CN106033504B - Software sequence code generation method based on extensible precision chaos heredity - Google Patents
Software sequence code generation method based on extensible precision chaos heredity Download PDFInfo
- Publication number
- CN106033504B CN106033504B CN201510104571.4A CN201510104571A CN106033504B CN 106033504 B CN106033504 B CN 106033504B CN 201510104571 A CN201510104571 A CN 201510104571A CN 106033504 B CN106033504 B CN 106033504B
- Authority
- CN
- China
- Prior art keywords
- iteration
- value
- precision
- root
- orbit
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Expired - Fee Related
Links
Landscapes
- Complex Calculations (AREA)
Abstract
The invention discloses a software sequence code generation method based on extensible precision chaos heredity, wherein the basic structure of an extensible precision chaos track comprises a root gene position, a universal gene position and an independent gene position, and the method comprises the following steps: the first step, determining the length of the output software sequence codes and the quantity of the batch sequence codes, determining the root gene position and the universal gene position, and converting the root gene position and the universal gene position into decimal number serving as the Logistic equationx 0Determining the value of a control parameter by using an initial value; secondly, calculating by using a low-order iteration method, and iterating until the specified precision is not reached; when the specified precision is reached, outputting a sequence obtained by a low-order iteration method; and thirdly, writing the corresponding output sequence into a software data file as a software sequence code, and repeating the second step until the number of the specified batch sequence codes is met. The invention utilizes the characteristics of stable period and random diversity of independent gene positions and is suitable for protecting the legal use of computer software.
Description
Technical Field
The invention belongs to the technical field of computer software, and particularly relates to a method for generating a software sequence code by utilizing the genetic characteristic of extensible precision chaos genes to protect legal use of software.
Background
The invention relates to two aspects of the characteristics of the extendable precision chaotic gene-like inheritance in the chaos theory and the software sequence code in the technical field of computer software, and therefore, the technical background of the invention is explained from the two aspects.
(one) characteristics of scalable precision chaotic gene-like inheritance
The chaos phenomenon is widely distributed in nature. Chaos theory is also one of the research branches of physics, mathematics, meteorology, biology and information science.
The research of chaos can be divided into chaos in a continuous domain and chaos in a discrete space from a orbital space. The chaos in the continuous domain can be described as a trajectory of a chaotic power equation with continuous motion in real space. The chaos of the discrete space simulates the motion track of a chaotic dynamic equation in a limited digital space by using computing equipment such as a computer.
The chaotic orbit in the continuous domain is composed of real calculated values of a chaotic power equation under infinite precision, namely the chaotic orbit is composed of continuous points in a real space; which represents a true essential feature of chaos. The chaos of the discrete space calculates the iteration value of the chaos dynamic equation under the finite calculation precision of the computer, and the orbit space degenerates into a finite state machine.
In the research of the chaotic orbit, a plurality of methods and theories are used for revealing the characteristics of the chaotic orbit and the real essence of the chaos, and the main methods and theories can be summarized as follows: unstable periodic orbits in chaotic attractors (unstabilized periodic orbits), shadow lemma (Shadowing lemma), methods of statistical analysis, methods of number theory, and the like.
The shadow lemma establishes a bridge between real tracks and pseudo-random tracks to a certain extent, and real tracks can be continuously observed in a limited space. However, the theoretical verification thereof has great difficulty. In 2005, scholars in China, namely plum tree jun and the like, published research reports on dynamic characteristic analysis in one-dimensional linear chaotic mapping; the method explains the limitation of the shadow theory, and carries out systematic and theoretical analysis on the dynamic characteristic degradation problem of the one-dimensional linear chaotic mapping for the first time.
The unstable periodic orbit and the discrete period of the variation momenture thereof are greatly influenced by the calculation precision and the quantization error, and particularly the uncontrollable and random characteristics of the quantization error greatly influence the chaotic orbit. The statistical analysis method is an effective method for determining the influence of the calculation precision and the quantization error on the chaotic dynamic characteristic. In 2007, Otto (Oteo) et al performed statistical analysis of Logistic mapping and study of dynamic characteristics under the condition of double-precision floating-point arithmetic errors.
The randomly distributed quantization errors are closely related to the unstable periodic orbit of the chaos and the degradation problem of the chaos characteristic. However, the accuracy of the calculation in the computer has a great uncertainty about the influence of the quantization error. Currently, there is no systematic, theoretical analysis theory regarding computational accuracy and quantization error. Therefore, in order to reduce the influence of the quantization error on the dynamic characteristics of the chaos, increasing the calculation precision is undoubtedly one of the most effective methods for observing the essential characteristics of the chaos.
In 2010, scalable precision chaos was first proposed domestically. In 2011, the computing method of the extensible precision chaos is used for computing the chaos function step by step, and a dynamic array is used for storing a computing result. The stepwise calculation of the extensible precision chaos further reduces the influence of the quantization error on the dynamic characteristics of the chaos, so that the obtained chaos can be close to an ideal chaos state. And the design of the dynamic array can further expand the calculation precision, and lays a foundation for further observing the special phenomenon of the chaos real track. In 2012, Liu et al put forward a low-order iteration method for the first time, and the method lays a certain foundation for further revealing the true nature of chaos.
The short period disturbance of the unstable periodic orbit, i.e., the method of adding noise, destroys the occurrence of the short period to some extent. In 2013, Song et al further reported a short-period phenomenon of chaotic power systems, wherein due to the existence of calculation errors, chaotic orbits deviate from the original orbits in unpredictable states.
The Logistic equation is defined as follows:
x n+1= a*x n *(1- x n ), n = 0，1, … (1)
parameter(s)aIs a control parameter, and 0< a <4. Parameter(s)x n Is the first of the chaotic equationnThe value of the second iteration is,x 0is composed ofx n Initial iteration value, and 0< x n < 1。
Given Logistic equationx 0= 0.1 anda= 3.9. Assume that the calculation accuracy is set to 2. Iteration is carried out by a traditional computer floating point operation method, and points in the orbit of the Logistic equation are shown as follows.
0.35 -> 0.88 -> 0.41 -> 0.94 -> 0.21 -> 0.64 -> 0.89 -> 0.38 -> 0.91 -> 0.31 -> 0.83 -> 0.55 -> 0.96 -> 0.14 -> 0.46 -> 0.96
Under the calculation precision of 2 and the traditional computer floating point operation method, the track of the Logistic equation firstly passes through a transition period of 0.35- > … - > 0.55, then quickly enters a short period, namely 0.96- > 0.14- > 0.46, and enters a short period loop state at the iteration value of 0.96.
