A new pseudo-random number generation method based on multi-time-delay non-adjacent coupled lattices

Abstract

The invention discloses a novel pseudo-random number generation method based on multi-time-delay non-adjacent coupled lattices, comprising generating a chaotic sequence by cascading Logistic mapping and piecewise linear mapping (PWLCM); using an unscented Kalman filter algorithm to measure the errors of Chebyshev mapping and Logistic mapping, and compensating for the precision loss by adding random disturbances; using a time-delay time-varying function to disturb the time direction of the non-adjacent coupled mapping lattices, and solving the problems of short-period phenomenon, narrow parameter range and blank window occurring in the chaotic system by using a cascaded multiple chaos and error compensation method.

Description

Technical Field

[0001] The invention belongs to the field of information security, discloses a novel pseudo-random number generation method, and specifically relates to a novel pseudo-random number generation method based on multi-time-delay non-adjacent coupling lattices. Background Art

[0002] Pseudo-random sequences play a very important role in the field of information security. For example, in image encryption algorithms based on block ciphers, many researchers use pseudo-random sequences as key generators, and in stream ciphers, pseudo-random sequences are directly involved in the encryption process. In previous studies, we can conclude that "the performance of pseudo-random sequences can affect the security of an encryption system." Therefore, it is necessary to design a secure and efficient pseudo-random number generator.

[0003] Most pseudo-random number generators are generated by linear congruential generation, m-sequence generation, nonlinear congruential generation, Mersenne Twister generation, BBS sequence generation and sequence cryptography algorithms, based on coupled ordinary differential equations and cellular automata. These pseudo-random generators are very efficient in computer hardware, but the quality of the generated pseudo-random sequences is very worrying. For example, in a linear feedback shift register, the maximum period of the pseudo-random sequence is only 2n-1.

[0004] In addition to these pseudo-random sequence generators, many scholars have proposed new pseudo-random sequence generators in recent years. Pseudo-random generators designed based on chaos theory have become a new research hotspot, because the nonlinearity, non-periodicity, ergodicity, noise-likeness, initial value sensitivity and unpredictability of chaotic systems provide a theoretical basis for pseudo-random generators. Wang Xingyuan proposed a couple map lattice based on discrete chaotic iteration (CMLDCI) system in "A new pseudo-random number generator based on CML and chaoticiteration". Julian first proposed to use time-delay differential equations to simulate Brownian motion to construct a pseudo-random sequence generator, and passed the Big crush test project in TestU01. Although the pseudo-random sequence generator proposed by Julian does not have an obvious advantage in time, his scheme has no specific restrictions on generating numerical values. In the paper "Anovel pseudo-random number generator from coupled map lattice with time-varying delay", Liao Xiaofeng et al. introduced time-varying functions into coupled lattice mapping and proposed a pseudo-random sequence generator based on coupled lattice mapping. They used a series of experiments such as SP800-22 test and TestU01 test to measure the pseudo-random sequence.

[0005] However, in digital circuit design, due to the influence of truncation error, the digital chaotic system will deviate from the predetermined track during the iteration process, resulting in chaotic degradation behavior. Digital chaotic system refers to the simulation of chaotic system on the computer. However, due to the accuracy of the computer, the values ​​that can be evolved in theory cannot be calculated on the computer, resulting in short-cycle phenomena or blank windows. Therefore, how to overcome the problems of short-cycle phenomena, narrow parameter range and blank windows in chaotic systems has become a new research direction. Summary of the invention

[0006] The present invention is aimed at the problems of short-period phenomenon, narrow parameter range and blank window in chaotic systems in the prior art, and provides a novel pseudo-random number generation method based on multi-time-delay non-adjacent coupled lattices, including generating chaotic sequences by cascading Logistic mapping and piecewise linear mapping (PWLCM); using an unscented Kalman filter algorithm to measure the errors of Chebyshev mapping and Logistic mapping, and compensating for the precision loss by adding random disturbances; using a time-delay time-varying function to perturb the time direction of non-adjacent coupled mapping lattices, so as to solve the problem of uneven distribution of period windows and pseudo-random sequences in the iterative process of chaos, and can effectively combat the chaotic degradation behavior of chaotic systems.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is: a new pseudo-random number generation method based on multi-time-delay non-adjacent coupled grids, comprising the following steps:

