A source-independent quantum random number generation method

Abstract

The application discloses a kind of source-independent quantum random number generation methods, it mainly is how to complete the task of generating new random number under the premise that source equipment is not trusted in preparation quantum state using quantum access code model.First, using enough times of input on model, record corresponding output, estimate input-output probability by the frequency of input-output statistics;Second, the probability is substituted into a specific expression, and the so-called three-dimensional quantum witness value will be obtained;Third, according to the quantum witness value, optimization algorithm is carried out, and the randomness of random number is obtained;Finally, according to random number extraction machine, the real quantum random number is obtained.The application solves the shortcomings of the existing method, such as low efficiency of quantum random number generation, difficulty in preparing ideal quantum state, etc.

Description

Technical Field

[0001] This invention belongs to the field of cryptography and relates to encryption algorithms, particularly to a source-independent quantum random number generation method. Background Technology

[0002] In cryptography, random numbers are widely used as keys or cryptographic resources in information security systems, making their research increasingly important. With the development of computing technology and cryptography, information security applications not only require generators capable of outputting various forms of random numbers, but also necessitate more in-depth research and analysis of the randomness of random numbers to provide theoretical support for related applications.

[0003] Currently, with the rapid development of information technology, the demand for highly secure random numbers is gradually increasing. Random numbers generated by classical theory are deterministic; once an adversary knows the algorithm and starting conditions, they lose their randomness. Unlike classical theory, quantum theory possesses intrinsic randomness. Even if an adversary knows the random generation mechanism and its conditions, they still cannot control all random numbers. Therefore, quantum random numbers have higher security.

[0004] This invention utilizes three-dimensional quantum states and quantum measurement to construct a quantum random number generation mechanism. Even if an adversary acquires the quantum state preparation equipment, they can still generate secure random numbers. Random number generation curves are also provided. This actively promotes the practical application of quantum random number generators, especially in the key generation stage of encryption algorithms. It can be used to generate random numbers and extend existing random numbers. Summary of the Invention

[0005] Purpose of the invention: In cryptography, existing technologies suffer from low efficiency in generating quantum random numbers and difficulties in preparing ideal quantum states. This invention provides a source-independent quantum random number generation method, which improves the efficiency and practicality of random number generation.

[0006] Technical Solution: A source-independent quantum random number generation method generates new random numbers under the premise that the source device for preparing the quantum state is untrusted. The method is based on the source-device-independent quantum random number extension of the quantum random access code of the three-dimensional quantum state. First, based on the input and output of the quantum access code model, the input and output probabilities are estimated by statistically analyzing the frequencies of the input and output. Second, a three-dimensional quantum sighting value is calculated based on this probability. Third, based on the quantum sighting value, an optimization algorithm is performed to obtain the randomness of the random number. Finally, a true quantum random number is obtained using a random number scrambling machine.

[0007] The method utilizes a quantum state preparation device and a measurement device. The quantum state preparation device sends a three-dimensional quantum state to the measurement device, which then measures the received three-dimensional quantum state using mutually unbiased bases and outputs the result. Specifically, the method includes the following steps:

[0008] (1) Establish a three-dimensional quantum eyewitness account based on the probability distribution observed by the measuring equipment, determine the degree of attack by the adversary, and obtain the lower bound of the minimum entropy through the following optimization algorithm:

[0009]

[0010] Make: ;

[0011]

[0012] (2) Combine the lower bound of minimum entropy and generate random number strings through a randomness extractor.

[0013] Furthermore, the method involves two parties, Alice and Bob. Alice possesses an untrusted quantum state preparation device, determines the preparation of a three-dimensional quantum state, and then sends the prepared state to Bob. Bob possesses a trustworthy measurement device, which measures the received state using mutually unbiased bases and outputs the measurement results.

