CN113938267B - Method for constructing high-dimensional chaotic pseudorandom sequence generator based on periodic ring monitoring mechanism - Google Patents
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- H—ELECTRICITY
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
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- H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
- H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
- H04L9/065—Encryption by serially and continuously modifying data stream elements, e.g. stream cipher systems, RC4, SEAL or A5/3
- H04L9/0656—Pseudorandom key sequence combined element-for-element with data sequence, e.g. one-time-pad [OTP] or Vernam's cipher
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Abstract
The invention provides a method for constructing a high-dimensional chaotic pseudorandom sequence generator based on a periodic ring monitoring mechanism, which constructs a new chaotic model based on the chaotic periodic ring monitoring mechanism and a random refreshing method of initial conditions of a chaotic system, and then constructs the high-dimensional chaotic pseudorandom sequence generator with excellent performance by adopting a binary quantization method. The invention realizes random jump of chaotic tracks and fully improves various characteristics of chaos. The pseudo-random sequence generator has the advantages of good universality, easy hardware realization of structure, high operation speed, good binary sequence output performance and the like. The pseudo-random sequence generator can be used for constructing chaotic sequence passwords, has the characteristics of lightweight passwords, is high in safety and encryption speed, consumes less hardware resources, is very suitable for encrypting multimedia data with large data quantity and high redundancy such as color images, audios and videos, and can 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 ring 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 to some extent on the performance of the key stream output by the pseudo-random sequence generator, i.e. the binary sequence. Conventional pseudo-random sequence generators are constructed based on m-sequences, gold sequences, etc., and these pseudo-random sequences are not ideal in terms of security due to their linear structure being easily broken or low complexity. In recent years, chaotic systems are very suitable for generating pseudo random sequences due to the good characteristics of noise-like, initial value sensitivity, nonlinear structure, long-term unpredictability, inherent randomness and the like, and have become a new direction. Classical chaos theory is then defined on a continuous domain, whose dynamics will degrade when the chaotic system is implemented on a microprocessor of limited precision. For example, the original non-periodic chaotic sequence has short period phenomenon, and the characteristics of high sensitivity, intrinsic randomness, ergodic property and the like of the original condition are also greatly reduced.
Disclosure of Invention
Based on the defects, the invention provides a construction method of a high-dimensional chaotic pseudorandom sequence generator based on a periodic ring monitoring mechanism, which aims to improve the dynamics characteristic of a digitized 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 pseudorandom sequence generator based on a periodic ring monitoring mechanism comprises the following steps:
firstly, setting an iteration function of an N-dimension digital chaotic system as Chaos ((x) 1 (n),x 2 (n),…,x N (n)) as follows:
the linear congruence generator function is LCG (W (i)), which has the following formula:
W(i+1)＝(aW(i)+c)mod M, 0≤W(i)＜M (2)
wherein a is a multiplier c is an increment and M is a modulus;
the calculation precision of the hardware platform microprocessor is L bits, the decimal number occupies k bits, and the initial value variable of the N-dimension digital chaotic system is (X) 1 ,X 2 ,…,X N ) The initial value iteration variable of the linear congruence generator is W t Further defining variables required for chaotic periodic loop monitoring: slow pointer variable (slow) 1 ,slow 2 ,…,slow N ) And a fast pointer variable (fast 1 ,fast 2 ,…,fast N ) Iterative step variable step 1 And maximum step max ，index 1 And index 2 The method comprises the steps of respectively outputting index values of sequences for an N-dimension digital chaotic system and a linear congruence generator, and then executing the following steps:
step 1: initializing to index 1 ＝1，index 2 =1, initialized to step 1 ＝0，step max =2, further, the initial value (X 1 ,X 2 ,…,X N ) Assign to (slow) 1 ,slow 2 ,…,slow N ) And (fast) 1 ,fast 2 ,…,fast N )；
Step 2: performing one chaotic iteration operation Chaos ((fast) 1 ,fast 2 ,…,fast N ) Will generate a set of chaotic iteration variables (seq) 1 (index 1 ),seq 2 (index 1 ),…,seq N (index 1 ) This variable is then assigned to (fast) 1 ,fast 2 ,…,fast N ) The linear congruence generator function LCG (W t ) The iteration N times will output a set of variables (W (index 2 ),W(index 2 +1),…,W(index 2 +N-1)), the set of chaotic iteration variables (seq) generated before 1 (index 1 ),seq 2 (index 1 ),…,seq N (index 1 ) Each variable in (b) takes absolute value and then shifts left by kbits, i.e. (abs (seq) 1 (index 1 ))＜＜k,abs(seq 2 (index 1 ))＜＜k,…,abs(seq N (index 1 ) K), abs () takes absolute value, and the set of variables is combined with (W (index) 2 ),W(index 2 +1),…,W(index 2 +N-1)) to exclusive-or the variable by variable to obtain an improved chaotic sequence (Q) 1 (index 1 ),Q 2 (index 1 ),…,Q N (index 1 ) Is given by exclusive OR operation signEach element of the set of variables is subjected to a corresponding binary quantization process and a pseudo-random binary sequence (B (index) 2 ),B(index 2 +1),…,B(index 2 +n-1)), the binary quantization formula is as follows:
variable index 1 Step 1 Performing 1 adding operation and reassigning to index 1 Step 1 ，
Variable index 2 N adding operation is carried out and reassigned to index 2 W (index) 2 +N-1) assigning to W t ；
Step 3: if (fast) 1 ,fast 2 ,…,fast N ) Equal to (slow) 1 ,slow 2 ,…,slow N ) Then jump to step 5;
step 4: if step 1 Equal to step max Then assign 0 to step 1 Step is to max X2 assignment to step max Will (fast) 1 ,fast 2 ,…,fast N ) Assign to (slow) 1 ,slow 2 ,…,slow N ) Then jump to step 2 if step 1 Not equal to step max Directly jumping to the step 2;
step 5: after the step 2 is executed for one time, the step 6 is directly skipped;
step 6: if (fast) 1 ,fast 2 ,…,fast N ) Not equal to (slow) 1 ,slow 2 ,…,slow N ) Then go to step 2 and jump to step 6, if (fast 1 ,fast 2 ,…,fast N ) Equal to (slow) 1 ,slow 2 ,…,slow N ) If it is monitored that the current chaotic state variable enters the chaotic periodic ring orbit, the initial condition of the digital chaotic system needs to be randomly refreshed, namely (fast) 1 ,fast 2 ,…,fast N ) Taking absolute value, shifting left by k bits, then carrying out bit inversion on each element in the group of variables, and shifting right by k bits to obtain final randomly changed initial value (fast) 1 ′,fast 2 ′,…,fast′ N ) This value is then assigned to the initial variable (X 1 ,X 2 ,…,X N ) To realize random change of initial conditions; and then jumping to the step 1 if the generation of the pseudo-random sequence is to be continued, and ending if the generation of the pseudo-random sequence is not to be continued.
The invention has the advantages and beneficial effects that: the invention realizes random jump of chaotic tracks and fully improves various characteristics of chaos. The pseudo-random sequence generator has the advantages of good universality, easy hardware realization of structure, high operation speed, good binary sequence output performance and the like. The pseudo-random sequence generator can be used for constructing a chaotic sequence cipher, and outputs a binary sequence as a key stream for encryption, has the characteristics of lightweight cipher, has high security, high encryption speed and low hardware resource consumption, is very suitable for encrypting multimedia data with large data quantity and high redundancy such as color images, audios and videos, and can be also applied to the fields of secret communication and the like.
Drawings
FIG. 1 is a block diagram of a chaotic pseudorandom sequence generator design;
FIG. 2 is a diagram of the original Sprott system phase space;
FIG. 3 is a phase space diagram of the Sprott system modified by the present invention;
FIG. 4 is an original Sprott system autocorrelation test chart;
FIG. 5 is a chart of the autocorrelation test of the Sprott system after improvement of the present invention;
FIG. 6 original Sprott System frequency histogram;
fig. 7 shows a Sprott system frequency histogram modified by the present invention.
Detailed Description
The invention is further illustrated by the following examples according to the drawings of the specification:
example 1
The aim of the embodiment is to enhance the dynamics characteristic of the digital chaotic system by adopting a chaotic period loop monitoring mechanism and a chaotic system initial condition random refreshing method, and construct a chaotic pseudorandom sequence generator with excellent performance through a newly designed digital chaotic model, wherein the design block diagram is shown in figure 1.
Firstly, setting an iteration function of an N-dimension digital chaotic system as Chaos ((x) 1 (n),x 2 (n),…,x N (n)) whose general form is represented by the following expression:
in addition, in this embodiment, a linear congruence generator is used to improve the performance of the discrete chaotic sequence, and the linear congruence generator function is LCG (W (i)), and the 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 the hardware platform microprocessor is set to be L bits, decimal numbers occupy k bits, and the initial value variable of the N-dimension digital chaotic system is set to be (X 1 ,X 2 ,…,X N ) The initial value iteration variable of the linear congruence generator is W t . Further defining the variables required for chaotic periodic loop monitoring: slow pointer variable (slow) 1 ,slow 2 ,…,slow N ) And a fast pointer variable (fast 1 ,fast 2 ,…,fast N ) Iterative step variable step 1 And maximum step max 。index 1 And index 2 Respectively outputting index values of sequences for the N-dimension digital chaotic system and the linear congruence generator; and performs the steps of:
step 1: initializing to index 1 ＝1，index 2 =1. Initializing to step 1 ＝0，step max =2. Further, the initial value (X 1 ,X 2 ,…,X N ) Assign to (slow) 1 ,slow 2 ,…,slow N ) And (fast) 1 ,fast 2 ,…,fast N )。
Step 2: performing one chaotic iteration operation Chaos ((fast) 1 ,fast 2 ,…,fast N ) Will generate a set of chaotic iteration variables (seq) 1 (index 1 ),seq 2 (index 1 ),…,seq N (index 1 ) This variable is then assigned to (fast) 1 ,fast 2 ,…,fast N ). The linear congruence generator function LCG (W t ) The iteration N times will output a set of variables (W (index 2 ),W(index 2 +1),…,W(index 2 +N-1)), the set of chaotic iteration variables (seq) generated before 1 (index 1 ),seq 2 (index 1 ),…,seq N (index 1 ) Each variable in (b) takes absolute value and then shifts left by kbits, i.e. (abs (seq) 1 (index 1 ))＜＜k,abs(seq 2 (index 1 ))＜＜k,…,abs(seq N (index 1 ) K), abs () takes absolute value, and the set of variables is combined with (W (index) 2 ),W(index 2 +1),…,W(index 2 +N-1)) to exclusive-or the variable by variable to obtain an improved chaotic sequence (Q) 1 (index 1 ),Q 2 (index 1 ),…,Q N (index 1 ) Is given by exclusive OR operation signEach element of the set of variables is subjected to a corresponding binary quantization process and a pseudo-random binary sequence (B (index) 2 ),B(index 2 +1),…,B(index 2 +n-1)), the binary quantization formula is as follows:
variable index 1 Step 1 Performing 1 adding operation and reassigning to index 1 Step 1 Variable index 2 N adding operation is carried out and reassigned to index 2 W (index) 2 +N-1) assigning to W t 。
Step 3: if (fast) 1 ,fast 2 ,…,fast N ) Equal to (slow) 1 ,slow 2 ,…,slow N ) Then the process jumps to step 5.
Step 4: if step 1 Equal to step max Then assign 0 to step 1 Step is to max X2 assignment to step max Will (fast) 1 ,fast 2 ,…,fast N ) Assign to (slow) 1 ,slow 2 ,…,slow N ) After which the process jumps to step 2. If step 1 Not equal to step max The process goes directly to step 2.
Step 5: after performing step 2 one pass, the process jumps directly to step 6.
Step 6: if (fast) 1 ,fast 2 ,…,fast N ) Not equal to (slow) 1 ,slow 2 ,…,slow N ) Then go to step 2 and jump to step 6. If (fast) 1 ,fast 2 ,…,fast N ) Equal to (slow) 1 ,slow 2 ,…,slow N ) If it is monitored that the current chaotic state variable enters the chaotic periodic ring orbit, the initial condition of the digital chaotic system needs to be randomly refreshed, namely (fast) 1 ,fast 2 ,…,fast N ) Taking the absolute value, shifting left by k bits, then carrying out bit inversion on each element in the group of variables, and shifting right by k bits to obtain a final randomly changed initial value (fast' 1 ,fast′ 2 ,…,fast′ N ) This value is then assigned to the initial variable (X 1 ,X 2 ,…,X N ) To achieve random alteration of the initial conditions. And then jumping to the step 1 if the generation of the pseudo-random sequence is to be continued, and ending if the generation of the pseudo-random sequence is not to be continued.
Example 2
The three-dimensional digital Sprott chaotic system is taken as an example and a chaotic pseudorandom 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:
where T is the time step. Let t=1/2 here -3 Chaos initial value (X) 1 ,X 2 ,X 3 ) = (2, -1.125,3), calculation accuracy l=8, decimal k=4. Further, the original digital Sprott system and the digital Sprott system modified by the invention are subjected to performance comparison analysis, which includes phase space analysis, autocorrelation and frequency histogram analysis. As can be seen from the experimental results, the original Sprott system phase space only has a plurality of discrete points, and the improved Sprott system phase space is almost full of the whole phase space, shows good state space utilization rate and can preventPhase space reconstruction attacks are stopped. The autocorrelation can analyze the periodicity and randomness of the discrete sequences, and it can be seen from fig. 4 that the autocorrelation function of the original Sprott system has dense contour peak lines, shows short periodicity, and the autocorrelation of the improved Sprott system is similar to the impact function, and shows good randomness and long periodicity characteristics. As can be seen from the frequency histogram experiment, the original Sprott system is unevenly distributed, and the improved Sprott system frequency histogram has good balance and can resist frequency correlation attack. Further, we output binary sequences for frequency testing, period testing and complexity testing on the pseudo-random sequence generator constructed by the improved Sprott system, which all exhibit good performance.
Claims (1)
1. The method for constructing the high-dimensional chaotic pseudorandom sequence generator based on the periodic ring monitoring mechanism is characterized by comprising the following steps of: firstly, setting an iteration function of an N-dimension digital chaotic system as Chaos ((x) 1 (n),x 2 (n),…,x N (n)) as follows:
the linear congruence generator function is LCG (W (i)), which has the following formula:
W(i+1)＝(aW(i)+c)modM,0≤W(i)＜M (2)
wherein a is a multiplier c is an increment and M is a modulus;
the calculation precision of the hardware platform microprocessor is L bits, the decimal number occupies k bits, and the initial value variable of the N-dimension digital chaotic system is (X) 1 ,X 2 ,…,X N ) The initial value iteration variable of the linear congruence generator is W t Further defining variables required for chaotic periodic loop monitoring: slow pointer variable (slow) 1 ,slow 2 ,…,slow N ) And a fast pointer variable (fast 1 ,fast 2 ,…,fast N ) Iterative step variable step 1 And maximum step max ，index 1 And index 2 The method comprises the steps of respectively outputting index values of sequences for an N-dimension digital chaotic system and a linear congruence generator, and then executing the following steps:
step 1: initializing to index 1 ＝1，index 2 =1, initialized to step 1 ＝0，step max =2, further, the initial value (X 1 ,X 2 ,…,X N ) Assign to (slow) 1 ,slow 2 ,…,slow N ) And (fast) 1 ,fast 2 ,…,fast N )；
Step 2: performing one chaotic iteration operation Chaos ((fast) 1 ,fast 2 ,…,fast N ) Will generate a set of chaotic iteration variables (seq) 1 (index 1 ),seq 2 (index 1 ),…,seq N (index 1 ) This variable is then assigned to (fast) 1 ,fast 2 ,…,fast N ) The linear congruence generator function LCG (W t ) The iteration N times will output a set of variables (W (index 2 ),W(index 2 +1),…,W(index 2 +N-1)), the set of chaotic iteration variables (seq) generated before 1 (index 1 ),seq 2 (index 1 ),…,seq N (index 1 ) Each variable in (b) takes absolute value and then shifts left by kbits, i.e. (abs (seq) 1 (index 1 ))＜＜k,abs(seq 2 (index 1 ))＜＜k,…,abs(seq N (index 1 ) K), abs () takes absolute value, and the set of variables is combined with (W (index) 2 ),W(index 2 +1),…,W(index 2 +N-1)) to exclusive-or the variable by variable to obtain an improved chaotic sequence (Q) 1 (index 1 ),Q 2 (index 1 ),…,Q N (index 1 ) Is given by exclusive OR operation signEach element of the set of variables is subjected to a corresponding binary quantization process and a pseudo-random binary sequence (B (index) 2 ),B(index 2 +1),…,B(index 2 +n-1)), the binary quantization formula is as follows:
variable index 1 Step 1 Performing 1 adding operation and reassigning to index 1 Step 1 ，
Variable index 2 N adding operation is carried out and reassigned to index 2 W (index) 2 +N-1) assigning to W t ；
Step 3: if (fast) 1 ,fast 2 ,…,fast N ) Equal to (slow) 1 ,slow 2 ,…,slow N ) Then jump to step 5;
step 4: if step 1 Equal to step max Then assign 0 to step 1 Step is to max X2 assignment to step max Will (fast) 1 ,fast 2 ,…,fast N ) Assign to (slow) 1 ,slow 2 ,…,slow N ) Then jump to step 2 if step 1 Not equal to step max Directly jumping to the step 2;
step 5: after the step 2 is executed for one time, the step 6 is directly skipped;
step 6: if (fast) 1 ,fast 2 ,…,fast N ) Not equal to (slow) 1 ,slow 2 ,…,slow N ) Then go to step 2 and jump to step 6, if (fast 1 ,fast 2 ,…,fast N ) Equal to (slow) 1 ,slow 2 ,…,slow N ) If it is monitored that the current chaotic state variable enters the chaotic periodic ring orbit, the initial condition of the digital chaotic system needs to be randomly refreshed, namely (fast) 1 ,fast 2 ,…,fast N ) Taking absolute value, shifting left by k bits, then carrying out bit inversion on each element in the group of variables, and shifting right by k bits to obtain final randomly changed initial value (fast) 1 ′,fast 2 ′,…,fast′ N ) This value is then assigned to the initial variable (X 1 ,X 2 ,…,X N ) To realize random change of initial conditions; and then jumping to the step 1 if the generation of the pseudo-random sequence is to be continued, and ending if the generation of the pseudo-random sequence is not to be continued.
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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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| Title |
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| A Novel Algorithm for Detection and Localization of Periodic Phenomena of Chaotic Binary Sequences;Chunlei Fan等;International Journal of Bifurcation and Chaos;第29卷(第7期);第1-11页 * |
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