[0008] S1, set system parameters: set the unscented Kalman filter parameters and Logistic, Chebyshev functions, grid number and iteration number;

[0009] S2, construct the state equation and observation equation of the unscented Kalman filter to measure the Logistic function and Chebyshev function, and set the precision value of the quantization function;

[0010] S3, calculate the mean and variance of the state prediction, sample the prediction system, determine the sampling points, calculate the mean and covariance estimates of the sampling points; use the sampling points to perform nonlinear transfer on the Logistic function and Chebyshev function, and calculate the mean and variance of the prediction;

[0011] S4, measurement update, using the K-time sampling points and corresponding weights obtained in step S3 to calculate the mean, variance and covariance, and then calculate the filter gain, state estimate and estimated variance at time K+1, and obtain the state estimate values ​​of Logistic and Chebyshev;

[0012] S5, construct a time-varying system and generate disturbance weights: substitute the state estimation values ​​of Logistic and Chebyshev obtained in step S4 into the time-delay time-varying function to obtain disturbance weights; add the calculated disturbance weight value to the initial value given in step S1;

[0013] S6, substituting the disturbance weights, state estimation values, etc. calculated in steps S4 and S5 into the non-adjacent coupling lattice function to generate random numbers.

[0014] As an improvement of the present invention, the step S2 further comprises:

[0015] S21, after iterating the Logistic mapping and Chebyshev mapping for a specified number of times, the mean and variance of the iterated sequence are calculated;

[0016] S22, construct the state equation and observation equation of the unscented Kalman filter to measure the Logistic map and Chebyshev map;

[0017] S23, setting the precision value of the quantization function.

[0018] As an improvement of the present invention, the step S3 further comprises:

[0019] S31, select the Sigma sampling points of the Logistic map and Chebyshev map, assuming that there are 2n+1 Sigma sampling points, and use the following formula to calculate

[0020]

[0021] The corresponding mean weight and variance weight are:

[0022]

[0023] Where k is the scaling factor between the mean and the distance between Sigma sampling points; is the matrix (n+k)P x,x The i-th row or column of the square root matrix after Cholesky decomposition;

[0024] S32, using the proportional correction sampling strategy, calculate the 2n+1 sampling points χ′ of the Logistic and Chebyshev mappings respectively i And the corresponding weights and

[0025] As another improvement of the present invention, the step S4 further comprises:

[0026] S41, using the observation equations of the Logistic and Chebyshev mapping constructed in step S22 and the corresponding weights calculated in step S32, calculate the mean, variance and covariance corresponding to the k-th moment;

[0027] S42, using the mean, variance and covariance at time k calculated in step S41, calculate the filter gain at time k+1, as well as the state estimate and estimated variance, to obtain the state estimate of the Logistic;

[0028] S44, using the mean, variance and covariance at time k calculated in step S41, calculate the filter gain at time k+1, as well as the state estimate and estimated variance, to obtain the Chebyshev state estimate.

[0029] As a further improvement of the present invention, step S5 further comprises:

[0030] S51, construct the Chebyshev map τ using the system parameters specified in S1 1 and Sine map τ 2 of time-delay time-varying systems;

[0031] S52, performing a modulo 1 operation on the sum of the grid initial value and the state estimation value to obtain a new disturbance weight λ.

[0032] As a further improvement of the present invention, step S6 further comprises:

[0033] S61, using the system parameters of step S1, constructing a Logistic map, a Chebyshev map, and a LPWLCM map of a new pseudo-random number generator for multi-time-delay non-adjacent coupled lattices;

[0034] S62, the Logistic state estimation value in S43, the Chebyshev state estimation value in S44 and the disturbance weight in S52 are input into a new pseudo-random number generator of multi-time-delay non-adjacent coupled lattices to calculate a pseudo-random sequence.

