaluate and improve the actual security of a continuous variable source-independent quantum random number generator, the present invention proposes a randomness evaluation method and system for a continuous variable source-independent quantum random number generator based on a finite sampling interval.

[0009] In a first aspect, the present invention provides a method for evaluating the randomness of a continuous variable source-independent quantum random number generator based on a finite sampling interval, comprising: for an input unknown quantum state, when the sampling interval of an analog-to-digital converter ADC is finite, calculating the sum of the probabilities that a measurement result of the unknown quantum state measurement falls between the first and last quantization intervals of the ADC, and correcting a lower bound of the random number content that can be extracted from the measurement result based on the sum of the probabilities.

[0010] Furthermore, the modified extractable random number content H min (Q θ,δ |E) is bounded by:

[0011] H min (Q θ,δ |E)≥H min (Q δ )0>+log2(1-P)

[0012] Among them, H min (Q δ )0> represents the minimum entropy of the measurement result corresponding to the input vacuum state when the sampling interval of the analog-to-digital converter ADC is limited; P represents the probability and probability that the measurement result of the unknown quantum state falls into the first and last quantization intervals of the ADC; E represents the quantum system; Q represents the orthogonal component of the unknown quantum state, the subscript δ represents the measurement resolution of the ADC in vacuum units, and θ represents the phase angle of the current local oscillator light.

[0013] Furthermore, the measurement results of the vacuum state are set to satisfy the mean of 0 and the variance of Gaussian distribution, then when the sampling interval of the analog-to-digital converter ADC is limited, the minimum entropy H of the measurement result corresponding to the input vacuum state is calculated according to the following formula min (Q δ ) 0> :

[0014]

[0015] Among them, i min and i max Respectively represent the first and last quantization intervals of ADC. The ADC sampling interval is [-N-δ ADC / 2,N-δ ADC / 2], N is the total number of ADC sampling signals, δ ADC is the width of the minimum resolvable quantization interval of the ADC, σ v represents the standard deviation of vacuum noise, p guess represents the maximum guess probability of the eavesdropper about the measurement result, erf and erfc represent the error function and complementary error function respectively.

[0016] In a second aspect, the present invention further provides a continuous variable source-independent quantum random number generator system based on a finite sampling interval, comprising:

[0017] A data processing module is used for discarding all the measurement results of the unknown quantum state measured in the first and last quantization intervals of the ADC when the sampling interval of the analog-to-digital converter ADC is limited, so as to obtain the original random number;

[0018] A randomness evaluation module, used to calculate the lower bound of the modified extractable random number content using the randomness evaluation method as described in the first aspect;

[0019] The post-processing module is used to use the lower bound of the modified extractable random number content as a constraint condition to perform randomness extraction operations on the original random numbers using a post-processing method to obtain secure true random numbers.

[0020] Beneficial effects of the present invention:

[0021] (1) In the existing security analysis of source-independent quantum random number generators based on randomized local oscillator light, the security problem introduced by the limited sampling interval of the ADC is not considered. In the randomness evaluation method proposed in the present invention, the limited sampling interval of the actual ADC is considered. By introducing the measurement saturation probability of the ADC, the randomness evaluation formula is corrected, which can solve the security vulnerability problem introduced by the saturation measurement of the ADC. In addition, the ADC sampling interval parameters can be optimized to provide the optimal ADC sampling interval, which further improves the actual security and performance of the system and ensures the security of the output random numbers.

