CN114710262A - Novel pseudo-random number generation method based on multi-time-lag non-adjacent coupling lattices - Google Patents
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Abstract
The invention discloses a novel pseudo-random number generation method based on a multi-time-lag non-adjacent coupling lattice, which comprises the steps of generating a chaotic sequence by cascading Logistic mapping and piecewise linear mapping (PWLCM); error measurement is carried out on the Chebyshev mapping and the Logistic mapping by using an unscented Kalman filtering algorithm, and the precision loss is compensated by adding random disturbance; the time-delay time-varying function is used for disturbing the time direction of the non-adjacent coupling mapping lattices, and the problems of short period, narrow parameter range, blank windows and the like of the chaotic system are solved by using a method of cascading multiple chaos and error compensation.
Description
Technical Field
The invention belongs to the field of information security, discloses a novel pseudo random number generation method, and particularly relates to a novel pseudo random number generation method based on a multi-time-lag non-adjacent coupling lattice.
Background
Pseudo-random sequences play a very important role in the field of information security, for example, in block cipher-based image encryption algorithms, many researchers use pseudo-random sequences as key generators, whereas in stream ciphers, pseudo-random sequences are more directly involved in the encryption process. In previous studies, we could conclude that the performance of the pseudorandom sequence could affect the security of a cryptographic system. Therefore, it is necessary to design a secure and efficient pseudo-random number generator.
The pseudo-random number generator is mostly generated by a linear congruence generation method, an m sequence generation method, a nonlinear congruence generation method, a Mersene Twister generation algorithm, a BBS sequence generation algorithm and a sequence cipher algorithm, and is based on a coupled ordinary differential equation, a cellular automaton and the like. These pseudo-random generators are very computationally efficient in computer hardware, but the quality of the pseudo-random sequence produced is of great concern. For example, in a linear feedback shift register, the maximum period of the pseudo-random sequence is only 2 n-1.
In addition to these pseudo-random sequence generators, many scholars have recently introduced new pseudo-random sequence generators. The pseudo-random generator designed based on the chaos theory becomes a new research hotspot, and the properties of nonlinearity, non-periodicity, ergodicity, noise-like property, initial value item sensitivity, unpredictability and the like of the chaotic system provide theoretical basis for the pseudo-random generator. In the New pseudo-random number generator based on CML and kinetic iteration, the Wang proposes a manifold based on discrete kinetic iteration (CMLDCI) system. Julian first proposed to construct a pseudo-random sequence generator using time-lapse differential equations to mimic brownian motion and passed the Big sink test item in TestU 01. Although the pseudo-random sequence generator proposed by Julian has no significant advantage in time, his solution has no specific limitations in generating values. Liaoxianfeng et al, in A novel pseudo-random number generator from coupled grid mapping delay, introduced a time-varying function into the coupled grid mapping, and proposed a pseudo-random sequence generator based on the coupled grid mapping, which uses a series of experiments such as SP800-22 test and TestU01 test to measure the pseudo-random sequence.
However, in the digital circuit design, due to the influence of truncation errors, the digital chaotic system can deviate from a preset track in the iteration process, and chaotic degradation behaviors are caused. The digital chaotic system is a chaotic system which is simulated on a computer, however, the precision problem of the computer can cause a numerical value which can be completely evolved theoretically, the numerical value cannot be calculated in the computer, and the situation of a short period phenomenon or a blank window can occur. Therefore, how to overcome the problems of short period phenomenon, narrow parameter range, blank window and the like of the chaotic system becomes a new research direction.
Disclosure of Invention
The invention provides a novel pseudo random number generation method based on a multi-time-lag non-adjacent coupling lattice aiming at the problems of short period phenomenon, narrow parameter range, blank window and the like of a chaotic system in the prior art, and the method comprises the steps of generating a chaotic sequence by cascading Logistic mapping and piecewise linear mapping (PWLCM); error measurement is carried out on the Chebyshev mapping and the Logistic mapping by using an unscented Kalman filtering algorithm, and the precision loss is compensated by adding random disturbance; time-lag time-varying functions are used for disturbing the time direction of non-adjacent coupling mapping lattices, the problem that the cycle window and the pseudo-random sequence are not uniformly distributed in the iterative process of chaos is solved, and the chaos degradation behavior of a chaotic system can be effectively resisted.