[0035] Compared with the prior art: the novel pseudo-random number generation method based on multi-time-delay non-adjacent coupled lattices disclosed in the present invention, firstly, proposes a Logistic-PWLCM mapping by cascading Logistic mapping and piecewise linear mapping (PWLCM), which effectively solves the chaotic period window problem and the pseudo-random sequence distribution is more uniform than the Logistic mapping; secondly, an unscented Kalman filter algorithm is used to measure the error of the Chebyshev mapping and the Logistic mapping, and the chaotic degradation behavior of the spatiotemporal chaotic system is effectively counteracted by adding disturbances; in addition, a time-delay time-varying function based on the Chebyshev and Sine mapping is proposed, and the time direction of the non-adjacent coupled mapping lattice is disturbed by this function, which improves the complexity of the proposed system. The method solves the problem of uneven distribution of period windows and pseudo-random sequences that appear in the iterative process of chaos, and can effectively counteract the chaotic degradation behavior of the chaotic system, and can be applied to cryptographic fields such as digital signatures, key generation, hash-based message authentication codes, and deterministic random bit generators. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1It is a flow chart of the steps of the novel pseudo-random number generation method based on multi-time-delay non-adjacent coupled grids of the present invention;

[0037] Figure 2 This is a detailed algorithm flow chart of Example 1 of the present invention. DETAILED DESCRIPTION

[0038] The present invention will be further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0039] Example 1

[0040] DESCRIPTION OF SYMBOLS

[0041]

[0042] A new pseudo-random number generation method based on multi-time-delay non-adjacent coupled lattices, such as Figure 1 As shown, the pseudo-random number generation method proposed in the present invention is divided into three parts. The first part is to set the Logistic equation, the Chebyshev equation and the system initial value, and construct an unscented Kalman filter to perform nonlinear prediction on the Logistic equation and the Chebyshev equation to obtain the state estimation values ​​of the Logistic and Chebyshev, involving steps S1-S4; the second part is to calculate the disturbance weight generated by the time-delay time-varying system, involving step S5; the third part is the pseudo-random number generation process, using a multi-time-delay non-adjacent coupled lattice formula to generate pseudo-random numbers, involving step S6.

[0043] Step S1, setting system parameters, includes the following sub-steps:

[0044] S11, construct the state equation and observation equation for Logistic mapping. The state equation needs to set a non-zero mean sequence, and the observation equation sets a non-zero mean sequence, which is different from the non-zero mean sequence of the state equation; similarly, construct the state equation and observation equation for nonlinear prediction of the Chebyshev equation, and the state equation needs to set a non-zero mean sequence;

[0045] S12, set the number of lattices L of the multi-delay non-adjacent coupled lattice mapping, the initial value x of the Logistic mapping and Chebyshev mapping 1 , x 2 , and the number of iterations of the system N1.

[0046] Step S2, constructing the state equation and observation equation of the unscented Kalman filter to measure the Logistic function and the Chebyshev function, and setting the precision value of the quantization function, includes the following sub-steps:

[0047] (2.1) Construct the state equation for nonlinear prediction of Chebyshev equation. The state equation is:

[0048] x i+1 =B(cos(w×arccos(x i )),P)+w k ,

[0049] in P = 8;

[0050] (2.2) Construct the observation equation for nonlinear prediction of Chebyshev equation. The observation equation is:

[0051] y i =B(x i ,P)+v k ,

[0052] in P = 16;

[0053] (2.3) Construct the state equation for nonlinear prediction of the Logistic equation. The state equation is:

[0054] x i+1 =B(μx i (1-x i ),P)+w k ,

[0055] in P = 8;

[0056] (2.4) Construct the observation equation for nonlinear prediction of the Logistic equation. The observation equation is:

[0057] y i =B(x i ,P)+v k ,

[0058] in P = 16;

[0059] Step S3, calculate the mean and variance in the state prediction process, sample the prediction system, determine the sampling points, and calculate the mean of the sampling points and the covariance estimate P 0,0 ; Use sampling points to perform nonlinear transfer on the Logistic function and Chebyshev function to calculate the predicted mean and variance, including the following sub-steps:

[0060] (3.1) Iterate the Logistic equation, and the value after n iterations is recorded as x 0 ;

[0061] (3.2) Calculate x 0 The mean and variance of

[0062]

[0063] (3.3) Iterate the Chebyshev function n times and record the value x after iteration 0 ;

[0064] (3.4) Calculate x 0 The mean and variance P 0,0 ,

[0065]

[0066] (3.5) Select the sampling points of Logistic and Chebyshev functions Sigma, and the calculation formula is as follows:

[0067]

[0068] Assume that the number of sampling points is l=2n, and there are 2n+1 Sigma sampling points in total, where k is the proportional factor between the mean and the distance between the Sigma sampling points. is the matrix (n+k)P x,x The square root matrix after Cholesky decomposition.