[0022] (2) In the improved source-independent quantum random number generator system based on randomized local oscillator light proposed in the present invention, the output signals falling in the first and last quantization intervals of the ADC are discarded. By estimating the ADC measurement saturation probability, an improved evaluation formula for the extractable random number content is given, thereby preventing the eavesdropper Eve from carrying out an ADC sampling saturation attack and further improving the actual security of the source-independent quantum random number generator system. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A schematic flow chart of a randomness evaluation method for a continuous variable source-independent quantum random number generator based on a finite sampling interval provided in an embodiment of the present invention;

[0024] Figure 2 Schematic diagram of a continuous variable source-independent quantum random number generator device based on phase randomized local oscillator light;

[0025] Figure 3 The impact of the limited sampling range of the ADC provided by the embodiment of the present invention on the extractable random number content;

[0026] Figure 4 A schematic diagram of the structure of a continuous variable source-independent quantum random number generator system based on a finite sampling interval provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution in the embodiment of the present invention will be clearly described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] Example 1

[0029] In a continuous variable source-independent quantum random number generator, it is generally believed that the measurement device is trustworthy, while the quantum source is untrustworthy. The unknown quantum state ρ of the input A It may be prepared or fully controlled by the eavesdropper Eve, who has access to the quantum system E associated with the legitimate user Alice's system A, which together constitute a pure state ρ AE , the quantum state ρ can be obtained through purification operation A All information of A =Tr E [ρ AE ]. If Eve can obtain the quantum state ρ ABy using all the information, we can improve the probability of Alice's measurement results, thereby improving the probability of successfully predicting the output random number.

[0030] By randomly changing the phase angle of the local oscillator light, the input quantum state ρ can be realized. A The random measurement of the two orthogonal components of is further used to estimate the lower bound of the extractable random number content using the entropy uncertainty principle. The security of the continuous variable source-independent quantum random number generator comes from randomly changing the phase of the local oscillator light. In the continuous variable source-independent quantum random number generator based on phase randomized local oscillator light, this core requirement can be achieved without adding additional phase modulation devices.

[0031] The continuous variable source-independent quantum random number generator based on phase randomized local oscillator light uses the pulse light output by the gain-switched laser as the local oscillator light. The output pulse light has a random phase angle θ, so that user Alice can use a balanced homodyne detector to measure the quantum state ρ A The orthogonal components Then the electrical signal output by the balanced homodyne detector will be sampled by the ADC as a digital signal, and the original random number will be output.

[0032] Due to the limited sampling resolution of the ADC, the electrical signal will be discretized into a digital signal, resulting in the continuous output result x being discretized into x k Correspondingly, we can get a coarse-grained version of the orthogonal operator The measurement resolution δ in vacuum unit can be calculated based on the sampling resolution δ of ADC. ADC get.

[0033] All possible results of the discretization output can be represented by the set Indicates that k represents the index of the ADC quantization interval. Alice has a quantum state ρ A Performing generalized quantum measurement (POVM) And the measurement result x k Stored in classical memory, where the POVM element Output measurement result x k The probability of Tr means trace.

[0034] The eavesdropper Eve maximizes the guess probability by choosing an optimal measurement strategy The probability of this guess depends on the quantum condition minimum entropy H min (Q θ,δ |E), that is, the conditional minimum entropy when the eavesdropper Eve holds any classical information or quantum side information. Alice estimates the quantum conditional minimum entropy H min (Q θ,δ|E), we can derive a lower bound on the random number content that can be extracted from each measurement result.

[0035] Existing literature has proved that by using phase randomized local oscillator light to make the quantum state ρ A Under phase randomness, Eve's optimal eavesdropping strategy is to input quantum state ρ A is the vacuum state, ρ A =|0><0|, under this condition, Eve has the highest probability of successfully guessing the measurement result, and the quantum conditional minimum entropy H min (Q θ,δ |E)Satisfy:

[0036] H min (Q θ,δ |E)≥H min (Q δ ) |0> (1)

[0037] When the input quantum state is an ideal vacuum state, the measurement result is <0|x> 2 The mean is 0 and the variance is σ 2 = 1 / 2 Gaussian distribution, we can get the corresponding minimum entropy:

[0038]

[0039] The measurement resolution in vacuum units is represents the output voltage variance of pure vacuum noise. Therefore, the measurement accuracy δ is first estimated by the calibration procedure, and then the lower bound of the random number content that can be extracted from each measurement result can be estimated according to formula (1).