In order to achieve the purpose, the invention adopts the technical scheme that: the novel pseudo-random number generation method based on the multi-time-lag non-adjacent coupling lattices comprises the following steps:
s1, setting system parameters: setting unscented Kalman filter parameters, Logistic, Chebyshev functions, lattice numbers and iteration times;
s2, constructing a state equation and an observation equation of an unscented Kalman filter for measuring a Logistic function and a Chebyshev function, and setting the precision value of a quantization function;
s3, calculating the mean and variance of the state prediction, sampling the prediction system, determining sampling points, and calculating the mean and covariance estimation of the sampling points; carrying out nonlinear transfer on the Logistic function and the Chebyshev function by using a sampling point, and calculating a predicted mean value and a predicted variance;
s4, measuring and updating, namely calculating a mean value, a variance and a covariance by using the sampling points at the K moment obtained in the step S3 and the corresponding weights, and further calculating a filtering gain, a state estimation and an estimation variance at the K +1 moment to obtain state estimation values of Logistic and Chebyshev;
s5, constructing a time-varying system, generating a disturbance weight: substituting the state estimation values of Logistic and Chebyshev obtained in the step S4 into a time-lag time-varying function to obtain a disturbance weight; adding the calculated disturbance weight value to the initial value given in step S1;
and S6, substituting the disturbance weight value, the state estimation value and the like obtained in the steps S4 and S5 into the non-adjacent coupling lattice function, and calculating and generating a random number.
As a refinement of the present invention, the step S2 further includes:
s21, after iterating the Logistic mapping and the Chebyshev mapping for a specified number of times, counting the mean value and the variance of the iterated sequence;
s22, constructing a state equation and an observation equation of unscented Kalman filter measurement Logistic mapping and Chebyshev mapping;
s23, setting the precision value of the quantization function.
As a modification of the present invention, the step S3 further includes:
s31, selecting Sigma sampling points of Logistic mapping and Chebyshev mapping, and calculating by using the following formula under the assumption that 2n +1 Sigma sampling points are provided
The corresponding mean weight and variance weight are:
where k is a scaling factor of the distance between the mean and the Sigma sample points;
is the matrix (n + k) Px,xThe ith row or column of the square root matrix after Cholesky decomposition;
s32, calculating 2n +1 sampling points χ 'of Logistic and Chebyshev mapping respectively by using a proportional modified sampling strategy'iAnd the corresponding weight value
And
as another improvement of the present invention, the step S4 further includes:
s41, calculating the mean, variance and covariance of the corresponding k time by using the observation equation of Logistic and Chebyshev mapping constructed in the step S22 and the corresponding weight calculated in the step S32;
s42, calculating the filtering gain at the k +1 moment, and the state estimation and estimation variance by using the k moment mean, variance and covariance calculated in the step S41 to obtain a Logistic state estimation value;
and S44, calculating the filter gain at the k +1 moment and the state estimation and estimation variance by using the mean, variance and covariance at the k moment calculated in the step S41 to obtain a state estimation value of Chebyshev.
As a further improvement of the present invention, the step S5 further includes:
s51, constructing Chebyshev mapping tau by using system parameters specified in S11And Sine mapping τ2Time-lapse time-varying systems of (a);
and S52, performing 1 operation on the sum of the initial lattice value and the state estimation value to obtain a new disturbance weight lambda.
As a further improvement of the present invention, the step S6 further includes:
s61, constructing Logistic mapping, Chebyshev mapping and LPWLCM mapping of a novel pseudo random number generator of a multi-lag non-adjacent coupling grid by using the system parameters of the step S1;
and S62, inputting the state estimation value of Logistic in S43, the state estimation value of Chebyshev in S44 and the disturbance weight of S52 into a novel pseudo-random number generator of a multi-time-lag non-adjacent coupling grid, and calculating to obtain a pseudo-random sequence.