[0069] (3.6) Calculate the mean weight and variance weight corresponding to the sampling points of the Logistic and Chebyshev functions Sigma. The formula is as follows:

[0070]

[0071] (3.7) Use sampling points to perform nonlinear transfer on the Logistic function and Chebyshev, the formula is as follows: γ i k+1|k =f(χ i ), f() is the state equation of Logistic and Chebyshev in S21 and S23.

[0072] (3.8) Calculate the mean and variance of the state prediction of the Logistic and Chebyshev functions, the formula is as follows:

[0073]

[0074] Step S4, measurement update, using the K-time sampling points and corresponding weights obtained in S3 to calculate the mean, variance and covariance, and then calculate the filter gain, state estimate and estimated variance at the K+1 time, and obtain the Logistic and Chebyshev state estimates;

[0075] (4.1) Use the 2n+1 sampling points of the Logistic equation calculated in S3 Predicted mean and variance P k+1,k The observation equation is used to calculate the predicted value of the sampling point. The calculation formula is: h() is the observation equation of Logistic in S12.

[0076] (4.2) ζ obtained using S41 i k+1,k Calculate the mean, variance, and covariance using the following formula:

[0077]

[0078] (4.3) Using z calculated in S42 k+1 , calculate the filter gain K at time k+1 k+1 , as well as the state estimate and estimated variance, the formula is as follows:

[0079]

[0080] Get the state estimate of Logistic

[0081] (4.4) Using the 2n+1 sampling points of the Chebyshev equation calculated in S3 The predicted mean and variance P k+1,k , use the observation equation to calculate the predicted value of the sampling point, the calculation formula is: h() is the observation equation of Chebyshev in S14.

[0082] (4.5) ζ obtained using S41 i k+1,k Calculate the mean, variance, and covariance using the following formula:

[0083]

[0084] (4.6) Using z calculated in S42 k+1 , calculate the filter gain K at time k+1 k+1 , as well as the state estimate and estimated variance, the formula is as follows:

[0085]

[0086] Get Chebyshev's state estimate

[0087] Step S5, constructing a time-varying system and generating disturbance weights: substituting the state estimation values ​​of Logistic and Chebyshev obtained in step S4 into the time-delay time-varying function to obtain disturbance weights; adding the calculated disturbance weight value and the initial value given in step S1, including the following sub-steps:

[0088] (5.1) The time-delayed time-varying Chebyshev Map is used to calculate the delay parameter, which is defined as follows:

[0089]

[0090] Where N is the total delay and n is the current time.

[0091] (5.2) The delay parameter is calculated using the new time-delayed time-varying Sine Map, which is defined as follows:

[0092]

[0093] Where N is the total delay and n is the current time.

[0094] (5.3) Use the time-varying system to generate the perturbation weight λ, as follows:

[0095]

[0096] LATTICE is the number of grids in the multi-delay non-adjacent coupled grids;

[0097] (5.4) Calculate the state value, the formula is as follows:

[0098]

[0099] x(n,i) and x(n,j) are the initial values ​​of the grid

[0100] Step S6, substituting the disturbance weights and state estimation values ​​calculated in S4 and S5 into the non-adjacent coupling lattice function, and calculating and generating random numbers includes the following sub-steps:

[0101] (6.1) Define the multi-time-delay non-adjacent coupled lattice formula:

[0102]

[0103] in:

[0104]

[0105] (6.2) Substitute the values ​​calculated by S4 and S5 into S61 to generate a pseudo-random number.

[0106] It should be noted that the above content only illustrates the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications all fall within the protection scope of the claims of the present invention.