[0040] However, in actual systems, the sampling interval of the ADC is limited, and the lower bound of the quantum conditional minimum entropy given by formula (1) does not take into account the situation where the system output signal exceeds the ADC sampling interval. If the eavesdropper Eve uses this part of the information to carry out an eavesdropping attack, and the legitimate user Alice cannot accurately obtain the information that exceeds the sampling interval, and cannot use this data to accurately evaluate security parameters, then the actual security of the quantum random number generator system will be seriously threatened. Therefore, in order to improve the actual security of the source-independent quantum random number generator, it is necessary to consider the measurement saturation problem caused by the limited sampling interval of the ADC, and modify the estimation formula for the extractable random content accordingly. Combined with Figure 1 As shown, an embodiment of the present invention provides a randomness evaluation method for a continuous variable source-independent quantum random number generator based on a finite sampling interval, comprising the following steps:

[0041] S101: When the ADC sampling interval is limited, the signal beyond the ADC sampling interval will fall into the first and last quantization intervals of the ADC. In order to simplify the analysis and ensure the security of the output random number, all the measurement results falling into the first and last quantization intervals of the ADC are discarded, and the probability and probability that the measurement result of the unknown quantum state measurement falls into the first and last quantization intervals of the ADC are calculated;

[0042] S102: Based on the probability and calculated in the above steps, the lower bound of the random number content that can be extracted from each measurement result is given by the following formula:

[0043] H min (Q θ,δ |E)≥H min (Q δ ) |0> +log2(1-P) (3)

[0044] Where P represents the probability of the output signal of the unknown quantum state falling into the first and last quantization intervals of the ADC, which can be considered as the probability of the ADC measuring saturation. If the number of signals falling into the first and last sampling intervals of the ADC is N1, and the total number of ADC sampling signals is N, then P = N1 / N.

[0045] In addition, when the ADC sampling interval is limited, the minimum entropy corresponding to the ideal vacuum state of the input quantum state may not satisfy formula (2). When the ADC sampling interval is small, the probability that the measurement result falls in the first or last quantization interval of the ADC may be higher than the probability in the middle quantization interval, resulting in a higher probability of the measurement result being guessed, that is, Eve's maximum guess probability changes. Assume that the measurement result of the vacuum state satisfies the mean of 0 and the variance is Gaussian distribution, considering the influence of ADC sampling interval, the corresponding minimum entropy H of the measurement result min (Q δ ) |0> Should be corrected to

[0046]

[0047] Among them, i min and i max Indicates the first and last quantization sampling intervals of ADC. The ADC sampling interval is [-N-δ ADC / 2,N-δ ADC / 2]. Substituting formula (4) into formula (3), we can get the estimation formula of the modified quantum conditional minimum entropy.

[0048] Therefore, in a continuous variable source-independent quantum random number generator based on phase randomized local oscillator light, as long as the parameters δ and P are determined, the lower bound of the randomness content that can be extracted by the quantum random number generator system can be obtained.

[0049] Example 2

[0050] Figure 2 The schematic diagram of the experimental device of a continuous variable source-independent quantum random number generator based on phase randomized local oscillator light is shown. Figure 2 The experimental device is given. On the basis of the above embodiment, the embodiment of the present invention carries out the following simulation process to verify the effectiveness of the solution of the present invention.

[0051] (1) Calibration phase: Block the beams output by the gain-switched laser and the unknown quantum source, and obtain the electronic noise variance based on the output voltage data. Block the beam output by the unknown quantum source, turn on the gain-switched laser so that the output light pulse can be transmitted to the beam splitter, and obtain the total variance of vacuum noise and electronic noise based on the output voltage data. According to the voltage variance and The total variance of the vacuum noise is calculated as and the measurement resolution δ in vacuum units;

[0052] (2) Random number generation stage: Keep the optical pulse power output by the gain-switched laser unchanged, turn on the gain-switched laser and the unknown quantum source signal, and measure the total variance of the signal accordingly: The ADC discretizes and samples the electrical signal output by the balanced zero-beat detector, discards the data falling into the first and last sampling intervals of the ADC, obtains the original random number, and counts the data falling into the first and last sampling intervals of the ADC, recorded as N1, and the total number of ADC samples is N;

[0053] (3) Post-processing stage: Calculate the extractable randomness content H according to formula (3) min (Q δ |E), and then use the post-processing method to perform randomness extraction operations on the original random numbers to obtain secure true random numbers.