Compared with the prior art: the invention discloses a novel pseudo-random number generation method based on a multi-time-lag non-adjacent coupling lattice, which comprises the following steps of firstly, providing Logistic-PWLCM mapping through cascading Logistic mapping and piecewise linear mapping (PWLCM), effectively solving the problem of a chaotic period window, and enabling pseudo-random sequence distribution to be more uniform than the Logistic mapping; secondly, error measurement is carried out on the Chebyshev mapping and the Logistic mapping by using an unscented Kalman filtering algorithm, and the chaotic degradation behavior of the space-time chaotic system is effectively resisted by adding disturbance; in addition, a time-lag time-varying function based on Chebyshev and Sine mapping is provided, the time direction of non-adjacent coupling mapping grids is disturbed, the complexity of the system provided by the inventor is improved, the method solves the problem that the cycle window and the pseudo-random sequence are not uniformly distributed in the iteration process of chaos, can effectively resist the chaos degradation behavior of the chaos system, and can be applied to the password fields of digital signatures, key generation, hash-based message authentication codes, deterministic random bit generators and the like.
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FIG. 1 is a flow chart of the steps of the novel pseudo random number generation method based on multi-lag non-adjacent coupled lattices;
fig. 2 is a detailed algorithm flowchart of embodiment 1 of the present invention.
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention.
Example 1
Description of the embodiments
A novel pseudo-random number generation method based on a multi-time-lag non-adjacent coupling lattice is disclosed, as shown in figure 1, the pseudo-random number generation method provided by the invention is divided into three parts, the first part is to set a Logistic equation, a Chebyshev equation and a system initial value, construct an unscented Kalman filter to perform nonlinear prediction on the Logistic equation and the Chebyshev equation to obtain state estimation values of the Logistic equation and the Chebyshev, and the method relates to steps S1-S4; the second part is to calculate the time-varying system of time lag and produce the disturbance weight, involve step S5; the third part is a pseudo-random number generation process, which generates pseudo-random numbers using a multi-lag non-adjacent coupled lattice formula, involving step S6.
Step S1, setting system parameters, including the following sub-steps:
s11, constructing a state equation and an observation equation for Logistic mapping, wherein the state equation needs to be provided with a non-zero mean sequence, and the observation equation is provided with a non-zero mean sequence which is different from the non-zero mean sequence of the state equation; similarly, a state equation and an observation equation for carrying out nonlinear prediction on the Chebyshev equation are constructed, and the state equation needs to be provided with a nonzero mean value sequence;
s12, setting the grid number L of the multi-lag non-adjacent coupling grid mapping, the initial value x of the Logistic mapping and the Chebyshev mapping1，x2And the number of iterations of the system N1.
Step S2, constructing a state equation and an observation equation of the unscented Kalman filter for measuring Logistic function and Chebyshev function, and setting the precision value of the quantization function, wherein the method comprises the following substeps:
(2.1) constructing a state equation for carrying out nonlinear prediction on the Chebyshev equation, wherein the state equation is as follows:
xi+1＝B(cos(w×arccos(xi)),P)+wk，
wherein
P＝8；
(2.2) constructing an observation equation for carrying out nonlinear prediction on the Chebyshev equation, wherein the observation equation is as follows:
yi＝B(xi,P)+vk，
wherein
P＝16；
(2.3) constructing a state equation for carrying out nonlinear prediction on the Logistic equation, wherein the state equation is as follows:
xi+1＝B(μxi(1-xi),P)+wk，
wherein
P＝8；
(2.4) constructing an observation equation for carrying out nonlinear prediction on the Logistic equation, wherein the observation equation is as follows:
yi＝B(xi,P)+vk，
wherein
P＝16；
Step S3, calculating the mean and variance in the state prediction process, sampling the prediction system, determining the sampling points, calculating the mean of the sampling points
Estimation of sum covariance P0,0(ii) a Carrying out nonlinear transfer on a Logistic function and a Chebyshev function by using a sampling point, and calculating a predicted mean value and a predicted variance, wherein the method comprises the following sub-steps:
(3.1) iterating Logistic equation, and recording the value after iterating n times as x0；
(3.2) calculating x0The mean and the variance of (a) is,
(3.3) iterating the Chebyshev function n times, and recording the iterated value x0；
(3.4) calculating x0Mean value of
Sum variance P0,0，
(3.5) sampling points of Logistic and Chebyshev functions Sigma are selected, and the calculation formula is as follows:
assuming that the number of samples is 2n, the Sigma samples are 2n +1 in total, where k is a scaling factor of the distance between the mean and the Sigma sample.
