CN113938267A - Method for constructing high-dimensional chaotic pseudorandom sequence generator based on periodic loop monitoring mechanism - Google Patents
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Abstract
The invention provides a method for constructing a high-dimensional chaotic pseudo-random sequence generator based on a periodic loop monitoring mechanism. The invention realizes the random jump of the chaotic orbit and fully improves various chaotic characteristics. The pseudo-random sequence generator has the advantages of good universality, easy hardware realization of the structure, high operation speed, good performance of outputting binary sequences and the like. The pseudo-random sequence generator can be used for constructing a chaotic sequence password, has the characteristics of light-weight passwords, is high in safety, high in encryption speed and low in hardware resource consumption, is very suitable for encrypting multimedia data with large data volume and high redundancy such as color images, audios and videos, and can also be applied to the fields of secret communication and the like.
Description
Technical Field
The invention belongs to the field of chaotic cryptography, and particularly relates to a method for constructing a high-dimensional chaotic pseudorandom sequence generator based on a periodic loop monitoring mechanism.
Background
The pseudo-random sequence generator is a core component of the sequence cipher, and the encryption strength of the sequence cipher depends on the performance of the key stream, i.e. the binary sequence, output by the pseudo-random sequence generator to some extent. The traditional pseudo-random sequence generator is constructed based on m sequences, gold sequences and the like, and the pseudo-random sequences have poor safety because of the problems that the pseudo-random sequences have linear structures and are easy to crack or low in complexity and the like. In recent years, the chaotic system is suitable for generating a pseudorandom sequence due to a plurality of good characteristics such as noise-like property, initial value sensitivity, nonlinear structure, long-term unpredictability and inherent randomness, and is a new direction at present. Then, the classical chaos theory is defined on a continuous domain, and when the chaotic system is realized on a microprocessor with limited precision, the dynamic characteristics of the chaotic system are degraded. For example, the original aperiodic chaotic sequence has a short period phenomenon, and the characteristics of high sensitivity to the initial condition, intrinsic randomness, ergodicity and the like are greatly reduced.
Disclosure of Invention
Based on the defects, the invention provides a method for constructing a high-dimensional chaotic pseudorandom sequence generator based on a periodic loop monitoring mechanism, which aims to improve the dynamic characteristics of a digitalized chaotic system and improve the performance of a chaotic pseudorandom sequence.
The technical scheme adopted by the invention is as follows: a method for constructing a high-dimensional chaotic pseudo-random sequence generator based on a periodic loop monitoring mechanism comprises the following steps:
firstly, an iterative function of the N-dimensional digital chaotic system is set as Chaos ((x)1(n),x2(n),…,xN(n))), the expression formula is as follows:
the linear congruential generator function is LCG (W (i)) and is formulated as follows:
W(i+1)＝(aW(i)+c)mod M, 0≤W(i)＜M (2)
in the above formula, a is a multiplier c and M is a modulus;
firstly, setting the calculation precision of a hardware platform microprocessor as L bits, the decimal number as k bits, and setting the initial value variable of an N-dimensional digital chaotic system as (X)1,X2,…,XN) The initial iteration variable of the linear congruence generator is WtFurther defining variables required by chaotic periodic loop monitoring: slow pointer variable (slow)1,slow2,…,slowN) And fast pointer variable (fast)1,fast2,…,fastN) Step, iteration step variable1And maximum step size stepmax，index1And index2Respectively outputting the index values of the output sequences of the N-dimensional digital chaotic system and the linear congruence generator, and then executing the following steps:
step 1: initialized to index1＝1，index2Initialized to step 11＝0，stepmaxFurther, the initial value (X) is set to 21,X2,…,XN) Are respectively assigned to (slow)1,slow2,…,slowN) And (fast)1,fast2,…,fastN)；