[0054] Assuming that the fractional ratio of the beam splitter satisfies 50:50, the quantum efficiency of the two photodetectors in the balanced zero-beat detector is η = 1. and unknown signal light The optical beam splitter performs complete interference. The two output light signals in the optical beam splitter are incident on the photodiode and converted into photocurrent signals. After differentiation, they are amplified by the gain G of the detector. The output voltage signal U can be expressed as

[0055]

[0056] Among them, the orthogonal components of the unknown signal light field The corresponding variance of the output voltage signal is

[0057]

[0058] Among them, |α LO | 2 Represents the number of photons of the local oscillator light. If the input signal is in vacuum state, according to The variance of vacuum noise can be obtained

[0059] Under the source-independent protocol, the input signal light may not be in a vacuum state, but in an unknown quantum state such as a thermal state or a compressed state. Then the total quantum noise variance of the measurement is Vacuum noise variance and other quantum noise variances Due to the non-ideal characteristics of the experimental device, classical electrical noise is inevitably introduced during the experiment. It is independent of quantum noise and is considered to conform to the Gaussian distribution. The variance of electronic noise is Therefore, when the input signal is in a vacuum state, the total noise variance of the measurement is When the input signal is an unknown quantum state, the total noise variance of the measurement is

[0060] Take the input unknown signal as an example, Then the continuous signal a output by the balanced homodyne detector satisfies the mean value μ ts , the variance is A Gaussian random variable with a probability density function of

[0061]

[0062] After ADC discrete sampling, the output discrete result a i The probability density function of

[0063]

[0064] where i min and i max Indicates the first and last quantization sampling intervals of the ADC.

[0065] In order to carry out numerical simulation analysis, the relevant parameters are set as follows: |α LO | 2 =5×10 8 , G = 2 × 10 -7 V / photon, then the vacuum noise variance The vacuum noise variance is normalized to Other quantum noise variances The variance of the classical electrical noise is The mean satisfies μ ts =0, ADC sampling accuracy n = 6, sampling range N = kσ ts According to formulas (2) and (3), the random number content H that can be extracted by the system without considering the limited sampling interval of the ADC and considering the limited sampling interval of the ADC can be estimated respectively: min (Q θ,δ |E).

[0066] Figure 3 The relationship between the extractable random number content under two conditions and the ADC sampling range when the mean of the measured signal is 0 is given. When the ADC sampling interval is small, if the estimation of the extractable random number content by the ADC limited sampling interval is not considered, the extractable random number content in the system will be overestimated. As the sampling interval increases, the probability of ADC measurement saturation gradually decreases until it approaches 0, and the extractable random number content estimated by the two methods tends to be the same. When considering the influence of the ADC limited sampling interval, the extractable random number content first increases and then decreases as the sampling interval increases. It can be seen that there is an optimal sampling interval.

[0067] According to the randomness evaluation method of the continuous variable source-independent quantum random number generator based on a finite sampling interval proposed by the present invention, the output signals falling in the first and last quantization intervals of the ADC are discarded, and an improved extractable random number content evaluation formula is given by estimating the ADC measurement saturation probability, thereby preventing the eavesdropper Eve from carrying out ADC sampling saturation attacks and further improving the actual security of the source-independent quantum random number generator system. At the same time, the method can also provide the optimal ADC sampling interval to improve the actual performance of the quantum random number generator.

