Random number post-processing method for quasi-polarization state entropy gain

Abstract

The invention relates to the field of random number post-processing, in particular to a random number post-processing method for quasi-polarization state entropy gains, which comprises the following steps of: taking an original photon column which is generated by a photon generator and carries bit information as a post-processing object, presetting a random bit seed, and constructing a polarizer, a filter and a decision maker according to the random bit seed; the original photon column is converted into a polarization state photon column through a polarizer and then input into a filter, and if the included angle between the polarization state photon column and the filter meets the specification, the filter directly outputs a result random number; otherwise, outputting the photon column to a decision maker, and outputting a final result random number by the decision maker. Quantum key distribution is used for reference, random bit seeds are introduced to carry out quasi-skewed entropy gain post-processing, real-time performance and wide applicability are achieved, output bit randomness is improved through asymmetric linear superposition, different random seed progressive operation is adopted, results gradually tend to be evenly distributed, and autocorrelation is reduced.

Description

Technical Field

[0001] The present invention relates to the field of random number post-processing. Background Art

[0002] Random numbers are non-deterministic sequences that satisfy certain statistical properties and lack periodicity or obvious patterns. They are widely used in fields such as defense and cryptography. Currently, widely used random number generators are inevitably affected by classical noise and hardware devices, resulting in raw random numbers that often contain bias and autocorrelation. This flaw compromises the effectiveness of random number applications. Therefore, post-processing techniques for raw random numbers to overcome these flaws have been a focus of research. Existing random number post-processing methods often struggle to balance performance (such as achieving NIST indicators, uniform distribution, and autocorrelation) with efficiency (such as run time). To ensure efficiency, they typically only perform a single operation on the raw random numbers, resulting in limited improvement in their randomness. Summary of the Invention

[0003] In order to overcome the problem that existing random number post-processing methods are difficult to achieve both processing effect and processing efficiency and have limited randomness improvement, the present invention provides a random number post-processing method with pseudo-polarization state entropy gain.

[0004] The technical solution adopted by the present invention to achieve the above-mentioned purpose is: a random number post-processing method of pseudo-polarization state entropy gain, comprising the following steps: S1. Setting the original random number to be post-processed to the original photon sequence carrying bit information generated by the photon generator; S2. Preset a random number sequence as a random bit seed, and use the random bit seed to construct a polarizer, a filter, and a decision maker; S3, inputting the original photon train into a polarizer, and the polarizer converting the original photon train into a polarized photon train; S4, inputting the polarized photon sequence into the filter. When the angle between the polarized photon sequence and the filter plate forms a specified angle, the filter outputs a random number resulting from post-processing. Otherwise, the filter outputs a filtered photon sequence and executes step S5. S5. Input the filtered photon sequence into the decision maker, and the decision maker outputs a random number of the result after the processing is completed.

[0005] Preferably, in step S3, the polarizer converts the original photon train into a polarization state vector, and the polarization state vector includes four directions, and the angles of the four directions are 0 degrees, 45 degrees, 90 degrees and 135 degrees respectively.

[0006] Preferably, in step S3, the first bit is repeated as a synchronization mark, and a two-bit fixed-length window is moved on the bit sequence, with the window moving one bit each time, and the polarization state of the input photon is determined according to a specific combination of bits in the window.

[0007] Preferably, in step S4, the first bit is used to repeatedly set the filter direction. When the polarization state photon is 0 degrees to the filter direction, the bit value corresponding to the polarization state photon is directly output. When the polarization state photon is 90 degrees to the filter direction, the bit value corresponding to the polarization state photon is inverted and output. When the polarization state photon is 45 degrees or 135 degrees to the filter direction, the polarization state photon is input into the decision maker.

[0008] Preferably, in step S5, if the current bit of the decision maker is 0, then 0 is output; otherwise, 1 is output.