Step 2: performing Chaos iterative operation on one time (fast)1,fast2,…,fastN) Will generate a set of chaotic iteration variables (seq)1(index1),seq2(index1),…,seqN(index1) Then assigns this variable to (fast)1,fast2,…,fastN) Linear congruential generator function LCG (W)t) Iterating N times will output a set of variables (W (index)2),W(index2+1),…,W(index2+ N-1)), the set of previously generated chaotic iteration variables (seq) is compared1(index1),seq2(index1),…,seqN(index1) Each variable in (a) is left shifted by kbits after taking the absolute value, i.e., (abs (seq))1(index1))＜＜k,abs(seq2(index1))＜＜k,…,abs(seqN(index1) K), abs () is the absolute value, the set of variables is summed with (W (index)2),W(index2+1),…,W(index2+ N-1)) modified chaotic sequence (Q) by XOR operation on variables one by one1(index1),Q2(index1),…,QN(index1) Hetero) ofOr the operation symbol is
Performing corresponding binary quantization processing on each element of the set of variables and outputting a pseudo-random binary sequence (B (index)2),B(index2+1),…,B(index2+ N-1)), the binary quantization formula is as follows:
will variable index1And step1Carry out the operation of adding 1 and assign value to index again1And step1，
Variable index2Carry out N adding operation and assign value to index2Let W (index)2+ N-1) to Wt；
And step 3: if (fast)1,fast2,…,fastN) Is equal to (slow)1,slow2,…,slowN) Skipping to step 5;
and 4, step 4: if step1Is equal to stepmaxThen assign 0 to step1Step tomax X 2 assignment to stepmaxWill (fast)1,fast2,…,fastN) Assign value to (slow)1,slow2,…,slowN) Then jump to step 2, if step1Not equal to stepmaxDirectly jumping to the step 2;
and 5: directly jumping to the step 6 after the step 2 is executed for one time;
step 6: if (fast)1,fast2,…,fastN) Is not equal to (slow)1,slow2,…,slowN) Go to step 2 and then jump to step 6, if (fast)1,fast2,…,fastN) Is equal to (slow)1,slow2,…,slowN) If the chaos state variable enters the chaos periodic loop orbit, the initial condition of the digital chaos system needs to be refreshed randomly, and the method also monitors that the current chaos state variable enters the chaos periodic loop orbit and the initial condition of the digital chaos system needs to be refreshed randomlyNamely (fast)1,fast2,…,fastN) After taking the absolute value, left-shifting k bits, then performing bitwise negation on each element in the set of variables, and right-shifting k bits to obtain the final randomly-changed initial value (fast)1′,fast2′,…,fast′N) Then, the value is assigned to the initial value variable (X) of the chaotic system1,X2,…,XN) To achieve random alteration of the initial conditions; and then jumping to the step 1 if the pseudo-random sequence is continuously generated, and otherwise, ending.
The invention has the advantages and beneficial effects that: the invention realizes the random jump of the chaotic orbit and fully improves various chaotic characteristics. The pseudo-random sequence generator has the advantages of good universality, easy hardware realization of the structure, high operation speed, good performance of outputting binary sequences and the like. The pseudo-random sequence generator can be used for constructing a chaotic sequence password, outputs a binary sequence as a key stream for encryption, has the characteristic of light-weight passwords, has high safety and high encryption speed, consumes small hardware resources, is very suitable for encrypting multimedia data with large data volume and high redundancy such as color images, audios and videos, and can also be applied to the fields of secret communication and the like.
Drawings
FIG. 1 is a block diagram of a chaotic pseudo-random sequence generator design;
FIG. 2 original Sprott System phase space diagram;
FIG. 3 is a Sprott system phase space diagram after modification by the present invention;
FIG. 4 original Sprott System autocorrelation test plots;
FIG. 5 is a Sprott system autocorrelation test chart after modification by the present invention;
FIG. 6 original Sprott System frequency histogram;
fig. 7 is a Sprott system frequency histogram after the present improvement.
Detailed Description
The invention is further illustrated by way of example in the accompanying drawings of the specification:
example 1
The purpose of this embodiment is to enhance the dynamic characteristics of the digital chaotic system by using a chaotic cycle loop monitoring mechanism and a chaotic system initial condition random refreshing method, and to construct a chaotic pseudorandom sequence generator with excellent performance by using a newly designed digital chaotic model, and a design block diagram of the chaotic pseudorandom sequence generator is shown in fig. 1.
Firstly, an iterative function of the N-dimensional digital chaotic system is set as Chaos ((x)1(n),x2(n),…,xN(n))), the general form of which is specifically expressed as follows:
in addition, in this embodiment, a linear congruence generator is also used to improve the performance of the discrete chaotic sequence, and the linear congruence generator function is LCG (w (i)), whose mathematical formula is as follows:
W(i+1)＝(aW(i)+c)mod M, 0≤W(i)＜M (2)
in the above formula, a, c and M are respectively a multiplier, an increment and a modulus.
Before algorithm execution, the calculation precision of a hardware platform microprocessor is set to be L bits, the decimal number occupies k bits, and the initial value variable of the N-dimensional digital chaotic system is set to be (X)1,X2,…,XN) The initial iteration variable of the linear congruence generator is Wt. Variables required by chaotic periodic loop monitoring are further defined: slow pointer variable (slow)1,slow2,…,slowN) And fast pointer variable (fast)1,fast2,…,fastN) Step, iteration step variable1And maximum step size stepmax。index1And index2Respectively outputting index values of the output sequences of the N-dimensional digital chaotic system and the linear congruence generator; and the following steps are carried out:
step 1: initialized to index1＝1，index 21. Initialization to step1＝0，step max2. Further, the initial value (X)1,X2,…,XN) Are respectively assigned to (slow)1,slow2,…,slowN) And (fast)1,fast2,…,fastN)。
Step 2: performing Chaos iterative operation on one time (fast)1,fast2,…,fastN) Will generate a set of chaotic iteration variables (seq)1(index1),seq2(index1),…,seqN(index1) Then assigns this variable to (fast)1,fast2,…,fastN). Linear congruential generator function LCG (W)t) Iterating N times will output a set of variables (W (index)2),W(index2+1),…,W(index2+ N-1)), the set of previously generated chaotic iteration variables (seq) is compared1(index1),seq2(index1),…,seqN(index1) Each variable in (a) is left shifted by kbits after taking the absolute value, i.e., (abs (seq))1(index1))＜＜k,abs(seq2(index1))＜＜k,…,abs(seqN(index1) K), abs () is the absolute value, the set of variables is summed with (W (index)2),W(index2+1),…,W(index2+ N-1)) modified chaotic sequence (Q) by XOR operation on variables one by one1(index1),Q2(index1),…,QN(index1) Xor operation symbol of
Performing corresponding binary quantization processing on each element of the set of variables and outputting a pseudo-random binary sequence (B (index)2),B(index2+1),…,B(index2+ N-1)), the binary quantization formula is as follows:
will variable index1And step1Carry out the operation of adding 1 and assign value to index again1And step1Index, variable2Carry out N adding operation and assign value to index2Let W (index)2+ N-1) to Wt。
And step 3: if (fast)1,fast2,…,fastN) Is equal to (slow)1,slow2,…,slowN) It jumps to step 5.
And 4, step 4: if step1Is equal to stepmaxThen assign 0 to step1Step tomax X 2 assignment to stepmaxWill (fast)1,fast2,…,fastN) Assign value to (slow)1,slow2,…,slowN) And then jumps to step 2. If step1Not equal to stepmaxAnd directly jumping to the step 2.
And 5: after step 2 is executed once, the process jumps directly to step 6.
Step 6: if (fast)1,fast2,…,fastN) Is not equal to (slow)1,slow2,…,slowN) Then go to step 2 and then go to step 6. If (fast)1,fast2,…,fastN) Is equal to (slow)1,slow2,…,slowN) If the chaos state variable enters the chaos periodic loop orbit at present, the initial condition of the digital chaos system needs to be refreshed randomly, namely, fast1,fast2,…,fastN) Taking the absolute value and then shifting the absolute value to the left by k bits, and then carrying out bitwise inversion on each element in the set of variables and then shifting the absolute value to the right by k bits to obtain the final randomly-changed initial value (best'1,fast′2,…,fast′N) Then, the value is assigned to the initial value variable (X) of the chaotic system1,X2,…,XN) To effect a random alteration of the initial conditions. And then jumping to the step 1 if the pseudo-random sequence is continuously generated, and otherwise, ending.
Example 2
The three-dimensional digital Sprott chaotic system is taken as an example and the chaotic pseudo-random sequence generator is constructed according to the method of the embodiment 1 of the invention. The iterative formula of the digital Sprott chaotic system is as follows:
in the above formula, T is a time step. Where T is 1/2-3Initial value of chaos (X)1,X2,X3) (2, -1.125,3), the calculation accuracy L is 8 and the decimal place k is 4. Further, the original digital Sprott system and the digital Sprott system improved by the invention are subjected to performance comparative analysis, wherein the performance comparative analysis comprises phase space analysis, autocorrelation and frequency histogram analysis. From the experimental results, the original Sprott system phase space only has a plurality of discrete points, and the improved Sprott system phase space almost fills the whole phase space, shows good state space utilization rate and can prevent phase space reconstruction attack. The autocorrelation can analyze the periodicity and randomness of the discrete sequence, and as can be seen from fig. 4, the autocorrelation function of the original Sprott system has dense contour peak spectral lines and shows short periodicity, while the autocorrelation of the improved Sprott system is similar to an impact function and shows good randomness and long period characteristics. As can be seen from the frequency histogram experiment, the original Sprott system is not uniformly distributed, and the frequency histogram of the improved Sprott system has good equalization and can resist frequency-dependent attack. Further, the pseudo-random sequence generator constructed by the improved Sprott system outputs a binary sequence to perform frequency test, period test and complexity test, and the binary sequence shows good performance.
