A random number post-processing method for quasi-polarization state entropy gain

Abstract

The present application relates to the field of random number post-processing, in particular to a random number post-processing method with polarization state entropy gain, which takes the original photon series carrying bit information generated by a photon generator as a post-processing object, sets a random bit seed in advance, and constructs a polarizer, a filter and a decision maker according to the random bit seed, the original photon series is converted into a polarization state photon series by the polarizer, and then is input into the filter, if the included angle between the polarization state photon series and the filter meets the regulation, the filter directly outputs the result random number, otherwise, the output photon series is input into the decision maker, and the final result random number is output by the decision maker. The present application learns from quantum key distribution, introduces a random bit seed for post-processing with polarization state entropy gain, has real-time performance and wide applicability, improves the output bit randomness through asymmetric linear superposition, uses different random seeds for progressive operation, makes the result gradually tend to uniform distribution, and reduces autocorrelation.

Description

Technical Field

[0001] This invention relates to the field of random number post-processing. Background Technology

[0002] Random numbers are non-deterministic sequences that satisfy certain statistical properties and do not exhibit 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 limitations, resulting in raw random numbers that always contain bias and autocorrelation. This deficiency affects the effectiveness of random number applications. Therefore, post-processing techniques for raw random numbers to overcome these shortcomings have been a key focus for researchers. Existing random number post-processing methods typically struggle to simultaneously achieve both high processing effectiveness (NIST metric achievement, uniform distribution, autocorrelation, etc.) and high processing efficiency (running time). Furthermore, to ensure processing efficiency, only a single operation can usually be performed on the raw random numbers, resulting in limited improvement in the randomness of the raw numbers. Summary of the Invention

[0003] To overcome the problem that existing random number post-processing methods struggle to achieve both processing effectiveness and efficiency while offering limited improvement in randomness, this 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 objectives is: a random number post-processing method for pseudo-polarization state entropy gain, comprising the following steps:

[0005] S1. Set the original random number that needs to be post-processed to the original photon sequence carrying bit information generated by the photon generator.

[0006] S2. Pre-set the random number sequence as a random bit seed, and use the random bit seed to construct the bias generator, filter and decision unit;

[0007] S3. Input the original photon train into the polarizer, and the polarizer converts the original photon train into a polarized photon train.

[0008] S4. Input the polarized photon array into the filter. When the angle between the polarized photon array and the filter plate is at a specified angle, the filter outputs a random number of the processed result. Otherwise, the filter outputs the filtered photon array and proceeds to step S5.

[0009] S5. Input the filtered photon sequence into the decision generator, and the decision generator outputs a random number of the processed result.

[0010] Preferably, in step S3, the polarizer converts the original photon column into a polarization state vector, which contains four directions with angles of 0 degrees, 45 degrees, 90 degrees and 135 degrees respectively.

[0011] Preferably, in step S3, the first bit is repeated as a synchronization marker, and a two-bit fixed-length window moves through the bit sequence, moving one bit each time, and the polarization state of the input photon is determined according to the specific combination of bits within the window.

[0012] Preferably, in step S4, the filter direction is set by repeating the first bit. When the polarized photon is at 0 degrees to the filter direction, the bit value corresponding to the polarized photon is directly output. When the polarized photon is at 90 degrees to the filter direction, the bit value corresponding to the polarized photon is inverted and output. When the polarized photon is at 45 degrees or 135 degrees to the filter direction, the polarized photon is input into the decision unit.

[0013] Preferably, in step S5, if the current bit of the decision-maker is 0, then output 0; otherwise, output 1.

[0014] The beneficial effects of this invention are as follows:

[0015] This invention draws upon the quantum key distribution framework, introduces random bit seeds, and performs quasi-biased entropy gain post-processing on the original random numbers. It achieves real-time performance while meeting NIST performance standards, satisfying various application scenarios and realizing a balance between processing effectiveness and efficiency. Furthermore, by performing asymmetric linear superposition on the input original random numbers, this invention enhances the randomness and unpredictability of the output bit sequence, achieving entropy-enhanced output results. Finally, by employing a progressive operation on the original random numbers using different random seeds, this invention achieves a gradually uniform distribution of the final processing result while meeting NIST performance standards. The output result reduces the autocorrelation of the original random numbers, and the autocorrelation coefficient does not show a significant change trend with the shift in latency. Attached Figure Description