Claims

1. A novel pseudo-random number generation method based on multi-time-delay non-adjacent coupled lattices, characterized in that: The steps include: S1, set system parameters: set the unscented Kalman filter parameters and Logistic, Chebyshev functions, grid number and iteration number; S2, construct the state equation and observation equation of the unscented Kalman filter to measure the Logistic function and Chebyshev function, and set the precision value of the quantization function; S3, calculate the mean and variance of the state prediction, sample the prediction system, determine the sampling points, and calculate the mean of the sampling points and the covariance estimate P 0,0 ; Use sampling points to perform nonlinear transfer on the Logistic function and Chebyshev function to calculate the predicted mean and variance; including the following sub-steps: S31: Iterate the Logistic equation, and the value after n iterations is recorded as x0; S32: Calculate the mean and variance of x0, S33: Iterate the Chebyshev function n times and record the value x0 after iteration; S34: Calculate the mean of x0 and variance P 0,0 , S35: Select the sampling points of Logistic and Chebyshev functions Sigma, and the calculation formula is as follows: Assume that the number of sampling points is l=2n, and there are 2n+1 Sigma sampling points in total, where k is the proportional factor between the mean and the distance between Sigma sampling points. is the matrix P x,x (n+k) square root matrix after Cholesky decomposition; S36: Calculate the mean weight and variance weight corresponding to the sampling points of the Logistic and Chebyshev functions Sigma. The formula is as follows: S37: Use sampling points to perform nonlinear transfer on the Logistic function and Chebyshev, the formula is as follows: γ i k+1,k =f(χ i ), f() is the state equation of Logistic and Chebyshev; S38: Calculate the mean and variance of the state predictions of the Logistic and Chebyshev functions, the formula is as follows: S4, measurement update, using the K-time sampling points and corresponding weights obtained in step S3 to calculate the mean, variance and covariance, and then calculate the filter gain, state estimate and estimated variance at time K+1, and obtain the state estimate values ​​of Logistic and Chebyshev; S5, construct a time-varying system and generate disturbance weights: substitute the state estimation values ​​of Logistic and Chebyshev obtained in step S4 into the time-delay time-varying function to obtain disturbance weights; add the calculated disturbance weight value to the initial value given in step S1; It includes the following sub-steps: S51: Use the time-delayed time-varying Chebyshev Map to calculate the delay parameters, which are defined as follows: Where N is the total delay and n is the current time; S52: Calculate the delay parameters using the new time-delay time-varying Sine Map, which is defined as follows: Where N is the total delay and n is the current time; S53: Use the time-varying system to generate the perturbation weight λ, the formula is as follows: LATTICE is the number of grids in the multi-delay non-adjacent coupled grids; S54: Calculate the status value, the formula is as follows: x(n,i) and x(n,j) are the initial values ​​of the grid; S6, substituting the disturbance weight and state estimation value calculated in step S4 and step S5 into the non-adjacent coupling lattice function to calculate and generate a random number; comprising the following sub-steps: S61: Define the multi-time-delay non-adjacent coupled grid formulation: in: S62: Substitute the values ​​calculated in S4 and S5 into S61 to generate a pseudo-random number.

2. The novel pseudo-random number generation method based on multi-time-delay non-adjacent coupled grids as claimed in claim 1, characterized in that The step S1 further comprises: S11, construct the state equation and observation equation for Logistic mapping. The state equation needs to set a non-zero mean sequence, and the observation equation sets a non-zero mean sequence, which is different from the non-zero mean sequence of the state equation; similarly, construct the state equation and observation equation for nonlinear prediction of the Chebyshev equation, and the state equation needs to set a non-zero mean sequence; S12, set the number of lattices L of the multi-delay non-adjacent coupled lattice mapping, the initial value x of the Logistic mapping and Chebyshev mapping i , and the number of iterations of the system.

3. The novel pseudo-random number generation method based on multi-time-delay non-adjacent coupled grids as claimed in claim 1, characterized in that The step S2 further comprises: S21, after iterating the Logistic mapping and Chebyshev mapping for a specified number of times, the mean and variance of the iterated sequence are calculated; S22, construct the state equation and observation equation of the unscented Kalman filter to measure the Logistic map and Chebyshev map; S23, setting the precision value of the quantization function.

4. The novel pseudo-random number generation method based on multi-time-delay non-adjacent coupled grids as claimed in claim 3 is characterized in that The step S4 further comprises: S41, using the observation equations of the Logistic and Chebyshev mapping constructed in step S22 and the corresponding weights calculated in step S32, calculate the mean, variance and covariance corresponding to the k-th moment; S42, using the k-time mean value calculated in step S41, calculate the filter gain at time k+1, as well as the state estimate and the estimated variance, to obtain the state estimate of the Logistic; S43, using the mean value at time k calculated in step S41, calculate the filter gain at time k+1, as well as the state estimate and the estimated variance, to obtain the Chebyshev state estimate.

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