Is the matrix (n + k) Px,xSquare root matrix after Cholesky decomposition.
(3.6) calculating a mean weight and a variance weight corresponding to the Logistic function and the Chebyshev function Sigma sampling point, wherein the formula is as follows:
(3.7) nonlinear transfer of Logistic functions and Chebyshev using sampling points, the formula is as follows: gamma rayi k+1|k＝f(χi) And f () is the state equation for Logistic and Chebyshev in S21 and S23.
(3.8) calculating the mean and variance of the Logistic and Chebyshev function state prediction, wherein the formula is as follows:
step S4, measuring and updating, namely calculating a mean value, a variance and a covariance by using the sampling points at the K moment obtained in the step S3 and corresponding weights, and further calculating a filtering gain, a state estimation and an estimation variance at the K +1 moment to obtain state estimation values of Logistic and Chebyshev;
(4.1) 2n +1 sample points of Logistic equation calculated in S3
Predicted mean value
Sum variance Pk+1,kAnd (3) calculating the predicted value of the sampling point by using an observation equation, wherein the calculation formula is as follows:
h () is the observation equation of Logistic in S12.
(4.2) Zeta obtained by Using S41i k+1,kCalculating the mean, variance and covariance according to the following formula:
(4.3) Using z calculated in S42k+1Calculating the filter gain K at the time K +1k+1And state estimates and estimated variances, the formula is as follows:
obtaining the state estimation value of Logistic
(4.4) 2n +1 sample points of the Chebyshev equation calculated in S3
Predicted mean value
Sum variance Pk+1,kAnd calculating the predicted value of the sampling point by using an observation equation, wherein the calculation formula is as follows:
h () is the observation equation of Chebyshev in S14.
(4.5) Zeta obtained by Using S41i k+1,kCalculating the mean, variance and covariance according to the following formula:
(4.6) Using z calculated in S42k+1Calculating the filter gain K at the time K +1k+1And state estimates and estimated variances, the formula is as follows:
obtaining a state estimation value of Chebyshev
Step S5, constructing a time-varying system, generating a disturbance weight: substituting the state estimation values of Logistic and Chebyshev obtained in the step S4 into a time-lag time-varying function to obtain a disturbance weight; adding the calculated disturbance weight value to the initial value given in step S1, including the following sub-steps:
(5.1) calculating a delay parameter using a time-lapse Chebyshev Map, defined as follows:
where N is the total delay and N is the current time.
(5.2) calculating a delay parameter by using the new time-lapse varying Sine Map, and defining the time-lapse parameter as follows:
where N is the total delay and N is the current time.
(5.3) generating the disturbance weight λ using a time-varying system, the formula being:
LATTICE is the number of grids of the multi-lag non-adjacent coupled grid;
(5.4) calculating a state value, wherein the formula is as follows:
x (n, i) and x (n, j) are the initial values of the grid
Step S6, substituting the disturbance weight, the state estimation value, and the like calculated in S4 and S5 into the non-adjacent coupling lattice function, and calculating and generating the random number includes the following substeps:
(6.1) defining a multiple-lag non-adjacent coupling lattice formula:
wherein:
(6.2) substituting the values obtained in S4 and S5 into S61 to generate pseudo random numbers.
It should be noted that the above-mentioned contents only illustrate the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and it is obvious to those skilled in the art that several modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations fall within the protection scope of the claims of the present invention.
Claims (7)
1. The novel pseudo-random number generation method based on the multi-time-lag non-adjacent coupling lattices is characterized by comprising the following steps of:
s1, setting system parameters: setting unscented Kalman filter parameters, Logistic, Chebyshev functions, lattice numbers and iteration times;
s2, constructing a state equation and an observation equation of an unscented Kalman filter for measuring a Logistic function and a Chebyshev function, and setting the precision value of a quantization function;
s3, calculating the mean and variance of the state prediction, sampling the prediction system, determining sampling points, and calculating the mean and covariance estimation of the sampling points; carrying out nonlinear transfer on a Logistic function and a Chebyshev function by using a sampling point, and calculating a predicted mean value and a predicted variance;
s4, measuring and updating, namely calculating a mean value, a variance and a covariance by using the sampling points at the K moment obtained in the step S3 and the corresponding weights, and further calculating a filtering gain, a state estimation and an estimation variance at the K +1 moment to obtain state estimation values of Logistic and Chebyshev;
s5, constructing a time-varying system, generating a disturbance weight: substituting the state estimation values of Logistic and Chebyshev obtained in the step S4 into a time-lag time-varying function to obtain a disturbance weight; adding the calculated disturbance weight value to the initial value given in step S1;
and S6, substituting the disturbance weight value, the state estimation value and the like obtained in the steps S4 and S5 into the non-adjacent coupling lattice function, and calculating and generating a random number.