[0016] Figure 1 This is a flowchart of an embodiment of the present invention;

[0017] Figure 2 This is a schematic diagram of the experimental results of iterative operations on Gaussian distributed raw random numbers according to an embodiment of the present invention;

[0018] Figure 3 These are experimental results from embodiments of the present invention regarding the autocorrelation coefficient of Gaussian distributed raw random numbers;

[0019] Figure 4 This is a schematic diagram of the execution process of an embodiment of the present invention. Detailed Implementation

[0020] Embodiments of the present invention provide a random number post-processing method for pseudo-polarization state entropy gain, such as... Figure 1 As shown, it includes the following steps:

[0021] S1. The original random number is a random bit sequence with a value of 0 or 1. The original random number that needs to be post-processed is set to the original photon sequence carrying bit information generated by the photon generator, and the length of the photon sequence is n.

[0022] S2. A random number sequence is pre-set as a random bit seed. The random bit seed is used 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 sequence. The random bit seed length of the decision-maker is 0.5n. Here, the random bit seed length is set to assign a specific polarization direction to each input bit and set a corresponding filter direction to ensure a one-to-one mapping relationship between the input bits and the filter. The length of the decision-maker is set to half the length of the input bit sequence because decision problems often exhibit a near-uniform probability distribution, that is, there is about a 1 / 2 probability of encountering a specific decision scenario.

[0023] S3. The original photon train is segmented and sequentially input into the polarizer. In the QKD framework, the polarizer converts the original photon train into a polarized photon train, that is, it converts the original photon train into a polarization vector. The polarization vector contains four directions with angles of 0 degrees, 45 degrees, 90 degrees, and 135 degrees. In the random bit seed of the polarizer, consecutive two random bits (00 for 0 degrees, 10 for 45 degrees, 11 for 90 degrees, and 01 for 135 degrees) are used. The first bit is repeated as a synchronization marker at the beginning of encoding or decoding. A specific bit (or a set 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 across the bit sequence. During each processing, the two bits in the current window are considered. The fixed window slides bit by bit across 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 combination of the two bits includes 00, 01, 10, and 11, which reduces the loss of the random bit seed and improves the efficiency of random number extraction.

[0024] S4. In this embodiment, the filter is similar to the receiver in the QKD framework. The polarized photon array is input into the filter. When the angle between the polarized photon array and the filter plate is a specified angle, the filter outputs a random number of the result after processing. Otherwise, the filter outputs a filtered photon array and proceeds to step S5.

[0025] The filter direction is set by repeating the first bit. When the polarized photon is at 0 degrees to the filter direction, the bit value corresponding to the polarized photon is directly output. When the polarized photon is at 90 degrees to the filter direction, the bit value corresponding to the polarized photon is inverted and output. When the polarized photon is at 45 degrees or 135 degrees to the filter direction, the polarized photon is input into the decision unit to increase the randomness of the output random bit sequence.

[0026] S5. Input the filtered photon sequence into the decision-maker. According to Malus's law, the probability of photon transmission in this case is 0.5. Whether to transmit or not is determined by the decision-maker. If the current bit of the decision-maker is 0, output 0; otherwise, output 1. After the decision-maker finishes outputting, it processes the result into a random number. The length of the output result number is n.

[0027] The following calculation example is provided in this embodiment:

[0028] The pre-segmented input random number [10101101] is passed through a polarizer (Polarizer=[00101101]), a filter (Filter=[01010101]), and a decisioner (Decider=

[10001] ) constructed from random bit seeds, to obtain the final output result Output=[11010001].