Under the same control parameters, i.e.a= 3.9, initial value set tox 0= 0.960167, set precision 6, iterate with traditional computer floating point arithmetic, points in the orbit of Logistic equation are as follows:
0.960167 -> 0.149160 -> 0.494954 -> 0.974900 -> 0.095432 -> 0.336666 -> 0.870955 -> 0.438330 -> 0.960167
as can be seen from the above iteration results, the track has no transition period, and the loop state is directly entered at the initial iteration point.
The difficulty in determining the quantization error further increases the difficulty in studying real and pseudo-random tracks. It is also the reason that the characteristics of the real chaos orbit are difficult to observe, and it is the quantization error that hides and covers the characteristics of the chaos inheritance-like.
The low order iteration method is one of the methods for effectively observing the real chaos orbit, and the low order iteration method is further compared with the traditional computer floating point operation method.
The standard IEEE 754 is adopted for a general floating-point operation method of a computer, and includes three operation modes: single precision (32-bit), double precision (64-bit) and extended precision (80-bit). The basic principle of the floating point operation method of the computer is as follows: the value of the specified accuracy, i.e. the maximum available accuracy that can be represented, is stored in the memory of the computer. When the computed value exceeds the precision specified by the computer, the upper part of the computed value is retained, while the lower part exceeding the maximum valid precision is discarded as the quantization error of the computer.
In the chaos equation calculation process, the calculation precision of the true values of the continuous points in the real orbit is increased after each iteration. When the calculation accuracy of the chaotic equation exceeds the maximum effective accuracy provided by the computer, the lower bits of the numerical solution of the chaotic equation iteration are discarded, so that the lower bits of the numerical solution cannot be obtained.
The following example is intended to compare the difference between real tracks and pseudo-random tracks.
In Logistic equations, initial iteration values are setx 0= 0.5 and control parametersaAn iterative initial condition of = 3.85, the Logistic equation is as follows for successive points in the real trajectory in real space of the continuous domain.
x 0 = 0.5
x 1 = 0.9625
x 2 = 0.1389609375
x 3 = 0.4606555620941162109375
x 4 = 0.9565402585425997111462927423417568206787109375
It is advantageous to observe this particular phenomenon of a real track if the digital bits of the last bits of the true values of successive dots of a real track are written in the form as follows.
0.5
0.9625
0.1389609375
0.… 109375
0.… 7109375
From the iteration valuex 2Starting at subsequent iteration values, all of the lower bits of which appear to have a common digital bit "09375", in further iterations the iteration valuex 3Andx 4all have a common digit "1", i.e., a common low digit "109375".
From basic knowledge of genetics, it can be similarly deducedx 3All subsequent iterations of the start, i.e.x 2All have a common genetic gene "09375" which is completely duplicated, in other words, the successive points of the orbit all have the essential characteristics of this family in the process of evolution.
Let us look at another example. Based on computer floating point operation, assuming that the maximum effective precision is 3, setting an initial iteration value in a Logistic equationx 0= 0.5 and control parametersaInitial condition of = 3.85, trajectory variation of Logistic equation in discrete space of computer is as follows.
x 0 = 0.5
x 1 = a* x 0 *(1- x 0) = 3.85*0.5*(1-0.5) = 0.9625。
Since the effective calculation accuracy set in the computer is 3, in other words, the minimum decimal number that the computer can represent is 0.001, i.e., the third digit after the decimal point. Therefore, the fractional part beyond the digital bit will be discarded.
Therefore, in the case of the limited accuracy 3,x 1= 0.962, the lower 0.0005 of the numerical solution will be truncated.
In the second iteration, the computer will usex 1And = 0.962, and the calculation procedure is as follows.
x 2= 3.85 × 0.962 = 1-0.962) = 0.1407406. Similar to the previous, the computer will discard the lower part of the numerical solution and use the truncated value 0.140 for the next iteration.
Continuous point truth of real track on continuous domainx 2= 0.1389609375, it is clear that the pseudo-random tracks have deviated from the continuous points of the true tracks, and furthermore, quantization errors of the computer with limited computational accuracy corrupt the lower part of the true values of the continuous points of the true chaotic tracks. And the properties of the chaotic and similar genetic genes hidden in the lower portion are destroyed by the quantization error.
The calculation of the continuous points of the chaotic real trajectory in real space cannot contain any calculation error, in other words, the true values of the continuous points of the real trajectory are calculated with absolute accuracy. Any calculation error will result in the loss of the lower digit bits of the numerical solution.
From the calculation process of the chaotic orbit, it can be found that the low-order numerical values of the continuous points of the real orbit can be obtained only when the calculation process cannot contain any calculation error. In other words, any calculation error destroys the law of the lower bits, and causes the track to jump to another track.
In order to research the low-order rule of continuous points of the chaotic real orbit, the following conditions need to be met:
condition _ 1: the calculation of the continuous points of the real chaotic orbit requires the calculation of absolute precision;
condition _ 2: the computing system can meet the requirement of continuous expansion of precision.
Condition _1 ensures the acquisition of the lower digital bits of the true values of successive points of the real track, otherwise quantization errors would corrupt the lower digital bits. Condition _2 ensures that the characteristic of true values of successive points of the real track can be observed continuously, in other words, that the characteristic is that of the real track over the whole space, not that of a limited space. However, in current computer computing systems, Condition _1 is satisfied to the extent that, within a given effective computational accuracy, absolute accuracy of the computation can be guaranteed as long as the accuracy of the value to be computed does not exceed the maximum effective accuracy of the computer.
Furthermore, Condition _2 is difficult to satisfy in any existing computing system. Initial iteration value of given Logistic equationx 0And control parametersaThe accuracy of the initial conditions of (1) is 1, for example:x 0= 0.1 andaiteration is carried out with = 3.9. After one iterationx 1The accuracy of (3). After the second iteration, the process is carried out,x 2the accuracy of (2) is 7. After 10 iterations of the process, the process was,x 10has an accuracy of 2047; after the passage of 20 iterations of the process,x 20accuracy of 2097151. After about 10 iterations, the precision of the iteration values is expanded by nearly 1000 times. The maximum precision of the corresponding decimal expressed by the IEEE 754 double-precision floating-point operation used in the conventional computer is about 15 bits, namely the minimum real number expressed is 10-15. Therefore, any computing system has difficulty in satisfying the extension of the accuracy of the iterative process.
In summary, Condition _2 is a barrier for observing the low order rule of the continuous points of the chaotic real track. The main limitation is that any current computing system computes with limited accuracy, in other words, the computational accuracy provided by the limited space of the computer memory cannot meet the requirement of infinite extension of the accuracy of the continuous points of the chaotic real orbit.
In order to observe the low-order rule of continuous points of the chaotic real track, the contradiction between the finite calculation precision and the infinite extension of the iteration precision of a computer must be solved. In other words, the specific problems are: and observing the low-order rule of continuous points of the real track by using the limited calculation precision of a computer.