Claims (1)
1. A method for constructing a high-dimensional chaotic pseudo-random sequence generator based on a periodic loop monitoring mechanism is characterized by comprising the following steps: firstly, an iterative function of the N-dimensional digital chaotic system is set as Chaos ((x)1(n),x2(n),…,xN(n))), the expression formula is as follows:
the linear congruential generator function is LCG (W (i)) and is formulated as follows:
W(i+1)＝(aW(i)+c)modM,0≤W(i)＜M (2)
in the above formula, a is a multiplier c and M is a modulus;
firstly, setting the calculation precision of a hardware platform microprocessor as L bits, the decimal number as k bits, and setting the initial value variable of an N-dimensional digital chaotic system as (X)1,X2,…,XN) The initial iteration variable of the linear congruence generator is WtFurther defining variables required by chaotic periodic loop monitoring: slow pointer variable (slow)1,slow2,…,slowN) And fast pointer variable (fast)1,fast2,…,fastN) Step, iteration step variable1And maximum step size stepmax，index1And index2Respectively outputting the index values of the output sequences of the N-dimensional digital chaotic system and the linear congruence generator, and then executing the following steps:
step 1: initialized to index1＝1，index2Initialized to step 11＝0，stepmaxFurther, the initial value (X) is set to 21,X2,…,XN) Are respectively assigned to (slow)1,slow2,…,slowN) And (fast)1,fast2,…,fastN)；
Step 2: performing Chaos iterative operation on one time (fast)1,fast2,…,fastN) Will generate a set of chaotic iteration variables (seq)1(index1),seq2(index1),…,seqN(index1) Then assigns this variable to (fast)1,fast2,…,fastN) Linear congruential generator function LCG (W)t) Iterating N times will output a set of variables (W (index)2),W(index2+1),…,W(index2+ N-1)), the set of previously generated chaotic iteration variables (seq) is compared1(index1),seq2(index1),…,seqN(index1) Each variable in (a) is left shifted by kbits after taking the absolute value, i.e., (abs (seq))1(index1))＜＜k,abs(seq2(index1))＜＜k,…,abs(seqN(index1) K), abs () is the absolute value, the set of variables is summed with (W (index)2),W(index2+1),…,W(index2+ N-1)) modified chaotic sequence (Q) by XOR operation on variables one by one1(index1),Q2(index1),…,QN(index1) Xor operation symbol of
Performing corresponding binary quantization processing on each element of the set of variables and outputting a pseudo-random binary sequence (B (index)2),B(index2+1),…,B(index2+ N-1)), the binary quantization formula is as follows:
will variable index1And step1Carry out the operation of adding 1 and assign value to index again1And step1，
Variable index2Carry out N adding operation and assign value to index2Let W (index)2+ N-1) to Wt；
And step 3: if (fast)1,fast2,…,fastN) Is equal to (slow)1,slow2,…,slowN) Skipping to step 5;
and 4, step 4: if step1Is equal to stepmaxThen assign 0 to step1Step tomaxX 2 assignment to stepmaxWill (fast)1,fast2,…,fastN) Assign value to (slow)1,slow2,…,slowN) Then jump to step 2, if step1Not equal to stepmaxDirectly jumping to the step 2;
and 5: directly jumping to the step 6 after the step 2 is executed for one time;
step 6: if (fast)1,fast2,…,fastN) Is not equal to (slow)1,slow2,…,slowN) Then, thenStep 2 is executed once, and then step 6 is skipped, if (fast)1,fast2,…,fastN) Is equal to (slow)1,slow2,…,slowN) If the chaos state variable enters the chaos periodic loop orbit at present, the initial condition of the digital chaos system needs to be refreshed randomly, namely, fast1,fast2,…,fastN) After taking the absolute value, left-shifting k bits, then performing bitwise negation on each element in the set of variables, and right-shifting k bits to obtain the final randomly-changed initial value (fast)1′,fast2′,…,fast′N) Then, the value is assigned to the initial value variable (X) of the chaotic system1,X2,…,XN) To achieve random alteration of the initial conditions; and then jumping to the step 1 if the pseudo-random sequence is continuously generated, and otherwise, ending.
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| CN102111262A (en) * | 2011-03-31 | 2011-06-29 | 河南工业大学 | Method for generating pseudo-random sequence based on space chaos |
| CN107678729A (en) * | 2017-08-30 | 2018-02-09 | 东南大学 | A kind of Lorenz chaos pseudo random sequence generators based on m-sequence |
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| CN102111262A (en) * | 2011-03-31 | 2011-06-29 | 河南工业大学 | Method for generating pseudo-random sequence based on space chaos |
| CN107678729A (en) * | 2017-08-30 | 2018-02-09 | 东南大学 | A kind of Lorenz chaos pseudo random sequence generators based on m-sequence |
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