2. The novel pseudo-random number generation method based on multi-lag non-adjacent coupled lattices as claimed in claim 1, wherein the step S1 further comprises:
s11, constructing a state equation and an observation equation for Logistic mapping, wherein the state equation needs to be provided with a non-zero mean sequence, and the observation equation is provided with a non-zero mean sequence which is different from the non-zero mean sequence of the state equation; similarly, a state equation and an observation equation for carrying out nonlinear prediction on the Chebyshev equation are constructed, and the state equation needs to be provided with a nonzero mean value sequence;
s12, setting the grid number L of the multi-lag non-adjacent coupling grid mapping, the initial value x of the Logistic mapping and the Chebyshev mappingiAnd the number of iterations of the system.
3. The novel pseudo-random number generation method based on multi-lag non-adjacent coupled lattices as claimed in claim 1, wherein the step S2 further comprises:
s21, after iterating the Logistic mapping and the Chebyshev mapping for a specified number of times, counting the mean value and the variance of the iterated sequence;
s22, constructing a state equation and an observation equation of unscented Kalman filter measurement Logistic mapping and Chebyshev mapping;
s23, setting the precision value of the quantization function.
4. The novel pseudo-random number generation method based on multi-lag non-adjacent coupled lattices as claimed in claim 1, wherein the step S3 further comprises:
s31, selecting Sigma sampling points of Logistic mapping and Chebyshev mapping, and calculating by using the following formula under the assumption that 2n +1 Sigma sampling points are provided
The corresponding mean weight and variance weight are:
where k is a scaling factor of the distance between the mean and the Sigma sample points;
is the matrix (n + k) Px,xThe ith row or column of the square root matrix after Cholesky decomposition;
s32, calculating 2n +1 sampling points χ 'of Logistic and Chebyshev mapping respectively by using a proportion correction sampling strategy'iAnd the corresponding weight Wi mAnd Wi c。
5. The novel pseudo-random number generation method based on multi-lag non-adjacent coupled lattices as claimed in claim 4, wherein the step S4 further comprises:
s41, calculating the mean value, the variance and the covariance of the corresponding k time by using the observation equation mapped by Logistic and Chebyshev constructed in the step S22 and the corresponding weight calculated in the step S32;
s42, calculating the filtering gain at the k +1 moment, and the state estimation and estimation variance by using the k moment mean value calculated in the step S41 to obtain a state estimation value of Logistic;
and S43, calculating the filter gain at the k +1 moment and the state estimation and estimation variance by using the k moment mean value calculated in the step S41 to obtain a state estimation value of Chebyshev.
6. The novel pseudo-random number generation method based on multi-lag non-adjacent coupled lattices as claimed in claim 5, wherein the step S5 further comprises:
s51, constructing Chebyshev mapping tau by using the system parameters specified in S11And Sine mapping τ2Time-lapse time-varying systems of (a);
and S52, performing 1 operation on the sum of the initial lattice value and the state estimation value to obtain a new disturbance weight lambda.
7. The novel pseudo-random number generation method based on multi-lag non-adjacent coupled lattices as claimed in claim 6, wherein the step S6 further comprises:
s61, constructing Logistic mapping, Chebyshev mapping and LPWLCM mapping of a novel pseudo random number generator of a multi-lag non-adjacent coupling grid by using the system parameters of the step S1;
and S62, inputting the Logistic state estimated value in S43, the Chebyshev state estimated value in S44 and the disturbance weight in S52 into a novel pseudo random number generator of a multi-time-lag non-adjacent coupling grid, and calculating to obtain a pseudo random sequence.
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| 缑景霞: "基于信道特性的密钥生成关键技术研究及实现", 《中国优秀硕士学位论文全文数据库》, 15 January 2022 (2022-01-15) * |
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