Obviously, the conventional calculation method has difficulty in solving this problem. The main reasons can be summarized as:
(1) the known calculation methods all adopt the method of reserving the high order of the calculation result, namely, the approximate value in the numerical calculation is obtained by discarding the low order part of the calculation value. The numerical calculation method in the computer system adopts the calculation method at present.
(2) The traditional calculation methods are all set in a mode of automatically keeping the precision, namely, the calculation precision is not controlled in the calculation process. Specifically, when an iterative process is performed, the computing system does not hint or provide the accuracy of the value of the current operation unless the user designs the process to provide the accuracy at his or her discretion. The method for automatically retaining the precision limits the calculation of absolute precision in the calculation process to a great extent; because the correctness of the calculated value, i.e. the calculation of the absolute accuracy, cannot be guaranteed if it is not known whether the accuracy of the currently calculated value exceeds the maximum accuracy provided by the computer.
Through the analysis, the traditional calculation method is difficult to solve the problem of observing the characteristic of the chaotic real orbit.
In order to solve the problem of observing the low-order law of continuous points of a real track by using the limited calculation precision of a computer, the following basic problems must be solved:
(1) the computational process of the computing system must be capable of precision control, i.e., the precision with which the numerical solution of the calculations currently being made can be obtained. The purpose of this is to enable the calculation of absolute accuracy with limited accuracy in a computer.
(2) The numerical calculation of the computing system must be able to retain the lower numerical bits of the calculated value. This feature of the chaotic real tracks is hidden in the lower order digital bits.
Under the framework, the characteristics of similar genetic genes of continuous points of the chaotic real orbit can be researched by adopting a low-order iteration method.
Before describing the low-order iteration method, some definitions are given herein to better illustrate the basic principles of the low-order iteration method.
Any decimal fractionxAnd 0 is< x <1, can be represented asx = 0.r 1 r 2…r i …r n Wherein the digital bitr i Belonging to the set 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Definition 1: in decimalxIn (1),r 1is defined asxThe highest number of bits of the data stream,r n is defined asxThe lowest digit bit of (a).
This definition enables distinguishing the position of the taken digital bit of the calculated value in a low-order iterative method.
Definition 2: when in user n When the value is not equal to 0, the value,nis defined asxThe accuracy of (2).
Definition 3: iteration value of Logistic equationx i = 0.r 1 r 2…r j …r n-2 r n-1 r n ，pnIs a positive integer other than 0, and has an iteration valuex i Is lowpnThe digital bit is defined as 0.r pn-k …r pn-2 r pn-1 r pn I.e. digital bitsr pn-k …r pn-2 r pn-1 r pn From the lowest positionr pn Initially continuouslypnDigital bits.
The definition is mainly used for calculating the lowest order bit of a numerical value exceeding the appointed value in the iteration process of the chaotic equationpnWhen, the calculated value is kept lowpnA bit. And lower the samepnThe bits are converted to a corresponding fractional form so that the fractional can be used for iteration in the next iteration. In conventional computer floating-point operations, low-order bits exceeding the computational accuracy are discarded, as opposed to low-order iteration. Definition 3 explicitly defines lowpnThe location of the bits in the calculated value and the method of translation.
Definition 4: absolute accuracy calculation is defined as calculation that does not involve any calculation error, and the accuracy of the obtained numerical solution is the true accuracy of the numerical value.
This definition is the computation of absolute accuracy that is achieved within the limited computational accuracy of the computing system, i.e., the maximum accuracy of the absolute accuracy computation cannot exceed the specified computational accuracy of the computing system.
The specific calculation process of the low-order iteration method of the continuous points of the real track of the extensible precision chaotic Logistic equation is defined as follows:
step _ 1: first step of calculating Logistic equation with absolute accuracyy = x*(1-x)；
Step _ 2: second step of calculating Logistic equation with absolute accuracyz = a*y；
Step _ 3: when the obtained iteration valuezIs less than or equal to a given precisionpnWhen the value of (2) is obtained, the iteration valuezAll digital bits of the digital code are reserved and used as iteration input values of the next step; otherwise, the obtained iteration value is usedzIs lowpnBit conversion to decimal 0.…r pn-2 r pn-1 r pn And returning as an input value for the next iteration.
The chaotic equation is calculated step by the low-order iteration method, so that the calculation error caused by the limitation of precision in the calculation process can be eliminated, and the Condition-1 is satisfied to realize the calculation of the absolute precision of the continuous points of the real track; in addition, the precision obtained by the calculation can be predicted by using the relational expression of the precision of the extensible precision chaos and the iteration number, and the precision control is realized.
The difference between the low-order iteration method and the conventional iteration method is also that: in the event that a given calculation accuracy conflicts with the current value of the calculation, the lower iteration method requires discarding the upper bits of the obtained value and retaining the digital bits starting from the lowest bit. Conventional iterative methods, in contrast, discard the low bits and leave the high bits when this occurs. Furthermore, conventional iterative methods generally do not require computational accuracy, i.e., absolute accuracy.
To further explain the low-order iteration method, an example is used herein to demonstrate the specific process of the low-order iteration method.
Initial values are set in the hypothesis Logistic equationx 0= 0.2 and control parametersa Initial condition of =3.3, in order to observe the low of the true value of the Logistic equation for the continuous points in the real trajectory in the real space of the continuous domainpnBit features, i.e. settingpn= 7, the effective accuracy of the computing system used by the computer is set to 20, and the specific calculation process of the lower iteration method is as follows.
x 0 = 0.2。
x 1=3.3 × 0.2 = 0.2) = 0.528, iteration value obtained over one iterationx 1Has an accuracy of 3, specifiedpn= 7, in Step _3, becausex 1Is less accurate than specifiedpnOf (a), thus, iterating over the valuesx 1All digital bits are retained for the next iteration.
x 23.3 × 0.528 × 1-0.528) = 0.8224128, iteration value obtainedx 2Has an accuracy of 7, specifiedpn= 7, in Step _3, becausex 2Is equal to specifiedpnOf (a), thus, iterating over the valuesx 2All digital bits are retained for the next iteration.
x 3 = 3.3*0.8224128*(1-0.8224128) = 0.481964955107328The obtained iteration valuex 3Has an accuracy of 15, specified in Step _3pn= 7 becausex 3Is more accurate than specifiedpnOf (a) and thus the resulting iteration valuex 3Is converted to a fraction 0.5107328 for the next iteration, i.e., usingx 3= 0.5107328 go on next iteration.
x 4 = 3.3*0.5107328*(1-0.5107328) = 0.824619863113728The obtained iteration valuex 4With an accuracy of 15, which is similar to the previous iteration,x 4is more accurate than specifiedpnOf (a) and thus the resulting iteration valuex 4Is converted to a fraction 0.3113728 for the next iteration, i.e., usingx 4= 0.3113728 go on next iteration.
