CN108984151A - A kind of chaotic binary sequences cycle detection and localization method - Google Patents
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Abstract
A kind of chaotic binary sequences cycle detection and localization method, the present invention relates to chaotic binary sequences cycle detection and localization methods.The purpose of the present invention is to solve the existing detections to sequence period phenomenon generally be directed to the detection method in sequence accurate period and approximate period phenomenon, these methods can only whether there is periodic phenomena from the global qualitative analytical sequence of angle in analytical sequence periodic phenomena, and it is less to certain periodic phenomena researchs potential in sequence subrange, and the problem of can not accomplish the accurate positioning of periodic phenomena.Detailed process are as follows: Two-Dimensional Reconstruction matrix is constructed according to binary sequence, cycle detection matrix is obtained based on Two-Dimensional Reconstruction matrix；According to cycle detection matrix, judge whether binary sequence has the accurate period；According to cycle detection matrix, judge whether binary sequence has approximate period；According to cycle detection matrix, judge whether binary sequence has local period.The present invention is used for binary sequence Randomness test field.
Description
Technical field
The present invention relates to chaotic binary sequences cycle detection and localization methods, belong to binary sequence Randomness test field.
Background technique
There are chaos system characteristics, these characteristics such as good pseudo-randomness, initial value sensitivity, noise like to make chaos system
System is widely used in secret communication, and presents significant advantage in the design of encryption system.However, either
The continuous times chaos system such as the discrete chaotic systems such as Logistic, Henon or Lorenz, Chen, Sprott, by its turn
It is changed to and requires to carry out quantification treatment for the discrete binary sequence needed for encrypting.And during quantization chaos system statistics
Characteristic and randomlikeness will be affected.Computational accuracy and quantization method are two key factors for influencing its characteristic variations.
Currently, due to can not whether be mathematically real randomizer to issuing a certificate to a generator,
Therefore some scholars can be gone by the Statistical Identifying Method of randomness measure randomizer statistical property, as ENT with
Machine test, Diehard Randomness test, NIST-800-22, TestU01 etc..These methods are using Shannon entropy, sequence from phase
Pass, cumulative and discrete Fourier transform etc. carry out randomness evaluation.However, people are while paying close attention to binary sequence randomness
Often have ignored the stability of sequence.It is some to seem random chaos sequence on the whole it is likely to occur one in subrange
A little local period phenomenons.Chaos system is quantized into after binary sequence the phenomenon that will appear randomness reduction in subrange.And
Current method can not carry out quantitative analysis to the periodic phenomena of binary sequence, and it is even more impossible to detect that the local period of sequence is existing
As.From the point of view of encryption application, influence of the stability of binary sequence to encryption application is great.In view of described above, research
Periodic phenomena in digital chaos binary sequence subrange has significant meaning to chaos digital secret communication.It is right at present
Detection method of the detection of sequence period phenomenon generally be directed to sequence accurate period and approximate period phenomenon, such as power spectrum point
Analysis method, discrete fourier variation, correlation method, approximate entropy, arrangement entropy and mode excavation and the analysis side based on period template
Method.However, these methods can only be from the global qualitative analytical sequence of angle with the presence or absence of week in analytical sequence periodic phenomena
Phase phenomenon.And it is less to certain periodic phenomena researchs potential in sequence subrange, and can not accomplish the accurate of periodic phenomena
Positioning.
Summary of the invention
The purpose of the present invention is to solve the existing detections to sequence period phenomenon generally be directed to the sequence accurate period
With the detection method of approximate period phenomenon, these methods can only be qualitative from global angle in analytical sequence periodic phenomena
Analytical sequence whether there is periodic phenomena, and less to certain periodic phenomena researchs potential in sequence subrange, and can not
The problem of accomplishing the accurate positioning of periodic phenomena, and propose a kind of chaotic binary sequences cycle detection and localization method.
A kind of chaotic binary sequences cycle detection and localization method detailed process are as follows:
Step 1: constructing Two-Dimensional Reconstruction matrix R according to binary sequence ε (t), period inspection is obtained based on Two-Dimensional Reconstruction matrix R
Survey matrix G；
Step 2: judging whether binary sequence ε (t) has the accurate period according to cycle detection matrix G；
Step 3: judging whether binary sequence ε (t) has approximate period according to cycle detection matrix G；
Step 4: judging whether binary sequence ε (t) has local period according to cycle detection matrix G.
The invention has the benefit that
The invention proposes a kind of UBSPD (Universal Binary Sequences Periodic Detection)
Whether algorithm, this algorithm accurately judge any chaotic binary sequences by building sequence restructuring matrix and cycle detection matrix
There are accurate period, approximate period and local periods；
In addition to this, the present invention can also extract binary sequence period template, can accurately be searched by UBSPD algorithm
And locating periodically template position, whether can be deposited from the global qualitative analytical sequence of angle in analytical sequence periodic phenomena
In periodic phenomena, certain periodic phenomenas potential in sequence subrange can be determined, can accomplish the accurate of periodic phenomena
Positioning, to carry out effective evaluation to the problems such as randomness, safety of this binary sequence；
The present invention extracts binary sequence period template, can accurately search simultaneously locating periodically mould by UBSPD algorithm
Plate position, accuracy rate reach 100%；
The present invention solves the existing detection to sequence period phenomenon generally be directed to sequence accurate period and approximate period
The detection method of phenomenon, these methods can only be from the global qualitative analytical sequence of angle in analytical sequence periodic phenomena
No there are periodic phenomenas, and less to certain periodic phenomena researchs potential in sequence subrange, and can not accomplish that the period existing
The problem of accurate positioning of elephant.