[0068] Example 3

[0069] like Figure 4 As shown, an embodiment of the present invention provides a continuous variable source-independent quantum random number generator system based on a finite sampling interval, including: a data processing module, a randomness evaluation module and a post-processing module.

[0070] The data processing module is used to discard all the measurement results of the unknown quantum state measurement falling in the first and last quantization intervals of the analog-to-digital converter (ADC) for the unknown input quantum state when the sampling interval of the analog-to-digital converter (ADC) is limited, and obtain the original random number. The randomness evaluation module is used to calculate the lower bound of the corrected extractable random number content using the randomness evaluation method mentioned above; the post-processing module is used to use the lower bound of the corrected extractable random number content as a constraint condition and use the post-processing method to perform randomness extraction operations on the original random number to obtain a secure true random number.

[0071] In the existing source-independent quantum random number generator system based on randomized local oscillator light, the security problem introduced by the limited sampling interval of the ADC is not considered. In the improved source-independent quantum random number generator system based on randomized local oscillator light proposed in the present invention, the limited sampling interval of the actual ADC is considered, and the randomness evaluation formula is corrected by introducing the measurement saturation probability of the ADC, which can solve the security vulnerability problem introduced by the ADC saturation measurement, and optimize the ADC sampling interval parameters, further improving the actual security and performance of the system, and ensuring the security of the output random numbers.

[0072] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A randomness evaluation method for a continuous variable source-independent quantum random number generator based on a finite sampling interval, characterized in that: include: For an unknown input quantum state, when the sampling interval of an analog-to-digital converter (ADC) is limited, the probability and probability that the measurement result of the unknown quantum state falls within the first and last quantization intervals of the ADC are calculated, and based on the probability and probability, a lower bound of the random number content that can be extracted from the measurement result is corrected.

2. The randomness evaluation method of the continuous variable source-independent quantum random number generator based on a finite sampling interval according to claim 1 is characterized in that: The modified extractable random number content H min (Q θ,δ |E) is bounded by: H min (Q θ,δ |E)≥H min (Q δ ) |0> +log2(1-P) Among them, H min (Q δ ) |0> It represents the minimum entropy of the measurement result corresponding to the input vacuum state when the sampling interval of the analog-to-digital converter ADC is limited; P represents the probability and probability that the measurement result of the unknown quantum state falls into the first and last quantization intervals of the ADC; E represents the quantum system; Q represents the orthogonal component of the unknown quantum state, the subscript δ represents the measurement resolution of the ADC in vacuum units, and θ represents the phase angle of the current local oscillator light.

3. The randomness evaluation method of the continuous variable source-independent quantum random number generator based on a finite sampling interval according to claim 2 is characterized in that: The measurement results of the vacuum state are assumed to satisfy the mean value of 0 and the variance of Gaussian distribution, then when the sampling interval of the analog-to-digital converter ADC is limited, the minimum entropy H of the measurement result corresponding to the input vacuum state is calculated according to the following formula min (Q δ ) |0> : Among them, i min and i max Respectively represent the first and last quantization intervals of ADC. The ADC sampling interval is [-N-δ ADC / 2,N-δ ADC / 2], N is the total number of ADC sampling signals, δ ADC is the width of the minimum resolvable quantization interval of the ADC, σ v represents the standard deviation of vacuum noise, p guess represents the maximum guess probability of the eavesdropper about the measurement result, erf and erfc represent the error function and complementary error function respectively.

4. A continuous variable source-independent quantum random number generator system based on a finite sampling interval, characterized in that: include: A data processing module is used for discarding all the measurement results of the unknown quantum state measured in the first and last quantization intervals of the ADC when the sampling interval of the analog-to-digital converter ADC is limited, so as to obtain the original random number; A randomness evaluation module, used for calculating a lower bound of a modified extractable random number content using the randomness evaluation method according to any one of claims 1 to 3; The post-processing module is used to use the lower bound of the modified extractable random number content as a constraint condition to perform randomness extraction operations on the original random numbers using a post-processing method to obtain secure true random numbers.

Images