It is worth noting that the points are continuous in the real track of the chaosx 4Is true value of
x 4 = 0.8239266326138737085064023113728
The precision of the true value is 31, the effective precision of a computing system used by a computer is 20, and the low-order iteration method obtains the value of the true value of the continuous point in the chaotic real track required to observe the low-order under the limited 20-order computing precision.
x 5 = 3.3*0. 3113728*(1-0. 3113728) = 0.707585272086528Similar to the previous iteration, the resulting iteration valuex 5Is converted to a fraction 0.2086528 for the next iteration, i.e., usingx 5= 0.2086528 go on next iteration.
To further verify the feasibility of this method, continuous points in the real orbit were chaoticx 5True values of (some digital bits in the middle are omitted):
x 5 = 0.4787360710…902862072086528
x 5the precision is 63, the low-order iteration method obtains the value of the lower 7 orders of the true value of the continuous point in the chaos real orbit under the limited calculation precision, and divides the value by lowpnThe values of the digital bits of other upper bits than the bits have a large difference.
In summary, it can be seen that the low-order iteration method can overcome the problem of the expansion of the precision of the true value of the continuous points of the chaotic real track under the limited calculation precision, and can continuously observe the low-order of the chaotic real track.
By using the low-order iteration method, the low-order rule of continuous points of the real chaotic track can be effectively observed, and a certain foundation is laid for revealing the nature of the chaos.
A true chaotic orbit is without cycles. Because the precision of continuous points in the real chaotic orbit is continuously expanded, the precision of the iteration value is larger and larger along with the increase of the iteration times, and the iteration values cannot be the same. However, in the discrete digital chaotic orbit simulated by the computer, the chaotic dynamic equation finally enters a loop due to a finite state.
Chaotic orbits typically contain two parts:
Part 1: x 1, x 2, …, x d
Part 2: x d+1, x d+2, …, x d+c
where Part 1 is referred to as the delay Part of the track and Part 2 is referred to as the loop Part of the track.cIs the period of the cyclic part of the track. It can be seen that the law of the low order of the real track occurs in the cyclic part.
Setting initial values in Logistic equationsx 0= 0.2 and control parametersaThe initial condition of =3.3 is exemplified by observing the lower bits of consecutive points in the real track in the real space of the consecutive domain using the lower iteration method. First, set uppnAnd =3, namely, observing the characteristics of the lower 3 bits of the true values of the continuous points of the real chaotic track.
The chaotic orbit obtained by using the low-order iteration method is as follows:
x0 = 0.2
x1 = 0.528 x2 = 0.128 x3 = 0.328 x4 = 0.728
x5 = 0.528 x6= 0.128 x7 = 0.328 x8 = 0.728
when in usepnIf =3, the lower bits of the chaotic orbit have obvious structural characteristics. Chaotic orbit at initial pointx 0Has passed through a delay section fromx 1Regular cycles are started. The period length of the cycle is equal to 4. It is noted that each successive point of the cyclic portion of the track has a common lower 2-bit digital bit "28".
In order to better reveal the characteristic of the low order bits of the chaotic track, some definitions are given in order to better illustrate the basic structure of the real track of the scalable precision chaotic.
Definition 5: root loci means that in the cyclic Part of the real track (Part 2), some of the lower digits of the true values of successive points of the track remain unchanged during the iteration, such digits being called root loci, i.e. rgp (root gene position).
The root gene locus is kept unchanged in the continuous change of the chaotic real orbit. A true orbit can be identified based on the root locus. It is characterized by a genetic pattern very similar to that of a gene, where the father inherits some genes of a family from the grandfather, and the son inherits the genes of the family from the father. For example: to some extent, the appearances of grandfather, father and son are similar, and the characteristic accords with the characteristic of gene self-replication. The essential features of the family can be determined from these genes.
The characteristic of chaos real orbit is also obvious. Although each successive point has a different true value in the successive iterations, the low order of its true value preserves the essential features of the track, which in further evolution is passed on to the next value, looping back and forth.
Setting initial value in Logistic equationx 0= 0.1 and control parametersaInitial conditions of = 3.9 are set as examplespn= 2, observing the characteristics of the lower 2 bits of the continuous points of the chaotic orbit by using a lower iteration method, as follows:
x0 = 0.1 x1 = 0.51
x2 = 0.61 x3 = 0.81 x4 = 0.21 x5 = 0.01
x6 = 0.61 x7 = 0.81 x8 = 0.21 x9 = 0.01
when in usepnIn case of = 2, chaotic orbit is inx 0Andx 1has passed through a delay section fromx 2Regular cycles are started. The period of the cycle can be seen to be equal to 4. The chaotic orbit is characterized in that the root gene bit has only 1 digital bit, and the value of the root gene bit is equal to 1.
TABLE 1 whenx 0 = 0.2, a= 3.9 andpnindependent loci of the same universal locus in case of = 4
CGP = “36” CGP = “56” CGP = “96” CGP = “76”
x2 = 0.0336 x3 = 0.7056 x4 = 0.1696 x5 = 0.9776
x6 = 0.3136 x7 = 0.4656 x8 = 0.4896 x9 = 0.8176
x10 = 0.7936 x11 = 0.6256 x12 = 0.6096 x13 = 0.2576
x14 = 0.4736 x15 = 0.1856 x16 = 0.5296 x17 = 0.2976
x18 = 0.3536 x19 = 0.1456 x20 = 0.2496 x21 = 0.9376
x22 = 0.4336 x23 = 0.5056 x24 = 0.7696 x25 = 0.1776
x26 = 0.7136 x27 = 0.2656 x28 = 0.0896 x29 = 0.0176
x30 = 0.1936 x31 = 0.4256 x32 = 0.2096 x33 = 0.4576
x34 = 0.8736 x35 = 0.9856 x36 = 0.1296 x37 = 0.4976
x38 = 0.7536 x39 = 0.9456 x40 = 0.8496 x41 = 0.1376
x42 = 0.8336 x43 = 0.3056 x44 = 0.3696 x45 = 0.3776
x46 = 0.1136 x47 = 0.0656 x48 = 0.6896 x49 = 0.2176
x50 = 0.5936 x51 = 0.2256 x52 = 0.8096 x53 = 0.6576
x54 = 0.2736 x55 = 0.7856 x56 = 0.7296 x57 = 0.6976
x58 = 0.1536 x59 = 0.7456 x60 = 0.4496 x61 = 0.3376
x62 = 0.2336 x63 = 0.1056 x64 = 0.9696 x65 = 0.5776
x66 = 0.5136 x67 = 0.8656 x68 = 0.2896 x69 = 0.4176
x70 = 0.9936 x71 = 0.0256 x72 = 0.4096 x73 = 0.8576
x74 = 0.6736 x75 = 0.5856 x76 = 0.3296 x77 = 0.8976
x78 = 0.5536 x79 = 0.5456 x80 = 0.0496 x81 = 0.5376
x82 = 0.6336 x83 = 0.9056 x84 = 0.5696 x85 = 0.7776
x86 = 0.9136 x87 = 0.6656 x88 = 0.8896 x89 = 0.6176
x90 = 0.3936 x91 = 0.8256 x92 = 0.0096 x93 = 0.0576
x94 = 0.0736 x95 = 0.3856 x96 = 0.9296 x97 = 0.0976
x98 = 0.9536 x99 = 0.3456 x100 = 0.6496 x101 = 0.7376
x102 = 0.0336 x103 = 0.7056 x104 = 0.1696 x105 = 0.9776
Definition 6: the universal Gene locus refers to a cyclic portion in a real orbit, and when the period of the lower bits of the orbit is equal to 4, such a locus is called a universal Gene locus, i.e., cgp (common Gene position).