[0009] The beneficial effects of the present invention are: The present invention draws on the quantum key distribution framework, introduces random bit seeds, and performs quasi-skewed entropy gain post-processing on the original random numbers. On the basis of passing the NIST indicators, it can have real-time performance, meet various application scenarios, and achieve both processing effect and processing efficiency; the present invention improves the randomness and unpredictability of the output bit sequence by asymmetric linear superposition of the input original random numbers, and achieves an entropy-enhanced output result; the present invention uses different random seeds to perform progressive operations on the original random numbers, so that the final processing results gradually tend to be uniformly distributed while passing the NIST indicators, the output results reduce the autocorrelation of the original random numbers, and the autocorrelation coefficient has no obvious change trend with the movement of delay time. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 is a flow chart of an embodiment of the present invention; Figure 2 2 is a schematic diagram of the experimental results of repeated operations on Gaussian distribution original random numbers according to an embodiment of the present invention; Figure 3 This is the experimental result of the embodiment of the present invention on the autocorrelation coefficient of the original random number of the Gaussian distribution; Figure 4 It is a schematic diagram of the execution process of an embodiment of the present invention. DETAILED DESCRIPTION

[0011] The embodiment of the present invention provides a random number post-processing method for pseudo-polarization state entropy gain, such as Figure 1 As shown, the following steps are included: S1. The original random number is a random bit sequence with a value of 0 or 1. The original random number to be post-processed is set to the original photon sequence carrying bit information generated by the photon generator, and the photon sequence length is n; S2. Pre-set the random number sequence as a random bit seed, and use the random bit seed to construct a polarizer, filter and decision maker. The random bit seed length of the polarizer and filter is n, which is consistent with the length of the photon column. The random bit seed length of the decision maker is 0.5n. The random bit seed length setting value here is for each input bit, giving it a specific polarization direction, and setting a corresponding filter direction to ensure a one-to-one mapping relationship between the input bit and the filter. The decision maker length is set to half the length of the input bit sequence because decision problems often present a probability characteristic close to a uniform distribution, that is, there is about a one-half probability of encountering a specific decision scenario.

[0012] S3. The original photon column is segmented and input into the polarizer in sequence. In the QKD framework, the polarizer converts the original photon column into a polarization state photon column, that is, the polarizer converts the original photon column into a polarization state vector. The polarization state vector contains four directions, and the angles of the four directions are 0 degrees, 45 degrees, 90 degrees and 135 degrees respectively. The two consecutive random bits 00 in the random bit seed of the polarizer represent 0 degrees, 10 represents 45 degrees, 11 represents 90 degrees, and 01 represents 135 degrees. The first bit is repeated as a synchronization mark at the starting position of encoding or decoding. A specific bit (or a group of bits) is repeatedly represented as a synchronization signal. After the synchronization signal, a fixed window of two bits in length is used to move on the bit sequence. Each time processing is performed, the two bits in the current window are considered. The fixed window slides bit by bit on the bit sequence. After each slide, the polarization state of the input photon is determined based on the specific combination of the two bits in the new window. The specific combinations of two bits include 00, 01, 10 and 11, which reduces the loss of random bit seeds and improves the efficiency of random number extraction.

[0013] S4. In this embodiment, the filter is similar to the receiving end in the QKD framework. The polarized photon sequence is input into the filter. When the angle between the polarized photon sequence and the filter plate is a specified angle, the filter outputs a photon sequence that is a random number resulting from the post-processing. Otherwise, the filter outputs a filtered photon sequence and executes step S5. The filter direction is set by repeating the first bit. When the polarization state photon is 0 degrees to the filter direction, the bit value corresponding to the polarization state photon is directly output. When the polarization state photon is 90 degrees to the filter direction, the bit value corresponding to the polarization state photon is inverted and output. When the polarization state photon is 45 degrees or 135 degrees to the filter direction, the polarization state photon is input into the decision maker to increase the randomness of the output random bit sequence.

[0014] S5. Input the filtered photon sequence into the decision maker. According to Malus's law, the probability of a photon passing through is 0.5 in this case. Whether it passes through is determined by the decision maker. If the current bit of the decision maker is 0, it outputs 0; otherwise, it outputs 1. The decision maker outputs a random number of the result after the processing is completed. The length of the output result number is n.