Detailed description of the invention
Fig. 1 is flow chart of the present invention；
UBSPD algorithm period when Fig. 2 is iteration precision M=16 of the present invention positions figure, and Column is column, and Row is row；
UBSPD algorithm period when Fig. 3 is iteration precision M=24 of the present invention positions figure, and ω is period template length, LTFor
Sequence period length；
UBSPD algorithm period when Fig. 4 is iteration precision M=32 of the present invention positions figure.
Specific embodiment
Specific embodiment 1: embodiment is described with reference to Fig. 1, a kind of chaotic binary sequences period of present embodiment
Detection and localization method detailed process are as follows:
Step 1: constructing Two-Dimensional Reconstruction matrix R according to binary sequence ε (t), period inspection is obtained based on Two-Dimensional Reconstruction matrix R
Survey matrix G；
Step 2: judging whether binary sequence ε (t) has the accurate period according to cycle detection matrix G；
Step 3: judging whether binary sequence ε (t) has approximate period according to cycle detection matrix G；
Step 4: judging whether binary sequence ε (t) has local period according to cycle detection matrix G.
Specific embodiment 2: the present embodiment is different from the first embodiment in that: according to two in the step 1
Value sequence constructs Two-Dimensional Reconstruction matrix R, obtains cycle detection matrix G based on Two-Dimensional Reconstruction matrix R；Detailed process are as follows:
UBSPD algorithm description:
Any randomly or pseudo-randomly binary sequence ε (t) for being n for length defines the two dimension weight of (n-1) * (n-1)
Sequence restructuring matrix of the structure matrix R as binary sequence ε (t), n are the length of binary sequence ε (t)；
Two-Dimensional Reconstruction matrix R is lower triangular matrix, and Two-Dimensional Reconstruction matrix R is expressed as following formula:
Wherein ε (i) and ε (j) is respectively i-th and j-th of element in binary sequence ε (t), Ri,jFor Two-Dimensional Reconstruction square
Element in battle array R, ⊙ are same or operation；
Wherein, 1≤i≤n-1,1≤j≤n-1；
ε (i+ ω -1)=ε (i+j) ε (i+j+1) ... ε (i+j+ ω -1) if binary sequence ε (t) meets ε (i) ε (i+1) ...,
Rising in the i-th bit of ε (t) and the i-th+j has continuous ω element equal, this situation is shown as in restructuring matrix in matrix R
J-th strip cornerwise the i-th to the i-th+ω -1 rise and there is continuous ω 1 to occur；ω is symbol string length；
The present invention is illustrated by taking ε (t)=1011011 as an example, if Q is the left top triangle matrix of (n-1) * (n-1),
Qi,j=ω indicates to act the phenomenon for having continuous ω element equal at i-th and i-th+j of ε (t).Square can be obtained according to above-mentioned definition
Battle array Q and sequence restructuring matrix R is as follows:
It can be found from matrix Q and sequence restructuring matrix R with specific corresponding relationship, as having Q in matrix Q1,3=4,
Then there are 4 continuous 1 to occur from the 3rd article of cornerwise 1st element of matrix R, similarly, works as Qi,jWhen=ω, then from square
Cornerwise i-th of the element of j-th strip of battle array R, which rises, has ω continuous 1 to occur.Above-mentioned phenomenon shows the week of Arbitrary Binary sequence
The position and sequence restructuring matrix that phase template occurs have specific corresponding relationship.
Assuming that SkIt (t) is kth diagonal line in sequence restructuring matrix R, LkFor the number of kth diagonal entry, k attaches most importance to
Diagonal line serial number in structure matrix R；For Sk(t) the α element value in, and 1≤α≤Lk；
By sequence Sk(t) it carries out folding the cycle detection matrix G for generating r row k column as the period using k, wherein [2, n/2] k ∈,
R is shown below:
The function that floor () function is realized in formula is to be rounded downwards；Mod is complementation operation；
Cycle detection matrix G is expressed as following formula:
Wherein G1,1For the first column element of the first row in cycle detection matrix G, G1,2For the first row in cycle detection matrix G
Two column elements, G1,kFor the first row kth column element in cycle detection matrix G, G2,1For the second row first in cycle detection matrix G
Column element, G2,2For second the second column element of row, G in cycle detection matrix G2,kIt is arranged for the second row kth in cycle detection matrix G
Element, Gr,1For the first column element of r row in cycle detection matrix G, Gr,2For r row secondary series member in cycle detection matrix G
Element, Gr,kFor r row kth column element in cycle detection matrix G,For Sk(t) the 1st element value in,
For Sk(t) the 2nd element value in,For Sk(t) k-th of element value in,For Sk(t)+1 member of kth in
Element value,For Sk(t)+2 element values of kth in,For Sk(t) the 2k element value in,For Sk(t) (r-1) * k+1 element value in,For Sk(t) (r-1) * k+2 in
Element value,For Sk(t) the r*k element value in.