Definition 7: the independent Gene locus refers to a digital locus which is combined with a universal Gene locus to express a random characteristic in a circulating part of a real orbit and is called as an independent Gene locus, namely IGP (induced Gene position).
TABLE 2 randomness of independent loci of truth values in the true orbitals of the Logistic equation
The initial condition of iteration of the Logistic equation is assumed to bex 0= 0.2 anda= 3.9, givenpn= 4, its iteration value may be expressed asx i = 0.r 1 r 2 r 3 r 4. Table 1 gives the independent loci of the same universal locus in the chaotic real trajectory. Digital bitr 3Andr 4 is a universal gene locus and is characterized in that,r 4is the root locus. The universal gene positions (CGP) are equal to "36", "56", "96" and "76", respectively.
Table 1, column 1, shows the iterative solution for an independent locus with the universal locus "36", like column 1, column 2 gives the iterative solution for an independent locus with the universal locus "56", and so on. Wherein the digital bitr 1Andr 2are independent loci.
Table 2 shows the independent locir 1Andr 2distribution of (2). As can be seen from Table 2, the independent locir 1Andr 2from 00 to 99. In other words, the independent loci traverse a real space with an accuracy of 2, i.e., all values from 0 to 0.99. The independent gene locus largely determines the random nature of the chaos.
The basic structure of the lower bits of the continuous points of the real track of the scalable precision Logistic chaos is shown in fig. 1. The trunk of the tree in FIG. 1 is the root locus (RGP); its 4 main branches are the universal loci (CGPs). In a further evolution, independent loci appear on the basis of the main branches, which represent the appearance of randomness.
In table 1, for example:x 2= 0.0336, the iteration value 0.0336 may be obtained at the first sub-branch (lowest) "0" of branch "336", i.e. the iteration value 0.0336 is obtainedx 2. By analogy, other iteration values at branch "336" can be obtained, for the second sub-branch "4x 22 = 0.4336, of the third subbranch "8x 42= 0.8336, etc. In addition, similar laws also occur in other branches.
In summary, the basic structure of the continuous points of the chaotic real trajectory of the Logistic equation can be divided into root loci (RGPs), common loci (CGPs), and independent loci (IGPs). The basic structure is the essential characteristic of the chaotic power system, and is independent of the quantization error, namely the characteristic of the similar genetic gene is independent of the quantization error.
The basic structure of the true track of the extensible precision chaos can further observe the essential characteristics of the chaos.
As can be seen from FIG. 1, the root loci of the loop portions of each real orbit are identical. In subsequent iterations, the continuum of its true trajectory retains the properties of this similar genetic gene, i.e., self-replicating and mutating.
Genetics (Genetics) is the science of studying the Genetics and variations of an organism, studying the structure, function, and how genes are transmitted during Genetics and varied in different offspring.
Genes or genetic factors are the main material of genetic variation. Genes have two main characteristics, namely, the genes can completely replicate themselves so as to maintain the basic characteristics of organisms; secondly, in the process of heredity, the genes show the characteristics of variation, have the characteristic of biological diversity or can be simply described as random diversity.
A typical example is that even a twin or a multi-twin, though inheriting many of the basic characteristics of parents, looks very similar; however, they are not identical, i.e., a variability between individuals is maintained. It is probably not possible to find all over the world that two people have exactly the same fingerprint. The diversity embodied in the heritage has very important significance.
The characteristic of the low order of the real track of the scalable precision chaos is very similar to the characteristics of the gene of genetics. In the evolution process of the chaotic equation, the subsequent iteration inherits the basic characteristics of the orbit, namely the root locus, which represents the basic characteristics of the orbit; its iterative descendants fully replicate this information. In addition, the independent loci exhibit the biodiversity of the chaotic equation, i.e., random diversity.
One fundamental problem in genetics is gene sequencing. Preliminary sequencing work was performed on the root loci herein.
When given an initial value of (x 0) And control parameters (a) When the last digit bit of (2) belongs to the integer Set1= {1, 2, 3, 4, 6, 7, 8, 9} or Set2= {5}, the chaotic equation has the characteristic of precision expansion. Obviously, the chaos equation shows richer gene locus diversity and regularity of the trajectory when it is defined on Set1, and therefore, some characteristics of the initial iteration condition of the chaos equation defined on Set1 are emphasized herein.
In the test analysis, the initial value (A) is selectedx 0) And control parameters (a) All have an accuracy of 1, i.e. an initial value (x 0) Taken from the Set (x 0) = 0.1, 0.2, 0.3, 0.4, 0.6, 0.7, 0.8, 0.9, and control parameter (c: (m) ((m))a) Is taken from the Set (a)={3.1, 3.2, 3.3, 3.4, 3.6, 3.7, 3.8, 3.9}。
The initial iteration condition of the real orbit of the chaotic equation can be described as a combined value of an initial value and a control parameter, which can be expressed as (a)x 0, a) I.e., (0.1, 3.1), (0.1, 3.2), …, (0.9, 3.9), etc.
The initial conditions are (0.1, 3.1) and (0.9, 3.1) iteration valuesx 1The latter values are the same.
When in usex 0 When the molar ratio is not less than 0.1,x 1 = a* x 0*(1- x 0)=3.1*0.1*(1-0.1) = 0.279。
when in usex 0 When the molar ratio is not less than 0.9,x 1 = a* x 0*(1- x 0)=3.1*0.9*(1-0.9) = 0.279。
thus, the initial condition is that (0.1, 3.1) and (0.9, 3.1) enter the same trajectory after the first iteration. In order to distinguish different tracksThe initial conditions (0.1, 3.1) and (0.9, 3.1) give only (0.1, 3.1), omitting (0.9, 3.1). Similar situations also exist for (0.2,a) And (0.8) of (A,a），（0.3，a) And (0.7) of (A,a），（0.4，a) And (0.6) of (A,a) And the like.
The sequencing results of the root genes were grouped as follows according to the length of the root locus.