[0015] This embodiment provides the following calculation example: The segmented input original random number [10101101] passes through the polarizer [00101101], filter [01010101], and decider

[10001] of the random bit seed architecture, resulting in the final output [11010001]. Specifically, if Figure 4 As shown in the figure, if Polarizer = [00101101], then the directions of the polarizers are 00 (0 degrees), 00 (0 degrees), 01 (135 degrees), 10 (45 degrees), 01 (135 degrees), 11 (90 degrees), 10 (45 degrees), and 01 (135 degrees). If Filter = [01010101], then the directions of the filter are 00 (0 degrees), 01 (135 degrees), 10 (45 degrees), 01 (135 degrees), 10 (45 degrees), and 01 (135 degrees) according to the principle of first-place repetition. To determine the angle between the polarized photon and the filter, the polarizer and filter directions are XORed item by item, yielding the following judgment: [11 10 00 00 00 01 11 11]. When 00 (the third, fourth, and fifth items), the angle is 90 degrees; 01 or 10 (the second and sixth items), the angles are 45 and 135 degrees, respectively; and when 11 (the first, seventh, and eighth items), the angle is 0 degrees. For the case of 11, the corresponding photon is output; for the case of 00, the result is inverted and output. For the cases of 01 or 10, the output result is determined by the bit value of the decision maker: the second item outputs 1, and the sixth item outputs 0. In summary, the final output bit sequence is [11010001]. The execution process of this embodiment uses only the XOR operation in logical operations to operate on the input bits bit by bit, with a computational complexity of O(n). Therefore, the post-processing results can be repeatedly processed based on the application scenario, using a progressive method with different random seeds.

[0016] This embodiment draws on the quantum key distribution framework, introduces random bit seeds, and performs quasi-skewed entropy gain post-processing on the original random numbers. On the basis of passing the NIST indicators, it can have real-time performance, meet various application scenarios, and achieve both processing effects and processing effects. The experimental results and running time comparison results of this embodiment with the von Neumann post-processing method and the Toeplitz post-processing method are shown in the following table; this embodiment improves the randomness and unpredictability of the output bit sequence by performing asymmetric linear superposition on the input original random numbers, and achieves entropy-enhanced output results; this embodiment uses different random seeds to perform progressive operations on the original random numbers, so that the final processing results gradually tend to be uniformly distributed while passing the NIST indicators, such as Figure 2 As shown, the output result reduces the autocorrelation of the original random number, and as Figure 3 The autocorrelation coefficients shown do not show a clear trend as the delay time shifts.

[0017] ;

[0018] The present invention is described by way of example, and those skilled in the art will appreciate that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. Furthermore, under the teachings of the present invention, these features and embodiments may be modified to suit specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are intended to be within the scope of the present invention.

Claims

1. A random number post-processing method for pseudo-polarization state entropy gain, characterized in that: The following steps are involved: S1. Setting the original random number to be post-processed to the original photon sequence carrying bit information generated by the photon generator; S2. Preset a random number sequence as a random bit seed, and use the random bit seed to construct a polarizer, a filter, and a decision maker; S3, inputting the original photon train into a polarizer, and the polarizer converting the original photon train into a polarized photon train; S4, inputting the polarized photon sequence into the filter. When the angle between the polarized photon sequence and the filter plate forms a specified angle, the filter outputs a random number resulting from post-processing. Otherwise, the filter outputs a filtered photon sequence and executes step S5. S5. Input the filtered photon sequence into the decision maker, and the decision maker outputs a random number of the result after the processing is completed.

2. The random number post-processing method of pseudo-polarization state entropy gain according to claim 1, characterized in that: In step S3, the polarizer converts the original photon column into a polarization state vector. The polarization state vector includes four directions, and the angles of the four directions are 0 degrees, 45 degrees, 90 degrees and 135 degrees respectively.

3. The random number post-processing method of pseudo-polarization state entropy gain according to claim 1, characterized in that: In step S3, the first bit is repeated as a synchronization mark, and a two-bit fixed-length window is moved on the bit sequence. The window moves one bit each time, and the polarization state of the input photon is determined according to the specific combination of bits in the window.

4. The random number post-processing method of pseudo-polarization state entropy gain according to claim 1, characterized in that: In step S4, the first bit is used to repeatedly set the filter direction. When the polarization state photon is 0 degrees to the filter direction, the bit value corresponding to the polarization state photon is directly output. When the polarization state photon is 90 degrees to the filter direction, the bit value corresponding to the polarization state photon is inverted and output. When the polarization state photon is 45 degrees or 135 degrees to the filter direction, the polarization state photon is input into the decision maker.

5. The random number post-processing method of pseudo-polarization state entropy gain according to claim 1, characterized in that: In step S5, if the current bit of the decision maker is 0, 0 is output; otherwise, 1 is output.

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