Other steps and parameter are same as the specific embodiment one.
Specific embodiment 3: the present embodiment is different from the first and the second embodiment in that: root in the step 2
According to cycle detection matrix G, judge whether binary sequence ε (t) has the accurate period；Detailed process are as follows:
Construct one-dimensional vectorWhereinIt is shown below:
In formula,For element in one-dimensional vector V；Index is the element numbers of one-dimensional vector V, 1≤index≤(n/2-
2)+1；K is diagonal line serial number in restructuring matrix R；
If all elements value is all 0 in vector V, accurate periodic phenomena is not present in binary sequence ε (t)；
If there are one or Num element value being 1 in vector V, there are accurate periodic phenomena in binary sequence ε (t),
Vector V is subjected to ascending order traversal by index inferior horn scale value and finds the element that first value is 1The superscript k of this element is
For the accurate cycle length of binary sequence ε (t)；
2≤Num≤(n/2-2)+1。
Other steps and parameter are the same as one or two specific embodiments.
Specific embodiment 4: unlike one of present embodiment and specific embodiment one to three: the step 3
It is middle according to cycle detection matrix G, judge whether binary sequence ε (t) has approximate period；Detailed process are as follows:
Step 3 one, building one-dimensional vector T=[T (1) ... T (m) ... T (k)], wherein T (m) is shown below:
In formula, T (m) is m-th of element in one-dimensional vector T, and T (m) value range is { 0,1 }；K is right in restructuring matrix R
Linea angulata serial number；For Sk(t) β * k+m element value in；
(there is longest in one-dimensional vector T in the starting point and ending point of 1 distance of swimming of longest in step 3 two, positioning one-dimensional vector T
Starting point and terminating point when continuous 1)；
Step 3 three, according to the position of the starting point and ending point of 1 distance of swimming of longest in one-dimensional vector T, obtain one-dimensional vector T
Starting point, terminating point and the run length of middle 1 distance of swimming of longest；
If the starting point of 1 distance of swimming of longest is tStart, terminating point tEnd, run length rLen；
TStart=rLen-tEnd+1；
If being unsatisfactory for rLen/k > threshold1, then approximate period is not present in binary sequence ε (t)；
If meeting rLen/k > threshold1, then there are approximate periods by binary sequence ε (t)；
Wherein threshold1For approximate period decision threshold, value range is (0,1), its bigger approximation of threshold value setting
Period is more obvious, and further approximate period is expressed from the next:
ε (tStart) ... ε (tEnd)=ε (tStart+ γ * k) ... ε (tEnd+ γ * k), 1≤γ≤(r-1) (6)
Binary sequence ε (t) can be accurately positioned by above formula, and there are the specific locations of approximate period；γ is approximate period positioning
Intermediate variable；
Other steps and parameter are identical as one of specific embodiment one to three.
Specific embodiment 5: unlike one of present embodiment and specific embodiment one to four: the step 3
In two position one-dimensional vector T in 1 distance of swimming of longest starting point and ending point (occur in one-dimensional vector T longest it is continuous 1 when rise
Initial point and terminating point), detailed process are as follows:
Step 321,
1 distance of swimming terminating point position tEnd=0 of longest is defined,
1 run length rLen=0 of longest is defined,
The intermediate variable tTmpEnd=0 of 1 distance of swimming terminating point position of longest is defined,
Define the intermediate variable tTmpCount=0 of 1 run length of longest；
Step 3 two or two, another m=1, judge whether T (m) is equal to 1, if T (m) is equal to 1, execute step step 3 two
Three；If T (m) is not equal to 1, step 3 two or four is executed；
Step 3 two or three, 1 run length of longest intermediate variable tTmpCount add 1, m value at this time is assigned to longest 1
The intermediate variable tTmpEnd of distance of swimming terminating point position；
Step 3 two or four judges whether the intermediate variable tTmpCount of 1 run length of longest is greater than 1 run length of longest
RLen executes step 3 two or five if tTmpCount is greater than rLen；If tTmpCount is less than or equal to rLen, step is executed
326；
The value of the intermediate variable tTmpCount of 1 run length of longest is assigned to rLen by step 3 two or five, by longest 1
The value of the intermediate variable tTmpEnd of distance of swimming terminating point position is assigned to 1 distance of swimming terminating point position tEnd of value longest；0 is assigned to
TTmpCount (tTmpCount clearing)；
Step 3 two or six, another m+1 re-execute the steps 322 to step 3 two or six, until m=k；Execute step 3
Two or seven；
Step 3 two or seven judges whether tTmpCount is greater than rLen,
If tTmpCount is greater than tCount, the value of tTmpCount is assigned to rLen, while the value of tTmpEnd being assigned
To tEnd；
If tTmpCount is less than or equal to rLen, rLen and tEnd value is constant.
Shown in the following pseudocode of its location algorithm:
Other steps and parameter are identical as one of specific embodiment one to four.
Specific embodiment 6: unlike one of present embodiment and specific embodiment one to five: the step 4
It is middle according to cycle detection matrix G, judge whether binary sequence ε (t) has local period；Detailed process are as follows:
One step 3 one, building matrix group J are shown below:
Wherein JxFor -1 element of xth, J in matrix group Jx(δ) is the sub- square extracted from cycle detection matrix G
Battle array, is shown below:
Wherein
For submatrix JxElement in (δ)；
It is as follows to construct one-dimensional row vector Y:
Wherein, Y (η) is one-dimensional the η element of row vector Y, and value range is { 0,1 }；For submatrix Jx(δ)
Middle element；
Step 3 two searches for longest 1 in one-dimensional row vector Y by 1 distance of swimming location algorithm of longest in approximate period diagnostic method
The starting point and ending point of the distance of swimming, if 1 distance of swimming starting point of longest is tStart, terminating point tEnd, run length rLen；
If being unsatisfactory for rLen* (x+1)/n >=threshold2, then there is no significant local periods to show by binary sequence ε (t)
As；
If meeting rLen* (x+1)/n >=threshold2, then there are significant local period phenomenons by binary sequence ε (t)；
Wherein, threshold2For significant local period decision threshold, value range is (0,1), and threshold value is set bigger
Its significant local period is more obvious；
The accurate positioning of the significant local period of binary sequence is expressed from the next:
Wherein l is that local period positions intermediate variable.
Other steps and parameter are identical as one of specific embodiment one to five.
Specific embodiment 7: unlike one of present embodiment and specific embodiment one to six: the step 3
The starting point of 1 distance of swimming of longest in one-dimensional row vector Y is searched in two by 1 distance of swimming location algorithm of longest in approximate period diagnostic method
And terminating point, detailed process are as follows:
Step 321,
1 distance of swimming terminating point position tEnd=0 of longest is defined,
1 run length rLen=0 of longest is defined,
The intermediate variable tTmpEnd=0 of 1 distance of swimming terminating point position of longest is defined,
Define the intermediate variable tTmpCount=0 of 1 run length of longest；
Step 3 two or two, another η=1, judge whether Y (η) is equal to 1, if Y (η) is equal to 1, execute step step 3 two or three；
If Y (η) is not equal to 1, step step 3 two or four is executed；
Step 3 two or three, 1 run length of longest intermediate variable tTmpCount add 1, η value at this time is assigned to longest 1
The intermediate variable tTmpEnd of distance of swimming terminating point position；
Step 3 two or four judges whether the intermediate variable tTmpCount of 1 run length of longest is greater than 1 run length of longest
RLen executes step 3 two or five if tTmpCount is greater than rLen；If tTmpCount is less than or equal to rLen, step is executed
326；
The value of the intermediate variable tTmpCount of 1 run length of longest is assigned to rLen by step 3 two or five, by longest 1
The value of the intermediate variable tTmpEnd of distance of swimming terminating point position is assigned to 1 distance of swimming terminating point position tEnd of value longest；0 is assigned to
TTmpCount (tTmpCount clearing)；
Step 3 two or six, another η+1 re-execute the steps 322 to step 3 two or six, until η=k；Execute step 3 two
Seven；
Step 3 two or seven judges whether tTmpCount is greater than rLen；
If tTmpCount is greater than tCount, the value of tTmpCount is assigned to rLen, while the value of tTmpEnd being assigned
To tEnd；
If tTmpCount is less than or equal to rLen, rLen and tEnd value is constant.
Shown in the following pseudocode of its location algorithm:
According to the position of the starting point and ending point of 1 distance of swimming of longest in one-dimensional row vector Y, obtain in one-dimensional row vector Y most
Starting point, terminating point and the run length of long 1 distance of swimming；
If the starting point of 1 distance of swimming of longest is tStart, terminating point tEnd, run length rLen；
TStart=rLen-tEnd+1.
Other steps and parameter are identical as one of specific embodiment one to six.
Specific embodiment 8: unlike one of present embodiment and specific embodiment one to seven: the accurate week
Phase, approximate period, the specific determination process of local period are as follows:
Continuous Positive Integer Set if it existsSo that binary sequence ε (t) is in [L1,Ln]
On,
Wherein, taFor relative position of a bit element within the scope of a cycle, t in period templateω+a-1For period template
In relative position of the ω+a-1 bit element within the scope of a cycle, a be [1, LT] on continuous positive integer, indicate two-value
Sequence position；ω is symbol string length, LTFor sequence period length, [L1,Ln] be binary sequence ε (t) on one section two
Value sequence, L1And LnRespectively this section of binary sequence ([L1,Ln]) initial position and final position element；
For any ta[1, (Ln-L1+1)/LT] on arbitrary integer b have following formula establishment:
ε(L1-1+ta)=ε (L1-1+(b-1)*LT+ta) (11)
Then claim binary sequence ε (t) in [L1,Ln] on there are a sequence period length be LTGeneralized Periodic phenomenon；
ε(L1-1+ta)ε(L1-1+ta+1)…ε(L1-1+tω+a-1) it is the symbol string periodically occurred in Generalized Periodic phenomenon
That is period template, symbol string length are ω；
If L1=1, Ln→+∞ and ta=a, a are [1, LT] on continuous positive integer, then ω=LT, formula (11) describes
A cycle is LTAccurate periodic phenomena；
If L1→1,Ln→+∞ and ω → LT, it is L that formula (11), which describes a cycle,TApproximate period phenomenon；
If [L1,Ln] it is some part in binary sequence, and 0 < ω < LT, formula (11) describes one in local model
Enclose the local period phenomenon of periodically appearance.
Other steps and parameter are identical as one of specific embodiment one to seven.
Beneficial effects of the present invention are verified using following embodiment:
Embodiment one:
The present embodiment is specifically to be prepared according to the following steps:
For example frequency communication is included there are pseudo-random sequence, the wind that air-conditioning is blown is there are pseudo-random sequence, and there are pseudorandoms for massage armchair
Sequence needs to assess these pseudo-random sequences, below with Logistic chaotic binary sequences distance explanation；
The period that UBSPD method goes to detect the Logistic chaotic binary sequences under different computational accuracies through the invention shows
As.Logistic system equation is defined as foloows:
xn+1=μ xn(1-xn),μ∈(0,4],xn∈(0,1)
When control parameter μ value is [3.5699456,4] in formula, Logistic mapping is in chaos state.Further may be used
If { xnIt is chaos real value sequence, { snIt is binary sequence after quantification treatment, quantitative formula is as follows:
Chaos real value sequence can be converted into chaotic binary sequences by this equation, in chaos equation by c=0.5 in formula
M=16,24,32 three kinds of iteration precisions are respectively adopted herein in terms of iteration precision.Testing result is as shown in Fig. 2, can from figure
There is accurate periodic phenomena in iteration precision M=16 time series out and locating periodically length is 79.When iteration precision is M=24
Algorithm detects that its sequence the period occurs for 272 approximate period phenomenon, period template length ω=247, and is accurately positioned
It is the 5th column to 251 column with 272 for the period to period template position.When iteration precision is M=32, algorithm detects it
There is significant local period phenomenon in sequence, this algorithm extracts the period template of significant local period phenomenon as shown in Fig. 4, from
It can be seen that in figure and work as LTWhen=166 the 130 to 138 of the 4 to 6th row list showed period template be ' 110111001 ' it is significant
Local period phenomenon.
The present invention can also have other various embodiments, without deviating from the spirit and substance of the present invention, this field
Technical staff makes various corresponding changes and modifications in accordance with the present invention, but these corresponding changes and modifications should all belong to
In the protection scope of the appended claims of the present invention.
Claims (8)
1. a kind of chaotic binary sequences cycle detection and localization method, it is characterised in that: the method detailed process are as follows:
Step 1: constructing Two-Dimensional Reconstruction matrix R according to binary sequence ε (t), cycle detection square is obtained based on Two-Dimensional Reconstruction matrix R
Battle array G；
Step 2: judging whether binary sequence ε (t) has the accurate period according to cycle detection matrix G；
Step 3: judging whether binary sequence ε (t) has approximate period according to cycle detection matrix G；
Step 4: judging whether binary sequence ε (t) has local period according to cycle detection matrix G.
2. a kind of chaotic binary sequences cycle detection and localization method according to claim 1, it is characterised in that: the step
Two-Dimensional Reconstruction matrix R is constructed according to binary sequence in one, cycle detection matrix G is obtained based on Two-Dimensional Reconstruction matrix R；Detailed process
Are as follows:
Any randomly or pseudo-randomly binary sequence ε (t) for being n for length, defines the Two-Dimensional Reconstruction square of (n-1) * (n-1)
Sequence restructuring matrix of the battle array R as binary sequence ε (t), n are the length of binary sequence ε (t)；
Two-Dimensional Reconstruction matrix R is lower triangular matrix, and Two-Dimensional Reconstruction matrix R is expressed as following formula:
Wherein ε (i) and ε (j) is respectively i-th and j-th of element in binary sequence ε (t), Ri,jFor in Two-Dimensional Reconstruction matrix R
Element, ⊙ are same or operation；
Wherein, 1≤i≤n-1,1≤j≤n-1；
If binary sequence ε (t) meets ε (i) ε (i+1) ..., ε (i+ ω -1)=ε (i+j) ε (i+j+1) ... ε (i+j+ ω -1), that is, exist
The i-th bit of ε (t) and the i-th+j, which rise, has continuous ω element equal, shows as in restructuring matrix diagonal in the j-th strip of matrix R
The the i-th to the i-th+ω -1 of line, which rises, has continuous ω 1 to occur；ω is symbol string length；
Assuming that SkIt (t) is kth diagonal line in sequence restructuring matrix R, LkFor the number of kth diagonal entry, k is reconstruct square
Diagonal line serial number in battle array R；For Sk(t) the α element value in, and 1≤α≤Lk；
By sequence Sk(t) it carries out folding the cycle detection matrix G for generating r row k column as the period using k, wherein [2, n/2] k ∈, r is as follows
Shown in formula:
Floor () function is to be rounded downwards in formula；Mod is complementation operation；
Cycle detection matrix G is expressed as following formula:
Wherein G1,1For the first column element of the first row in cycle detection matrix G, G1,2For the first row secondary series in cycle detection matrix G
Element, G1,kFor the first row kth column element in cycle detection matrix G, G2,1For the second row first row member in cycle detection matrix G
Element, G2,2For second the second column element of row, G in cycle detection matrix G2,kFor the second row kth column element in cycle detection matrix G,
Gr,1For the first column element of r row in cycle detection matrix G, Gr,2For the second column element of r row in cycle detection matrix G, Gr,kFor
R row kth column element in cycle detection matrix G,For Sk(t) the 1st element value in,For Sk(t) in
2nd element value,For Sk(t) k-th of element value in,For Sk(t)+1 element value of kth in,For Sk(t)+2 element values of kth in,For Sk(t) the 2k element value in,
For Sk(t) (r-1) * k+1 element value in,For Sk(t) (r-1) * k+2 element value in,For Sk(t) the r*k element value in.
3. a kind of chaotic binary sequences cycle detection and localization method according to claim 2, it is characterised in that: the step
According to cycle detection matrix G in two, judge whether binary sequence ε (t) has the accurate period；Detailed process are as follows:
Construct one-dimensional vectorWhereinIt is shown below:
In formula,For element in one-dimensional vector V；Index is the element numbers of one-dimensional vector V, 1≤index≤(n/2-2)+1；
K is diagonal line serial number in restructuring matrix R；
If all elements value is all 0 in vector V, accurate periodic phenomena is not present in binary sequence ε (t)；
It, will be to there are accurate periodic phenomena in binary sequence ε (t) if there are one or Num element value being 1 in vector V
Amount V carries out ascending order traversal by index inferior horn scale value and finds the element that first value is 1The superscript k of this element is two
The accurate cycle length of value sequence ε (t)；
2≤Num≤(n/2-2)+1。
4. a kind of chaotic binary sequences cycle detection and localization method according to claim 1, it is characterised in that: the step
According to cycle detection matrix G in three, judge whether binary sequence ε (t) has approximate period；Detailed process are as follows:
Step 3 one, building one-dimensional vector T=[T (1) ... T (m) ... T (k)], wherein T (m) is shown below:
In formula, T (m) is m-th of element in one-dimensional vector T, and T (m) value range is { 0,1 }；K is diagonal line in restructuring matrix R
Serial number；For Sk(t) β * k+m element value in；
The starting point and ending point of 1 distance of swimming of longest in step 3 two, positioning one-dimensional vector T；
Step 3 three, according to the position of the starting point and ending point of 1 distance of swimming of longest in one-dimensional vector T, obtain in one-dimensional vector T most
Starting point, terminating point and the run length of long 1 distance of swimming；
If the starting point of 1 distance of swimming of longest is tStart, terminating point tEnd, run length rLen；
TStart=rLen-tEnd+1；
If being unsatisfactory for rLen/k > threshold1, then approximate period is not present in binary sequence ε (t)；
If meeting rLen/k > threshold1, then there are approximate periods by binary sequence ε (t)；
Wherein threshold1For approximate period decision threshold, value range is (0,1), and approximate period is expressed from the next:
ε (tStart) ... ε (tEnd)=ε (tStart+ γ * k) ... ε (tEnd+ γ * k), 1≤γ≤(r-1) (6)
By above formula positioning binary sequence ε (t), there are the specific locations of approximate period；γ is that approximate period positions intermediate variable.
5. a kind of chaotic binary sequences cycle detection and localization method according to claim 2, it is characterised in that: the step
The starting point and ending point of 1 distance of swimming of longest in one-dimensional vector T, detailed process are positioned in three or two are as follows:
Step 321,
1 distance of swimming terminating point position tEnd=0 of longest is defined,
1 run length rLen=0 of longest is defined,
The intermediate variable tTmpEnd=0 of 1 distance of swimming terminating point position of longest is defined,
Define the intermediate variable tTmpCount=0 of 1 run length of longest；
Step 3 two or two, another m=1, judge whether T (m) is equal to 1, if T (m) is equal to 1, execute step step 3 two or three；If
T (m) is not equal to 1, executes step 3 two or four；
Step 3 two or three, 1 run length of longest intermediate variable tTmpCount add 1, it is whole that m value at this time is assigned to longest 1 distance of swimming
The intermediate variable tTmpEnd of dead-centre position；
Step 3 two or four judges whether the intermediate variable tTmpCount of 1 run length of longest is greater than 1 run length rLen of longest,
If tTmpCount is greater than rLen, step 3 two or five is executed；If tTmpCount is less than or equal to rLen, step 3 two is executed
Six；
The value of the intermediate variable tTmpCount of 1 run length of longest is assigned to rLen by step 3 two or five, and 1 distance of swimming of longest is whole
The value of the intermediate variable tTmpEnd of dead-centre position is assigned to 1 distance of swimming terminating point position tEnd of value longest；0 is assigned to
tTmpCount；
Step 3 two or six, another m+1 re-execute the steps 322 to step 3 two or six, until m=k；Execute step 3 two or seven；
Step 3 two or seven judges whether tTmpCount is greater than rLen；
If tTmpCount is greater than tCount, the value of tTmpCount is assigned to rLen, while the value of tTmpEnd being assigned to
tEnd；
If tTmpCount is less than or equal to rLen, rLen and tEnd value is constant.
6. a kind of chaotic binary sequences cycle detection and localization method according to claim 1, it is characterised in that: the step
According to cycle detection matrix G in four, judge whether binary sequence ε (t) has local period；Detailed process are as follows:
One step 3 one, building matrix group J are shown below:
Wherein JxFor -1 element of xth, J in matrix group Jx(δ) is the submatrix extracted from cycle detection matrix G, as follows
Shown in formula:
Wherein
For submatrix JxElement in (δ)；
It is as follows to construct one-dimensional row vector Y:
Wherein, Y (η) is one-dimensional the η element of row vector Y, and value range is { 0,1 }；For submatrix JxIt is first in (δ)
Element；
Step 3 two searches for 1 distance of swimming of longest in one-dimensional row vector Y by 1 distance of swimming location algorithm of longest in approximate period diagnostic method
Starting point and ending point, if 1 distance of swimming starting point of longest be tStart, terminating point tEnd, run length rLen；
If being unsatisfactory for rLen* (x+1)/n >=threshold2, then local period phenomenon is not present in binary sequence ε (t)；
If meeting rLen* (x+1)/n >=threshold2, then there are local period phenomenons by binary sequence ε (t)；
Wherein, threshold2For local period decision threshold, value range is (0,1)；
The positioning of binary sequence local period is expressed from the next:
Wherein l is that local period positions intermediate variable.
7. a kind of chaotic binary sequences cycle detection and localization method according to claim 2, it is characterised in that: the step
The starting point of 1 distance of swimming of longest in one-dimensional row vector Y is searched in three or two by 1 distance of swimming location algorithm of longest in approximate period diagnostic method
And terminating point, detailed process are as follows:
Step 321,
1 distance of swimming terminating point position tEnd=0 of longest is defined,
1 run length rLen=0 of longest is defined,
The intermediate variable tTmpEnd=0 of 1 distance of swimming terminating point position of longest is defined,
Define the intermediate variable tTmpCount=0 of 1 run length of longest；
Step 3 two or two, another η=1, judge whether Y (η) is equal to 1, if Y (η) is equal to 1, execute step step 3 two or three；If
Y (η) is not equal to 1, executes step step 3 two or four；
Step 3 two or three, 1 run length of longest intermediate variable tTmpCount add 1, it is whole that η value at this time is assigned to longest 1 distance of swimming
The intermediate variable tTmpEnd of dead-centre position；
Step 3 two or four judges whether the intermediate variable tTmpCount of 1 run length of longest is greater than 1 run length rLen of longest,
If tTmpCount is greater than rLen, step 3 two or five is executed；If tTmpCount is less than or equal to rLen, step 3 two is executed
Six；
The value of the intermediate variable tTmpCount of 1 run length of longest is assigned to rLen by step 3 two or five, and 1 distance of swimming of longest is whole
The value of the intermediate variable tTmpEnd of dead-centre position is assigned to 1 distance of swimming terminating point position tEnd of value longest；0 is assigned to
tTmpCount；
Step 3 two or six, another η+1 re-execute the steps 322 to step 3 two or six, until η=k；Execute step 3 two or seven；
Step 3 two or seven judges whether tTmpCount is greater than rLen；
If tTmpCount is greater than tCount, the value of tTmpCount is assigned to rLen, while the value of tTmpEnd being assigned to
tEnd；
If tTmpCount is less than or equal to rLen, rLen and tEnd value is constant；
According to the position of the starting point and ending point of 1 distance of swimming of longest in one-dimensional row vector Y, show that longest 1 is swum in one-dimensional row vector Y
Starting point, terminating point and the run length of journey；
If the starting point of 1 distance of swimming of longest is tStart, terminating point tEnd, run length rLen；
TStart=rLen-tEnd+1.
8. a kind of chaotic binary sequences cycle detection and localization method according to claim 1, it is characterised in that: described accurate
Period, approximate period, the specific determination process of local period are as follows:
Continuous Positive Integer Set if it existsSo that binary sequence ε (t) is in [L1,Ln] on,
Wherein, taFor relative position of a bit element within the scope of a cycle, t in period templateω+a-1It is in period template
Relative position of the ω+a-1 bit element within the scope of a cycle, a are [1, LT] on continuous positive integer, indicate binary sequence institute
In position；ω is symbol string length, LTFor sequence period length, [L1,Ln] be binary sequence ε (t) on one section of binary sequence,
L1And LnThe initial position of respectively this section binary sequence and final position element；
For any ta[1, (Ln-L1+1)/LT] on arbitrary integer b have following formula establishment:
ε(L1-1+ta)=ε (L1-1+(b-1)*LT+ta) (11)
Then claim binary sequence ε (t) in [L1,Ln] on there are a sequence period length be LTGeneralized Periodic phenomenon；
ε(L1-1+ta)ε(L1-1+ta+1)…ε(L1-1+tω+a-1) it is the symbol string i.e. week periodically occurred in Generalized Periodic phenomenon
Phase template, symbol string length are ω；
If L1=1, Ln→+∞ and ta=a, a are [1, LT] on continuous positive integer, then ω=LT, formula (11) describes one
Period is LTAccurate periodic phenomena；
If L1→1,Ln→+∞ and ω → LT, it is L that formula (11), which describes a cycle,TApproximate period phenomenon；
If [L1,Ln] it is part in binary sequence, and 0 < ω < LT, formula (11) describes a local period phenomenon.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112558924A (en) * | 2020-12-11 | 2021-03-26 | 黑龙江大学 | Rapid detection method for local weak random phenomenon of pseudorandom binary sequence |
| CN112948813A (en) * | 2021-03-09 | 2021-06-11 | 北方实验室(沈阳)股份有限公司 | Statistical probability-based password analysis system and method |
| CN113255261A (en) * | 2021-05-08 | 2021-08-13 | 黑龙江大学 | Pseudo-random sequence period detection method based on FPGA |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040086117A1 (en) * | 2002-06-06 | 2004-05-06 | Petersen Mette Vesterager | Methods for improving unpredictability of output of pseudo-random number generators |
| US20080147759A1 (en) * | 2006-04-20 | 2008-06-19 | Marco Fiorentino | Self-authenticating quantum random bit generators |
| CN101888282A (en) * | 2010-04-22 | 2010-11-17 | 北京邮电大学 | Randomness analysis-based data encryption function detection method |
| CN102495883A (en) * | 2011-12-08 | 2012-06-13 | 河海大学 | Mining method for asynchronous periodic pattern in hydrologic time series |
| US20150098568A1 (en) * | 2012-05-24 | 2015-04-09 | Enigmedia S.L. | Method for generating a pseudorandom sequence, and method for coding or decoding a data stream |
| CN107239256A (en) * | 2016-12-27 | 2017-10-10 | 中国福利彩票发行管理中心 | The randomness detecting method of lottery industry random sequence based on overall merit |
-
2018
- 2018-07-20 CN CN201810805529.9A patent/CN108984151B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20040086117A1 (en) * | 2002-06-06 | 2004-05-06 | Petersen Mette Vesterager | Methods for improving unpredictability of output of pseudo-random number generators |
| US20080147759A1 (en) * | 2006-04-20 | 2008-06-19 | Marco Fiorentino | Self-authenticating quantum random bit generators |
| CN101888282A (en) * | 2010-04-22 | 2010-11-17 | 北京邮电大学 | Randomness analysis-based data encryption function detection method |
| CN102495883A (en) * | 2011-12-08 | 2012-06-13 | 河海大学 | Mining method for asynchronous periodic pattern in hydrologic time series |
| US20150098568A1 (en) * | 2012-05-24 | 2015-04-09 | Enigmedia S.L. | Method for generating a pseudorandom sequence, and method for coding or decoding a data stream |
| CN107239256A (en) * | 2016-12-27 | 2017-10-10 | 中国福利彩票发行管理中心 | The randomness detecting method of lottery industry random sequence based on overall merit |
Non-Patent Citations (1)
| Title |
|---|
| 郑艳斌: "混沌序列密码周期现象的检测与抵抗研究", 《中国博士学位论文全文数据库 信息科技辑》, no. 04, pages 2 * |
Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112558924A (en) * | 2020-12-11 | 2021-03-26 | 黑龙江大学 | Rapid detection method for local weak random phenomenon of pseudorandom binary sequence |
| CN112558924B (en) * | 2020-12-11 | 2022-08-26 | 黑龙江大学 | Rapid detection method for local weak random phenomenon of pseudorandom binary sequence |
| CN112948813A (en) * | 2021-03-09 | 2021-06-11 | 北方实验室(沈阳)股份有限公司 | Statistical probability-based password analysis system and method |
| CN112948813B (en) * | 2021-03-09 | 2024-08-02 | 北方实验室(沈阳)股份有限公司 | Cryptographic analysis system and method based on statistical probability |
| CN113255261A (en) * | 2021-05-08 | 2021-08-13 | 黑龙江大学 | Pseudo-random sequence period detection method based on FPGA |
| CN113255261B (en) * | 2021-05-08 | 2023-03-14 | 黑龙江大学 | FPGA-based pseudorandom sequence period detection method |
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