The root length of the first grouping was 3, and the set was as follows:
Group_1 = {(0.2, 3.1), (0.3, 3.7)}.
TABLE 3 root locus mapping of Group _1
Initial iteration condition RGP
(0.2, 3.1) 504
(0.3, 3.7) 027
Table 3 shows the root locus map of Group _ 1. For example: taking initial iteration conditions (0.3, 3.7), setting the precision value of the low bit to be 6, namelypn And (6). The lower 6 bits of the true value of the continuous points of the chaotic real track are as follows:
x 1 = 3.7*0.3*(1-0.3) = 0.777。
x 2 = 3.7*0.777*(1-0.777) = 0.6411027taking the lower 6 digital bits, i.e.x 2 = 0.411027。
x 3 = 3.7*0.411027*(1- 0.411027) = 0.8957100795027And taking the lower 6 digital bits.
Thus, it is possible to providex 3 = 0.795027。
x 4 = 0.563027。
x 5 = 0.099027。
x 6 = 0.171027。
x 7 = 0.315027。
x 8 = 0.603027。
x 9 = 0.179027。
The root gene site is the lower 3, i.e. RGP = 027. The universal gene sites are '1027' and '5027',"3027", "9027". Fromx 6A loop state is started with a period length of 4.
The root locus length of the second grouping was 2, and the set was as follows:
Group_2 = {(0.1, 3.1), (0.4, 3.2), (0.1, 3.3), (0.2, 3.3), (0.3, 3.4), (0.3, 3.8)}.
TABLE 4 root Gene bitmap spectra of Group _2
Initial iteration condition RGP
(0.1, 3.1) 29
(0.4, 3.2) 32
(0.1, 3.3) 03
(0.2, 3.3) 28
(0.3, 3.4) 36
(0.3, 3.8) 48
Table 4 shows the root locus map of Group _ 2. For example: taking initial iteration conditions (0.2, 3.3), setting the precision value of the low bit to be 5, namelypn And (5). The lower 5 bits of the true value of the continuous points of the chaotic real track are as follows:
x 1 = 3.3*0.2*(1-0.2) = 0.528。
x 2=3.3 × 0.528 × 1-0.528) = 0.8224128, and the lower 5 digits are taken, that is, the digitsx 2 = 0. 24128。
x 3 = 3.3*0.24128*(1- 0.24128) = 0.60411107328And taking the lower 5 digital bits.
Thus, it is possible to providex 3 = 0.07328。
x 4 = 0.13728。
x 5 = 0.86528。
x 6 = 0.72128。
x 7 = 0.03328。
x 8 = 0.05728。
The root locus is the lower 2 position, i.e. RGP = 28. The universal gene positions are "128", "328", "728", "528", and the cycle length is 4.
TABLE 5 root Locus map of Group _3
Initial iteration condition RGP
(0.1, 3.9), (0.3, 3.9) 1
(0.1, 3.2), (0.2, 3.2), (0.2, 3.7), (0.3, 3.2), (0.4, 3.7) 2
(0.3, 3.3) 3
(0.1, 3.6), (0.2, 3.6), (0.3, 3.6), (0.4, 3.1), (0.4, 3.6) 4
(0.1, 3.4), (0.2, 3.4), (0.2, 3.9), (0.4, 3.4), (0.4, 3.9) 6
(0.1, 3.7) 7
(0.1, 3.8), (0.2, 3.8), (0.4, 3.3), (0.4, 3.8) 8
(0.3, 3.1) 9
The third grouping has a root length of 1, and is grouped as follows:
Group_3 = {(0.1, 3.2), (0.1, 3.4), (0.1, 3.6), (0.1, 3.7), (0.1, 3.8), (0.1, 3.9), (0.2, 3.2),
(0.2, 3.4), (0.2, 3.6), (0.2, 3.7), (0.2, 3.8), (0.2, 3.9), (0.3, 3.1), (0.3, 3.2),
(0.3, 3.3), (0.3, 3.6), (0.3, 3.9), (0.4, 3.1), (0.4, 3.3), (0.4, 3.4), (0.4, 3.6),
(0.4, 3.7), (0.4, 3.8), (0.4, 3.9)}
table 5 shows the root locus map of Group _ 3. For example: the initial iteration condition (0.1, 3.8) is taken and the lower bit precision value is set to be 4. The lower 4 bits of the true value of the continuous points of the chaotic real track are as follows:
x1 = 0.342
x2 = 0.1368 x3 = 0.5888 x4 = 0.5328 x5 = 0.1808
x6 = 0.3168 x7 = 0.3488 x8 = 0.6528
the initial iteration condition (0.2, 3.8) is taken and the lower bit precision value is set to be 4. The lower 4 bits of the true value of the continuous points of the chaotic real track are as follows:
x1 = 0.608 x2 = 0.6768 x3 = 0.8688 x4 = 0.8928
x5 = 0.1008 x6 = 0.9568 x7 = 0.8288 x8 = 0.4128
the initial iteration condition (0.4, 3.3) is taken and the lower bit precision value is set to be 4. The lower 4 bits of the true value of the continuous points of the chaotic real track are as follows:
x1 = 0.792
x2 = 0.6288 x3 = 0.4848 x4 = 0.7568 x5 = 0.7408
x6 = 0.0688 x7 = 0.9648 x8 = 0.1168
the initial iteration conditions (0.1, 3.8), (0.2, 3.8) and (0.4, 3.3) have the same root locus, i.e. RGP = 8. In other words, under the initial iteration condition, the lowest bits of the true values of the real tracks are all 8. However, the initial iteration conditions (0.1, 3.8) and (0.2, 3.8) have the same general gene positions "68", "28", "88" and "08". While the initial iteration conditions (0.4, 3.3) have universal gene positions "88", "48", "68" and "08".
Obviously, in real orbitals with the same root gene, there are different combinations of universal loci in the orbitals due to differences in initial conditions.
By root locus, the number of orbitals within a given condition can be analyzed. As can be deduced from tables 3, 4 and 5, the maps of root genes of the initial iteration condition with the precision of 1 can be divided into 3 groups, and there are 16 true chaotic orbits of the same root genes in the real space of the continuous domain, wherein 2 orbits are used for the length of the root genes, 6 orbits are used for the length of the root genes, and 8 orbits are used for the length of the root genes, 1. In addition, within the same root gene orbit, the characteristics of the similar orbitals, i.e., the basic characteristics of the same root orbit, can be analyzed by the universal gene locus.
In order to further understand the characteristics of the independent gene position, the characteristics of the unstable periodic orbit under the traditional computer floating point operation and the low-order period of the chaotic real orbit based on the low-order iteration method are compared. Table 6 gives a comparative analysis of the track cycle under both methods.