[0014] The specific handling process between Alice and Bob is as follows:

[0015] (a) Alice selects completely randomly As input, among which Alice then based on the input Preparing quantum states, adversaries This may interfere with the preparation of the quantum state, resulting in a quantum state. ,in It is the enemy's attack plan, and , Finally, Alice transmits the quantum state through a quantum channel. Send to Bob;

[0016] (b) After receiving the quantum state, Bob randomly selects the input. Then, based on mutually unbiased basis pairs of states Perform measurement and output the measurement results. ,in,

[0017]

[0018] .

[0019] The method described above, which uses three-dimensional quantum witnessing to determine the extent of an adversary's attack, includes the following steps:

[0020] (11) Statistics The frequency of occurrence is used to estimate the probability distribution. In theory, ;

[0021] (12) Construct a three-dimensional quantum witness Its expression is as follows:

[0022] ,

[0023] (13) The probability distribution estimated in step (11) can be used to calculate the following: The value;

[0024] Among them, the measurement Bob chose View as a guess The Bit information, output result Consider it a guess. It's about guessing the probability of success;

[0025] Based on quantum random access code theory, it is known that if the adversary possesses all of them... If all of them are interfered with into classical information, then If the enemy has all Interference is transformed into quantum information, then .

[0026] Furthermore, step (2) quantifies the randomness contained in the measurement results by using minimal entropy, and generates a random number string using a randomness extractor, as follows:

[0027] (21) Through a minimal entropy function To quantify the randomness of measurement results, where:

[0028] .

[0029] Minimal entropy depends only on the maximum probability in the probability distribution;

[0030] (22) Three-dimensional quantum witnessing was obtained through observation and calculation. The value of is determined by iterating through all available probability distributions and then considering the minimum entropy, thereby determining the minimum amount of randomness that should be included in the output.

[0031] Its optimization process traverses all three-dimensional Hilbert spaces by Selected quantum state and by and The defined measurement method with mutually unbiased bases ultimately yields a lower bound for the minimum entropy;

[0032] (23) Based on the obtained minimum entropy lower bound, the randomness extractor obtains the true random number.

[0033] Furthermore, the mathematical expression of step (22) for calculating the lower bound of the minimum entropy is as follows:

[0034]

[0035] Make: ;

[0036] .

[0037] Beneficial Effects: This invention provides a source-independent quantum random number generation method. Based on three-dimensional quantum random access codes, this method leverages the intrinsic randomness of quantum theory to generate highly secure random numbers, suitable for information processing tasks requiring high security. This invention serves as a solution for random number generation on untrusted devices. For the first time, it elevates the quantum state from two-dimensional to three-dimensional, significantly improving the efficiency of random number generation. Regarding quantum state preparation, only the generated three-dimensional quantum state is required. By introducing hidden parameters to represent the unknown influence on the preparation of the quantum state, the requirements for the precision of the preparation equipment are greatly reduced. Finally, optimized calculations provide function graphs of minimum entropy and quantum witness, allowing for rapid identification of the corresponding minimum entropy based on the graph, facilitating the determination of randomness in practice. Attached Figure Description

[0038] Figure 1 This is a model diagram illustrating an embodiment of the present invention;

[0039] Figure 2 This is a diagram showing the relationship between quantum witnessing and minimum entropy in the method described in this invention. Detailed Implementation

[0040] To illustrate the technical solutions disclosed in this invention in detail, the following description is provided in conjunction with the accompanying drawings.

[0041] First, combining existing cryptographic techniques, this invention aims to address the problem that the classical world is inherently deterministic, and random numbers generated within the classical framework are pseudo-random. The quantum world possesses intrinsic randomness and can generate truly random numbers. However, existing methods suffer from drawbacks such as low efficiency in quantum random number generation and difficulty in preparing ideal quantum states. Compared to existing methods, this invention improves the efficiency and practicality of random number generation.

[0042] This invention provides a source-independent quantum random number generation method, which mainly utilizes a quantum access code model to achieve the task of generating new random numbers under the premise that the source device for preparing the quantum state is untrusted. First, by performing a sufficient number of inputs on the model and recording the corresponding outputs, the input-output probabilities are estimated by statistically analyzing the input-output frequencies. Second, this probability is substituted into a specific expression to obtain the so-called three-dimensional quantum sighting value. Third, based on this quantum sighting value, an optimization algorithm is performed to determine the randomness of the random numbers. Finally, using a random number scrambler, the true quantum random number is obtained.

[0043] This invention is a source-device-independent quantum random number expansion method based on three-dimensional quantum state quantum random access codes, combined with... Figure 1 This involves a two-party system based on Alice and Bob. Alice possesses an untrusted quantum state preparation device, which can only confirm that a three-dimensional quantum state is being prepared. She then sends the prepared state to Bob, who possesses a trustworthy measurement device. Bob measures the received state using mutually unbiased basis functions and outputs the measurement results. A three-dimensional quantum witness is constructed by statistically analyzing the input-output frequencies to measure the degree of attack on the quantum state preparation device. The efficiency of random number generation is measured using a minimum entropy function. An optimization algorithm is then used to provide an image and analytical relationship between the three-dimensional quantum witness and the lower bound of the minimum entropy. The specific steps are as follows:

[0044] 1) Alice uses an untrusted source device to prepare a three-dimensional quantum state, while Bob uses a trusted measurement device composed of mutually unbiased bases to measure the quantum state.

[0045] 11) Alice is selected completely randomly. As input Alice then based on the input Preparing quantum states, adversaries This may interfere with the preparation of the quantum state, thus, the quantum state is obtained. ,in It is the enemy's attack plan, and , Finally, Alice transmits the quantum state via a quantum channel. Send it to Bob.

[0046] 12) After receiving the quantum state, Bob randomly selects the input. Then, using mutually unbiased basis pairs... Perform measurement and output the measurement results. ,in,

[0047]

[0048]

[0049] 2) Construct a three-dimensional quantum eyewitness using the observed probability distribution to determine the extent of the adversary's attack.

[0050] 21) Repeat step 1) more than 1000 times and count the results. The frequency of occurrence is used to estimate the probability distribution. In theory, .

[0051] 22) A three-dimensional quantum witness was constructed. ,

[0052] ,

[0053] 23) Based on the probability distribution estimated in step 21), the following can be calculated: The value of .

[0054] It should be noted that Bob chose the measurement View as a guess The Bit information, output result If we consider it a guess, then It's about guessing the probability of success. Based on quantum random access code theory, we know that if the adversary has all... If all the interference is converted into classic information, then:

[0055]

[0056] If the enemy has all Interference is transformed into quantum information, then

[0057] .

[0058] 3) The randomness in the measurement results is quantified by using minimum entropy, and a randomness extractor is used to generate random number strings.

[0059] 31) Through a minimal entropy function To quantify the randomness of measurement results, where

[0060] .

[0061] Note that the minimum entropy is only related to the maximum probability in the probability distribution.

[0062] 32) In step 2), a three-dimensional quantum eyewitness was obtained through observation and calculation. The value of is hereby explained, and it can be obtained that multiple different probability distributions can yield the same value. Therefore, this invention traverses all obtainable probability distributions and then considers the lowest minimum entropy to determine the minimum randomness that the output should contain. Its optimization process traverses all three-dimensional Hilbert spaces... Selected quantum state and by and The defined measurement method with mutually unbiased bases ultimately yields a lower bound for the minimum entropy. This process can be expressed as:

[0063]

[0064] Make: ;

[0065] .

[0066] Furthermore, the following diagram showing the relationship between three-dimensional quantum witnessing and the lower bound of minimal entropy can be obtained, as follows: Figure 2 As shown.

[0067] 33) After obtaining the lower bound of the minimum entropy, use a randomness extractor to obtain truly random numbers.

[0068] Based on the lower bound of the minimum entropy, a random number string can be obtained by using a randomness extractor, which is unpredictable.

[0069] This invention presents a method for generating new random numbers under the premise that the source device for preparing quantum states is untrusted, and provides the relationship between observation data and random number generation rate based on the proposed optimization algorithm and quantum witnessing.

Claims

1. A source-independent quantum random number generation method, which generates new random numbers under the premise that the source device for preparing the quantum state is untrusted, characterized in that: The method is a source-device-independent quantum random number generation based on quantum random access codes of three-dimensional quantum states. First, based on the input and output of the quantum access code model, the input and output probabilities are estimated by statistically analyzing the frequencies of the input and output. Second, a three-dimensional quantum sighting value is calculated based on this probability. Then, based on the quantum sighting value, an optimization algorithm is performed to obtain the randomness of the random number. Finally, using a random number generator, true quantum random numbers are obtained; The method includes a quantum state preparation device and a measurement device. The quantum state preparation device sends a three-dimensional quantum state to the measurement device, and the measurement device measures the received three-dimensional quantum state using mutually unbiased bases and outputs the result. Specifically, the method includes the following steps: (1) Establish a three-dimensional quantum eyewitness account based on the probability distribution observed by the measuring equipment, determine the degree of attack by the adversary, and obtain the lower bound of the minimum entropy through the following optimization algorithm: Make: ; (2) Combine the lower bound of minimum entropy and generate random number strings through a randomness extractor; Furthermore, this method determines the extent of an adversary's attack through three-dimensional quantum witnessing, including the following process: (11) Statistics The frequency of occurrence is used to estimate the probability distribution. In theory, ; (12) Construct a three-dimensional quantum witness Its expression is as follows: ， (13) Calculate the probability distribution estimated in step (11). The value; Among them, the measurement Bob chose View as a guess The Bit information, output result Consider it a guess. It's about guessing the probability of success; Based on quantum random access code theory, it is known that if the adversary possesses all of them... If all of them are interfered with into classical information, then If the enemy has all Interference is transformed into quantum information, then .

2. The source-independent quantum random number generation method according to claim 1, characterized in that: The scenario involves Alice and Bob. Alice possesses an untrusted quantum state preparation device, which determines the preparation of a three-dimensional quantum state. She then sends the prepared state to Bob, who possesses a trustworthy measurement device. Bob measures the received state using mutually unbiased bases and outputs the measurement results.

3. The source-independent quantum random number generation method according to claim 2, characterized in that: The specific handling process between Alice and Bob is as follows: (a) Alice selects completely randomly As input, among which Alice then based on the input Preparing quantum states, adversaries This may interfere with the preparation of the quantum state, resulting in a quantum state. ,in It is the enemy's attack plan, and , Finally, Alice transmits the quantum state through a quantum channel. Send to Bob; (b) After receiving the quantum state, Bob randomly selects the input. Then, based on mutually unbiased basis pairs of states Perform measurement and output the measurement results. ,in, 。 4. The source-independent quantum random number generation method according to claim 1, characterized in that: Step (2) quantifies the randomness in the measurement results using minimal entropy, and generates random number strings using a randomness extractor, as follows: (21) Through a minimal entropy function To quantify the randomness of measurement results, where: Minimal entropy depends only on the maximum probability in the probability distribution; (22) Three-dimensional quantum witnessing was obtained through observation and calculation. The value of is determined by iterating through all available probability distributions and then considering the minimum entropy, thereby determining the minimum amount of randomness that should be included in the output. Its optimization process traverses all three-dimensional Hilbert spaces by Selected quantum state and by and The defined measurement method with mutually unbiased bases ultimately yields a lower bound for the minimum entropy; (23) Based on the obtained minimum entropy lower bound, the randomness extractor obtains the true random number.

5. The source-independent quantum random number generation method according to claim 4, characterized in that: The mathematical expression for calculating the lower bound of the minimum entropy in step (22) is as follows: Make: ; 。

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