[0029] Specifically, such as Figure 4As shown, with Polarizer=[00101101], the polarizer directions 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) according to the first-first repetition principle. With Filter=[01010101], the filter directions are 00 (0 degrees), 01 (135 degrees), 10 (45 degrees), 01 (135 degrees), 10 (45 degrees), 01 (135 degrees), 10 (45 degrees), and 01 (135 degrees) according to the first-first repetition principle. To determine the angle between the polarized photon and the filter, the polarizer direction and the filter direction are XORed sequentially to obtain the following criteria: [11 10 00 00 00 01 11 11]. When 00 (the third, fourth, and fifth terms), the angle is 90 degrees; 01 or 10 (the second and sixth terms) indicate angles of 45 degrees and 135 degrees respectively; when 11 (the first, seventh, and eighth terms), 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 based on the bit value of the decision unit: the second term outputs 1, and the sixth term outputs 0. In summary, the final output bit sequence is [11010001]. This embodiment only uses the XOR operation in logical operations to perform bit-by-bit operations on the input bits, with a computational complexity of O(n). Therefore, the post-processing results can be iteratively processed according to the application scenario, i.e., iterative processing can be performed using different random seeds.

[0030] This embodiment draws upon the quantum key distribution framework, introducing random bit seeds and performing quasi-skewed entropy gain post-processing on the original random numbers. It achieves both real-time performance and meets various application scenarios while passing the NIST index, thus realizing a balance between processing efficiency and performance. The experimental results and runtime comparisons of this embodiment with the von Neumann and Toplitz post-processing methods are shown in the table below. This embodiment enhances the randomness and unpredictability of the output bit sequence by performing asymmetric linear superposition on the input original random numbers, achieving entropy-enhanced output results. This embodiment uses a progressive operation on the original random numbers with different random seeds, achieving a gradually more uniform distribution of the final processing result while still meeting the NIST index. Figure 2 As shown, the output reduces the autocorrelation of the original random numbers, and as... Figure 3 The autocorrelation coefficient shown does not exhibit a significant trend of change with the shift in time delay.

[0031] ;

[0032] This invention has been described through embodiments. Those skilled in the art will understand that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Furthermore, under the teachings of this invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the invention. Therefore, this invention is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of this invention.

Claims

1. A method of post-processing a random number with a quasi-polar state entropy gain, characterized in that, The method comprises the following steps: S1, setting an original random number needing post-processing as an original photon sequence carrying bit information generated by a photon generator; S2, setting a random number sequence as a random bit seed, and using the random bit seed to construct a polarizer, a filter and a decision maker; specifically, the random bit seed length for constructing the polarizer and the filter is consistent with the original photon sequence length, and the random bit seed length for constructing the decision maker is 0.5 times the original photon sequence length; when constructing the polarizer, the polarization direction is defined by the combination of two continuous bits in the random bit seed, and when constructing the filter, the filter direction is defined by the combination of two continuous bits in the random bit seed; S3, inputting the original photon sequence into the polarizer, and converting the original photon sequence into a polarization state photon sequence by the polarizer; S4, inputting the polarization state photon sequence into the filter, and when the included angle between the polarization state photon sequence and the filter is a specified angle, the filter outputs a result random number after post-processing, otherwise, the filter outputs a filtered photon sequence, and step S5 is implemented; S5, inputting the filtered photon sequence into the decision maker, and outputting a result random number after post-processing by the decision maker.

2. The method of claim 1, wherein the method further comprises: In the step S3, the polarizer converts the original photon sequence into a polarization state vector, and the polarization state vector contains four directions, and the four direction angles are 0 degrees, 45 degrees, 90 degrees and 135 degrees.

3. The method of claim 1, wherein the method further comprises: In the step S3, the first bit repetition is used as a synchronization mark, and a two-bit fixed-length window is moved on the bit sequence, the window is moved one bit each time, and the polarization state of the input photon is determined according to the combination of the bits in the window; specifically, the combination 00 corresponds to a 0-degree polarization state, the combination 10 corresponds to a 45-degree polarization state, the combination 11 corresponds to a 90-degree polarization state, and the combination 01 corresponds to a 135-degree polarization state.

4. The method of claim 1 wherein the post-processing of the random number with the pseudo-polarization state entropy gain is characterized by, In the step S4, the first bit repetition is used to set the filter direction, when the polarization state photon and the filter direction are 0 degrees, the bit value corresponding to the polarization state photon is directly outputted, when the polarization state photon and the filter direction are 90 degrees, the bit value corresponding to the polarization state photon is outputted after being inverted, and when the polarization state photon and the filter direction are 45 degrees or 135 degrees, the polarization state photon is inputted into the decision maker.

5. The method of claim 1 wherein, In the step S5, if the current bit of the decision maker is 0, 0 is outputted; otherwise, 1 is outputted.

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