TABLE 6 chaotic orbit period contrast analysis
Cycle length of orbital cycle low order iteration method of precision IEEE double-precision floating point operation
Transition period length cycle period length
1 0 4 1
5 20 177 500
8 345 11658 62500
10 39279 39358 1562500
11 65504 23603 7812500
12 27204 68678 39062500
14 669798 2312164 976562500
Table 6 shows the comparison of the orbit period of Logistic equation using double-precision floating-point operation of IEEE and low-order iteration method under the initial iteration condition of (0.1, 3.9). And calculating the period of the chaotic orbit by utilizing IEEE double-precision floating point operation in a computer. The period lengths of the low bits of the continuous points of the real track obtained by using the low-bit iteration method under different accuracies are compared.
Under the low-order iteration method, the low-order period of the continuous points of the real orbit is determined by the independent gene position, namely the independent gene position represents the characteristic of random diversity of the chaotic real orbit. As is apparent from Table 6, at an accuracy of 1, the lower iteration method obtained the root locus, and thus the period was 1. When the precision reaches 5, under the action of a low-order iteration method, independent gene positions already appear in low-order digit positions. The period of the lower bits of the continuous points of the chaotic real track obviously shows an increasing trend along with the increase of precision, namely along with the increase of the digital bits of the lower bits.
In the orbit of IEEE double-precision floating-point operations, the period fluctuates by the influence of quantization errors. For example: the cycle period length is 39358 at an accuracy of 10, and the phenomenon of instability occurs compared with the cycle period 23603 at an accuracy of 11. Although the influence of quantization errors on the track can be reduced by the step-by-step calculation of the extensible precision chaos, the method is close to the ideal chaos; however, the quantization error still has an uncertain effect on its periodicity.
Compared with the chaotic orbit period under the low-order iteration method, the chaotic orbit period has the obvious trend of increasing the stable period. The main reason is that the low-order iteration method is not influenced by quantization errors, absolute precision calculation is used, and the basic structural characteristics of the low order of the chaotic orbit are reserved. With the same precision, for example: when the precision is equal to 10, the orbit period (1562500) under the low-order iteration method is nearly 39 times the orbit period (cycle period length 39358) of the IEEE double-precision floating-point operation. At 14 f accuracy, nearly 422 times is achieved.
Therefore, the chaotic orbit keeps the basic characteristics of chaos, namely the characteristic of random diversity to the maximum extent under the low-order iteration method.
Based on the low-order iteration method, the low-order characteristics of continuous points of the chaotic real orbit are continuously observed, and basic structures existing in the chaotic real orbit can be found, wherein the basic structures comprise a root gene order, a universal gene order and an independent gene order. The chaotic real orbit shows the characteristic similar to the genetic gene under the basic structure, and in the continuous points of the real orbit, the subsequent iterations of the chaotic real orbit inherit common low bits, which are similar to the characteristic of self-replication in the gene, and the subsequent continuous points have the characteristic. The track with the precision of 1 under the initial condition is sequenced, and the map of the root gene locus and the characteristics of the universal gene locus of the same root gene locus are analyzed. The basic characteristics of the chaotic orbit, the offset of the chaotic orbit and other characteristics can be further determined under certain conditions.
Software sequence code
The software sequence code is a unique identification code authorized by a computer software producer to use the software for a legal user, and is generally a random number sequence with a certain length. After the user inputs the correct software sequence code, the user can use and install the software and obtain the technical support service provided by the software producer, and the like, thereby guaranteeing the legitimate rights and interests of the user. The software sequence code can avoid repeated registration and piracy of software, and is an effective method for protecting intellectual property rights.
The currently used software sequence code mainly generates a random number sequence through a random number generator, and due to the defects of the random number generator, the sequence code is easily repeated, so that the false phenomenon that a user uses piracy due to repeated registration is generated. In some chaotic random number generators, there are a large number of unstable periodic orbits that contain short periods that tend to make the random number sequence appear frequently, resulting in a large number of repetitions of the sequence code.
Disclosure of Invention
Technical problem to be solved
The invention aims to provide a software sequence code generation method based on extensible precision chaotic inheritance, which enables a software random number sequence generator to generate a sequence code with a stable period and ensures the safety of software.
(II) technical scheme
In order to solve the above technical problem, the present invention provides a method for generating a software sequence code by using a characteristic of scalable precision chaos inheritance-like, comprising:
first, determining the length of the output sequence code (pn) And the number of the serial codes in bulk, i.e., the number of output serial codes. Determining root and universal loci, and converting into decimal as Logistic equationx 0An initial value. Determining control parametersaThe numerical value of (c).
And secondly, calculating by using a low-order iteration method.
The iteration is performed until the specified accuracy is not reached. And when the specified precision is reached, outputting a sequence obtained by a low-order iteration method.
The low-order iteration method is described as follows:
step _ 1: first step of calculating Logistic equation with absolute accuracyy = x*(1-x)；
Step _ 2: second step of calculating Logistic equation with absolute accuracyz = a*y；
Step _ 3: when the obtained iteration valuezIs less than or equal to a given precisionpnWhen the value of (2) is obtained, the iteration valuezAll digital bits of the digital code are reserved and used as iteration input values of the next step; otherwise, the obtained iteration value is usedzIs lowpnBit conversion to decimal 0.…r pn-2 r pn-1 r pn And returning as an input value for the next iteration.
And thirdly, writing the corresponding output sequence into a software data file as a software sequence code. The second step is repeated until the specified number of bulk sequence codes is satisfied.
(III) advantageous effects
The invention has the beneficial effects that: the characteristic of the scalable precision chaotic genetic-like gene is fully utilized, a random number sequence with a stable period is generated in a designated space, and the sequence is used as a software serial number. Under the action of a low-order iteration method, the independent gene position of the extensible precision chaos has the characteristic of random diversity. Compared with the prior art, the independent gene position has the characteristic of stable period, and the influence of an unstable period orbit on a random number sequence is avoided, so that the randomness and the uniqueness of a software sequence code can be effectively ensured.
Drawings
Fig. 1 is a basic structure of lower bits of continuous points of a real track of a scalable precision Logistic chaos.
Detailed Description
In the embodiment, 2 software sequence codes are automatically generated in batch, each software sequence code has 10 bits, and the registration information is contained in a Dynamic Link Library (DLL) file of the software, so that a software producer can issue the DLL file together with an application program, call the sequence codes provided in the DLL file in a relevant module of the application program for comparison, and verify the legality of a user.
In the first step, it is determined that the length of the output sequence codes is 10, and the number of the batch sequence codes is 2, i.e., the number of the output sequence codes. The given root locus is 28 and the universal locus is528, determining root and universal loci, and converting to 0.528 decimal as Logistic equationx 0An initial value. Determining control parametersa Numerical value of = 3.3.
And secondly, calculating by using a low-order iteration method.
x 1=3.3 × 0.528 × 1-0.528) = 0.8224128, taking all lower digits, i.e. lower digitsx 1= 0.8224128. Because the obtained chaotic series does not reach the specified precision: (pn = 10), so the iteration continues.
x 2 = 3.3*0.8224128*(1- 0.8224128) = 0.481964955107328Taking the lower 10 digit and converting it into decimal number, so that it can obtain the productx 2= 0.4955107328. The output chaotic sequence reaches the specified precision, so the sequence code is output.
And thirdly, 4955107328 is written into the DLL file of the software to be used as the sequence code of the software. The operation of the data file of the next software is continued.
Go to the second step.
x 3 = 3.3*0. 4955107328*(1- 0. 4955107328) = 0.824933493384023113728。
Taking the lower 10 digit and converting it into decimal number, so thatx 3= 0.4023113728. The situation is similar to that described above.
And thirdly, 4023113728 is written into the DLL file of the software to be used as the sequence code of the software. The number of designated bulk sequence codes is satisfied. The process is ended.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (1)
1. A software sequence code generation method based on extensible precision chaos heredity is characterized in that:
the Logistic equation is defined as follows
xn+1=a*xn*(1-xn),n=0，1, …
Parameter(s)aIs a control parameter, and 0<a<4, parameter xnIs the nth iteration value, x, of the chaotic equation0Is xnInitial iteration value, and 0< xn <1; the basic structure of the real track comprises: root gene locus, universal gene locus and independent gene locus;
the root, universal and independent loci are defined as follows
The root locus means that in the circulation part of a real orbit, the digital bits in the lower bits of the truth values of the continuous points of the orbit are kept unchanged in the iteration process, and such bits are called root loci;
a universal locus refers to a circulating portion in a real orbit, and when the period of the lower order of the orbit is equal to 4, such a locus is called a universal locus;
the independent gene position refers to a digital position which is combined with a universal gene position to express the random characteristic in the circulating part of a real orbit and is called as an independent gene position;
the first step, determining the length of the output sequence codes and the quantity of the batch sequence codes, determining the root gene position and the universal gene position, and converting the root gene position and the universal gene position into decimal number serving as x of Logistic equation0Initial value, determining control parametersaThe value of (d);
secondly, calculating by using a low-order iteration method, iterating until the specified accuracy pn is not reached, and outputting a sequence obtained by the low-order iteration method after the specified accuracy pn is reached;
the principle of the low-order iteration method is as follows:
step _ 1: calculating the first step of Logistic equation y = x (1-x) with absolute accuracy;
step _ 2: second step z = calculation of Logistic equation with absolute accuracya*y；
Step _ 3: when the precision of the obtained iteration value z is less than or equal to the given pn value, all digital bits of the obtained iteration value z are reserved and used as the iteration input value of the next step; otherwise, converting the low pn position of the obtained iteration value z into a decimal and returning the decimal as an input value for carrying out the next iteration;
and thirdly, writing the corresponding output sequence into a software data file as a software sequence code, and repeating the second step until the number of the specified batch sequence codes is met.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510104571.4A CN106033504B (en) | 2015-03-11 | 2015-03-11 | Software sequence code generation method based on extensible precision chaos heredity |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510104571.4A CN106033504B (en) | 2015-03-11 | 2015-03-11 | Software sequence code generation method based on extensible precision chaos heredity |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106033504A CN106033504A (en) | 2016-10-19 |
| CN106033504B true CN106033504B (en) | 2019-12-27 |
Family
ID=57149761
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510104571.4A Expired - Fee Related CN106033504B (en) | 2015-03-11 | 2015-03-11 | Software sequence code generation method based on extensible precision chaos heredity |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106033504B (en) |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101834717A (en) * | 2010-04-22 | 2010-09-15 | 哈尔滨理工大学 | Parallel computing method capable of expanding precision Logistic chaotic sequence |
| CN102289425A (en) * | 2011-04-28 | 2011-12-21 | 哈尔滨工业大学 | Hash algorithm based on extensible precision chaos |
-
2015
- 2015-03-11 CN CN201510104571.4A patent/CN106033504B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN101834717A (en) * | 2010-04-22 | 2010-09-15 | 哈尔滨理工大学 | Parallel computing method capable of expanding precision Logistic chaotic sequence |
| CN102289425A (en) * | 2011-04-28 | 2011-12-21 | 哈尔滨工业大学 | Hash algorithm based on extensible precision chaos |
Non-Patent Citations (1)
| Title |
|---|
| The Property of Chaotic Orbits with Lower Positions of Numerical Solutions in the Logistic Map;jiahui Liu等;《Entropy》;20141231;第5623页第8段至5630页第8段 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106033504A (en) | 2016-10-19 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Haeupler et al. | Incremental cycle detection, topological ordering, and strong component maintenance | |
| Schank et al. | Approximating clustering coefficient and transitivity. | |
| Stich et al. | Optimization of convex functions with random pursuit | |
| CN109656798B (en) | Vertex reordering-based big data processing capability test method for supercomputer | |
| Hunter | The computation of the mean first passage times for Markov chains | |
| US10763890B2 (en) | Computational devices using thermometer coding and scaling networks on unary encoded data | |
| Surynek | On propositional encodings of cooperative path-finding | |
| Ellis et al. | Partition zeta functions, multifractal spectra, and tapestries of complex dimensions | |
| Drechsler et al. | Learning heuristics for OBDD minimization by evolutionary algorithms | |
| Sasao | Index Generation Functions: Tutorial. | |
| Schweizer et al. | Linear‐scaling Cholesky decomposition | |
| Cori et al. | Polynomial ideals for sandpiles and their Gröbner bases | |
| Hirata et al. | Reconstructing state spaces from multivariate data using variable delays | |
| CN110471644A (en) | Post-processing approach, device and the quantum random number generator of quantum random number | |
| CN106033504B (en) | Software sequence code generation method based on extensible precision chaos heredity | |
| Sofroniou et al. | Extrapolation methods in mathematica | |
| CN110472739A (en) | Efficient post-processing approach, device and the quantum random number generator of quantum random number | |
| Cervellera et al. | Local linear regression for function learning: an analysis based on sample discrepancy | |
| Keren | Reduction of average path length in binary decision diagrams by spectral methods | |
| Lu et al. | An extended XQDD representation for multiple-valued quantum logic | |
| Sliwinski et al. | Computational algorithms for wavelet identification of nonlinearities in Hammerstein systems with random inputs | |
| Gál et al. | Modified bacterial memetic algorithm used for fuzzy rule base extraction | |
| Chan | Rotor walks on transient graphs and the wired spanning forest | |
| Pan | Parallel complexity of computations with general and Toeplitz-like matrices filled with integers and extensions | |
| Gu et al. | Relaxed parallel two-stage multisplitting methods |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20191227 Termination date: 20210311 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |