CN101330378A - Method for generating chaos sequence - Google Patents
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- CN101330378A CN101330378A CNA2008100483124A CN200810048312A CN101330378A CN 101330378 A CN101330378 A CN 101330378A CN A2008100483124 A CNA2008100483124 A CN A2008100483124A CN 200810048312 A CN200810048312 A CN 200810048312A CN 101330378 A CN101330378 A CN 101330378A
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Abstract
The invention relates to a sequence generating method, in particular to a chaotic sequence generating method. A double Logistic mapping coupled structure is adopted, wherein one mapping is used as an excitation parameter generator, and the other mapping is used a chaotic sequence generator. Excitation parameters generated through the excitation parameter generator are utilized to update control parameters of the chaotic sequence generator, thereby enabling the track of the chaotic sequence generator for outputting sequences to conduct continuous transition on a chaotic mapping ensemble, so as to reach the purposes of prolonging the output track of the chaotic sequence and strengthening the uniform distribution of the output sequence, prevent a chaotic system from entering a short period track and resulting in the influence on the safety of chaotic password, and promote the real application of chaotic password.
Description
Technical field
The present invention relates to a kind of method for generating sequence, especially relate to a kind of method for generating chaos sequence.
Background technology
The ergodic of chaos, Combination, certainty and the sensitiveness of initial condition made the concept connection of obscuring and spread in itself and the conventional cipher scientific principle opinion, then chaology and purely this positive connection between the cryptography formed chaos cipher.Since the 1980s, many dissimilar chaos cipher systems have appearred, these cryptographic systems all are to utilize chaotic maps to produce chaos sequence, M.S.Baptista.Cryptography with chaos.Phys.Lett.A.1998,240 (1-2); W.-K.Wong.A modified chaotic cryptographic method.Comput.Phys.Commun, 2001,138 (3); Hu Chinese equality. a kind of Method for Generating Chaotic Key Stream. Chinese journal of computers, 2004 Vol.27 No.3; Jun Wei.A new chaoticcryptosyste m.Chaos Solitons and Fractals.2006 Vol.30 No.3; Zhou Hong etc. the m sequence disturbance of limited precision chaos system realizes. electronic letters, vol, 1997 Vol.25 No.7.
Chaos system is the infinite precision system theoretically, but all is to realize under the computing environment of limited precision in the real figure system, and this certainly exists the problem that dynamics is degenerated at digital space.Relevant document: Li Shujun.Pseudo-random bit generator based on couplechaotic systems and its application in stream-ciphers cryptography.Computer Science.2001 Vol.2247; Shujun Li.On the security of achaotic encryption scheme:Problems with computerized chaos infinite computing precision.Computer Physics Communications, 2003Vol.153 No.1; Zhang YiWei.A chaos-based image encryption algorithmusing alternate structure.Sci China Ser F-Inf Sci.2007 Vol.50 No.3; Pipe spring sun-light etc. a kind of cryptographic algorithm based on chaos sequence. Beijing Institute of Technology's journal, 2003Vol.23No.3.
At Baptista type chaos cipher algorithm, in order to solve the performance degradation that suppresses the digitlization chaos, researchers have proposed some improvement measures, and these improvement measures can be summed up as three classes: (1) improves digitized precision; (2) a plurality of digital chaotic system cascades; (3) add (puppet) random perturbation.
In order to improve digitized precision, utilize the computer realization digital chaos of higher word length, though this method can improve the length of average plan chaotic orbit, but no matter adopting how high word length still still is limited precision, but also there is a large amount of short chaotic orbits of intending, still can not well solve the degenerate problem of digitlization chaos, relevant document: G.M.Bernste in.Secure random numbergeneration using chaotic circuits.IEEE Trans.Circuits and Systems, 1990 Vol.37 No.9; Shujun Li.On the security of a chaotic encryptionscheme:Problems with computerized chaos in finite computingprecision.Computer Physics Communications, 2003 Vol.153No.1.
A plurality of digital chaotic system cascades are two or more chaos system cascades, though can improve the length of intending chaotic orbit effectively, but the outputting power that can influence chaos system is learned characteristic, make its output distribute more inhomogeneous, relevant document: Shujun Li.On the dynamical degradationof digital piecewise linear chaotic maps.Bifurcation and Chaos, 2005Vol.15 No.10; H.B.Ghobad.A chaotic direct-sequence spread-spectrumcommunication system.IEEE Trans.Communications, 1994 Vol.42No. (2/3/4).
Add (puppet) random perturbation, both can prolong the plan chaotic orbit, can improve the digitlization chaos again and export uneven dynamics, effect is better than preceding two kinds of methods.The disturbance that adds can be disturbance Control Parameter, disturbance variable or to both disturbances simultaneously, as Fig. 1, feedforward and rear feed disturbance strategy are two kinds of more feasible strategies.Relevant document: Tao Sang.Perturbance-based algorithmto expand cycle length of chaotic key stream.Electronics Letters, 1998 Vol.34 No.9; G.Ambikal.Noise induced resonance phenomena incoupled map lattices.Eur.Phys.J.B, 2006 Vol.49; Jun Wei.A newchaotic cryptosyste m.Chaos, Solitons and Fractals, 2006 Vol.30; YUSimin.New results of study on generating multiple-scroll chaoticattractors.Sci China Ser F-Inf Sci, 2003 Vol.46 No.2; Shujun Li.Statistical properties of digital piecewise linear chaotic maps andtheir roles in cryptography and pseudo-random coding.8th IMA, 2001Vol.2260; Naoki Masuda.Dynamical characterstics of discretizedchaotic permutations.Bifurcation and Chaos, 2002 Vol.12No.10; JunWei.Analysis and improvement for the performance of Baptista ' scryptographic scheme.Physics Letters A, 2006 Vol.354.
At present, add in the system of (puppet) random perturbation, majority all is to add the linear perturbation system, and such system is vulnerable to known-plaintext and correlation attack.
At present, product and the software systems based on the chaos sequence generator of disturbance thought also occur on market.
Summary of the invention
The present invention solves existing in prior technology no matter to adopt how high word length still or limited precision, but also has a large amount of short plan chaotic orbits, still can not well solve the technical problem of the degenerate problem etc. of digitlization chaos; Provide a kind of existence seldom even to have the short chaotic orbit of intending, can be good at solving the method for generating chaos sequence of the degenerate problem of digitlization chaos.
It is to solve the outputting power characteristic that existing in prior technology influences chaos system that the present invention also has a purpose, makes the technical problem of the more inhomogeneous grade of its output distribution; Provide a kind of outputting power that can not influence chaos system to learn characteristic, made its output distribution method for generating chaos sequence more uniformly.
It is that the solution existing in prior technology all is to add the linear perturbation system that the present invention has a purpose again, and such system is vulnerable to the technical problem of known-plaintext and correlation attack etc.; Provide a kind of system only can be subjected to seldom even can not being subjected to the method for generating chaos sequence of known-plaintext and correlation attack.
Above-mentioned technical problem of the present invention is mainly solved by following technical proposals:
Method for generating chaos sequence based on the Logistic mapping, is characterized in that, may further comprise the steps:
Step 2, it is (x that the chaos initial key is set respectively
0, b
0), and the disturbance initial key (x '
0, b '), wherein, x
0And x '
0All at (0,1) interior value, b
0And b ' is all in [3.57,4] interior value;
Step 3 is imported chaos initial key in the step 2 and disturbance initial key respectively in chaos sequence generator and the disturbance parameter generator, begins to carry out iteration;
Step 4 writes down the input value x of the chaos sequence generator after this iteration
nWith chaos output valve x
N+1, the input value x ' of disturbance parameter generator
nWith disturbance output valve x '
N+1, and iterations cnt,
Except that iteration first, after later each iteration, all chaos is exported x
N+1Feed back to the input value x of chaos sequence generator
n, feed back to the input value x ' of disturbance parameter generator
nValue be,
1., if as chaos output valve x
N+1With disturbance output valve x '
N+1The fractional part numerical value of addition institute value is not equal at 0 o'clock, with chaos output valve x after this iteration
N+1With disturbance output valve x '
N+1The fractional part of addition institute value feeds back to the input value x ' of disturbance parameter generator
n
2., if as chaos output valve x
N+1With disturbance output valve x '
N+1The fractional part numerical value of addition institute value equals at 0 o'clock, with the disturbance output valve x ' after this iteration
N+1Directly feed back to the input value x ' of disturbance parameter generator
n
Check disturbance output valve x ' simultaneously
N+1Whether satisfy 0.357≤x '
N+1≤ 0.4 and cnt 〉=200,
1., if satisfy 0.357≤x ' simultaneously
N+1≤ 0.4 and cnt 〉=200, then be provided with by 10x '
N+1Replace chaos sequence Control Parameter b
m, i.e. b
m=10x '
N+1, cnt is changed to 0 simultaneously, and continues repeating step 4;
2., if check disturbance output valve x '
N+1Do not satisfy 0.357≤x '
N+1≤ 0.4, during and 200≤cnt＜M, wherein, M is a set point one, writes down this iterations cnt, and continues repeating step 4;
Creatively by adopting two Logistic mapping coupled structures, a mapping is as the disturbance parameter generator in the present invention, and another is as chaos sequence generator.The disturbance parameter that uses the disturbance parameter generator to produce, go to upgrade the Control Parameter of chaos sequence generator, thereby make track constantly transition on the chaotic maps collection of chaos sequence generator output sequence, promptly reach the length that prolongs chaos sequence output track, the purpose that the uniformity that output sequence is distributed is strengthened.Avoid influencing the fail safe of chaos cipher, advance the real world applications of chaos cipher because of chaos system enters the short period track.
Step 5 produces N chaos output valve x
N+1Back iteration finishes, and obtains by N chaos output valve x
N+1The chaos sequence that constitutes, wherein, N is a set point two.
At above-mentioned method for generating chaos sequence, in the described step 4, when reaching set point one M as if cnt, disturbance output valve x '
N+1Do not have and once satisfy 0.357≤x '
N+1≤ 0.4, this seasonal x
n=x
N+1,
Write down the output valve x of the chaos sequence generator after this iteration
N+1Output valve x ' with the disturbance parameter generator
N+1, cnt is changed to 0 simultaneously, and continues repeating step 4.
Therefore, the present invention has following advantage: 1. exist seldom even not have the short chaotic orbit of intending, can be good at solving the degenerate problem of digitlization chaos; 2. the outputting power that can not influence chaos system is learned characteristic, makes its output distribute more even; 3. system only can be subjected to seldom even can not being subjected to known-plaintext and correlation attack.
Description of drawings
Fig. 1 is a principal function flow chart of the present invention; , among the figure, c is cnt;
Fig. 2 is an iteration 5 * 10
5When inferior, the chaos sequence that the present invention generates is at Control Parameter b
mTrack mapping graph under=3.57;
Fig. 3 is an iteration 5 * 10
5When inferior, the chaos sequence that the present invention generates is at Control Parameter b
mTrack mapping graph under=3.67;
Fig. 4 is an iteration 5 * 10
5When inferior, the chaos sequence that the present invention generates is at Control Parameter b
mTrack mapping graph under=3.87;
Fig. 5 is an iteration 5 * 10
5When inferior, the chaos sequence that the present invention generates is at Control Parameter b
mTrack mapping graph under=4;
Fig. 6 is an iteration 1 * 10
8When inferior, the chaos sequence that the present invention generates is at Control Parameter b
m=3.57, the track mapping graph under;
Fig. 7 is an iteration 1 * 10
8When inferior, the chaos sequence that the present invention generates is at Control Parameter b
m=3.67, the track mapping graph under;
Fig. 8 is an iteration 1 * 10
8When inferior, the chaos sequence that the present invention generates is at Control Parameter b
mTrack mapping graph under=3.87;
Fig. 9 is an iteration 1 * 10
8When inferior, the chaos sequence that the present invention generates is at Control Parameter b
mTrack mapping graph under=4;
Figure 10 is as Control Parameter b
m=3.88607940673828 o'clock, the output of disturbance parameter generator entered the track mapping graph of short period during track.
Figure 11 is as Control Parameter b
m=3.88607940673828 o'clock, the disturbance parameter generator entered the short period during track, as 10 figure, and the track mapping graph of chaos sequence generator output sequence.
Figure 12 is as Control Parameter b
m=3.88607940673828 o'clock, the output of disturbance parameter generator entered the track mapping graph of short period during track.
Figure 13 is as Control Parameter b
m=3.88607940673828 o'clock, the disturbance parameter generator entered the short period during track, as 12 figure, and the track mapping graph of chaos sequence generator output sequence.
Figure 14 is as Control Parameter b
m=3.96143920898438 o'clock, the output of disturbance parameter generator entered the track mapping graph of short period during track.
Figure 15 is as Control Parameter b
m=3.96143920898438 o'clock, the disturbance parameter generator entered the short period during track, as 14 figure, and the track mapping graph of chaos sequence generator output sequence.
Figure 16 is working as Control Parameter b
mThe distribution frequency figure of=3.57 o'clock output sequences of the present invention, wherein, abscissa is represented the scope [0,1] of output sequence x, and abscissa is divided into 512 subintervals, and on behalf of sequence x, ordinate fall into the frequency distribution in subinterval, and iterations is 10
6Inferior.
Figure 17 is working as Control Parameter b
mThe distribution frequency figure of=3.67 o'clock output sequences of the present invention, wherein, abscissa is represented the scope [0,1] of output sequence x, and abscissa is divided into 512 subintervals, and on behalf of sequence x, ordinate fall into the frequency distribution in subinterval, and iterations is 10
6Inferior.
Figure 18 is working as Control Parameter b
mThe distribution frequency figure of=3.87 o'clock output sequences of the present invention, wherein, abscissa is represented the scope [0,1] of output sequence x, and abscissa is divided into 512 subintervals, and on behalf of sequence x, ordinate fall into the frequency distribution in subinterval, and iterations is 10
6Inferior.
Figure 19 is working as Control Parameter b
mThe distribution frequency figure of=3.97 o'clock output sequences of the present invention, wherein, abscissa is represented the scope [0,1] of output sequence x, and abscissa is divided into 512 subintervals, and on behalf of sequence x, ordinate fall into the frequency distribution in subinterval, and iterations is 10
6Inferior.
Figure 20 is output sequence x of the present invention
N+1The section of fetching data 10
4To 2 * 10
4The time autocorrelation figure.
Figure 21 is output sequence x of the present invention
N+1The section of fetching data 10
5To 1.1 * 10
5The time autocorrelation figure.
Figure 22 is output sequence x of the present invention
N+1The section of fetching data 10
7To 1.001 * 10
7The time autocorrelation figure.
Figure 23 is output sequence x of the present invention
N+1The section of fetching data 10
8To 1.0001 * 10
8The time autocorrelation figure.
Embodiment
Below by embodiment, and in conjunction with the accompanying drawings, technical scheme of the present invention is described in further detail.
Embodiment:
As shown in Figure 1: method for generating chaos sequence, based on the Logistic mapping, it is characterized in that, may further comprise the steps:
Step 2, it is (x that the chaos initial key is set respectively
0, b
0), and the disturbance initial key (x '
0, b '), wherein, x
0And x '
0All at (0,1) interior value, b
0And b ' is all in [3.57,4] interior value, in the present embodiment, and x
0Value 0.2361089, b
0Value 3.6814902, x '
0Value 0.9157241, b ' value 3.9165309;
Step 3 is imported chaos initial key and disturbance initial key respectively in chaos sequence generator and the disturbance parameter generator then, begins to carry out iteration;
Step 4 writes down the input value x of the chaos sequence generator after this iteration
nWith chaos output valve x
N+1, the input value x ' of disturbance parameter generator
nWith disturbance output valve x '
N+1, and iterations cnt,
Except that iteration first, after later each iteration, all chaos is exported x
N+1Feed back to the input value x of chaos sequence generator
n, feed back to the input value x ' of disturbance parameter generator
nValue be,
If condition A is as chaos output valve x
N+1With disturbance output valve x '
N+1The fractional part numerical value of addition institute value is not equal at 0 o'clock, with chaos output valve x after this iteration
N+1With disturbance output valve x '
N+1The fractional part of addition institute value feeds back to the input value x ' of disturbance parameter generator
n
If condition B is as chaos output valve x
N+1With disturbance output valve x '
N+1The fractional part numerical value of addition institute value equals at 0 o'clock, with the disturbance output valve x ' after this iteration
N+1Directly feed back to the input value x ' of disturbance parameter generator
n
The feedback formula of condition A and condition B is as follows:
Check disturbance output valve x ' simultaneously
N+1Whether satisfy 0.357≤x '
N+1≤ 0.4 and cnt 〉=200,
1., if satisfy 0.357≤x ' simultaneously
N+1≤ 0.4 and cnt 〉=200, then be provided with by 10x '
N+1Replace chaos sequence Control Parameter b
m, i.e. b
m=10x '
N+1, cnt is changed to 0 simultaneously, and continues repeating step 4;
2., if check disturbance output valve x '
N+1Do not satisfy 0.357≤x '
N+1≤ 0.4, during and 200≤cnt＜M, wherein, M is a set point one, writes down this iterations cnt, and continues repeating step 4;
Step 5 produces N chaos output valve x
N+1Back iteration finishes, and obtains by N chaos output valve x
N+1The chaos sequence that constitutes, wherein, N is a set point two.
Remove above-mentioned two kinds of conditions, promptly condition 1. with condition 2. outside, under few situation, in the time of cnt can occurring and reach set point M, disturbance output valve x '
N+1Do not have and once satisfy 0.357≤x '
N+1≤ 0.4 situation, this season
Write down the output valve x of the chaos sequence generator after this iteration
N+1Output valve x ' with the disturbance parameter generator
N+1, cnt is changed to 0, and continues repeating step 4.The M value here is b
mThe maximum that is not updated (promptly do not satisfy condition 1. with condition 2., disturbance output valve x ' appears
N+1Do not have and once satisfy 0.357≤x '
N+1≤ 0.4 situation), not the controlling value that iteration finishes, the iterations N that iteration finishes may be far longer than the M value.
In the present embodiment, set point one M and set point two N are no fixed value, set point one M desirable in the present embodiment 65535.According to the practical application needs, setting the iterations that needs in the practical application is set point two N, and in the present embodiment, set point two N get 10
10, after the iterations value reached set point two N, iteration finished, and just obtained the chaos sequence that is made of N output sequence value thus,
Prototype of the present invention is:
As Fig. 1:
x
n+1＝b
mx
n(1-x
n) (1)
x′
n+1＝b′x′
n(1-x′
n) (2)
b
m=10x '
N+1(0.357≤x '
N+1≤ 0.4 and cnt 〉=200) (3)
x
n＝x
n+1 (5)
Wherein, x
nBe the feedback input value of chaos sequence generator, b
mBe the chaos sequence Control Parameter of chaos sequence generator, x
N+1Be the chaos sequence output valve; X '
nBe the feedback input value of disturbance parameter generator, b ' is the disturbance Control Parameter of disturbance parameter generator, x '
N+1Be the disturbance output valve.x
n，x′
n∈(0，1)。Cnt is the last b of renewal of formula (1)
mAfter iterations, stipulate b here for guaranteeing chaotic characteristic
m, b ' ∈ [3.57,4].
This method is the combination of formula (1), (2), (3), (4), (5).Formula (1) and formula (2) are two independently Logistic mapping chaos systems.The output x ' of formula (2)
N+1At satisfied 0.357≤x '
N+1During≤0.4 and cnt 〉=200 conditions, by 10x '
N+1The Control Parameter b of replacement formula (1)
mWhen upgrading Control Parameter, the variable in the formula (2) is added a disturbance, this disturbance is the output x of through type (1) and formula (2)
N+1And x '
N+1Addition and get mantissa and feed back to x '
nOr with x '
N+1Directly feed back to x '
n, suc as formula (4).X after each iteration
N+1Directly feed back to x
n
Constraints: when cnt=M, can't satisfy 0.357≤x '
N+1≤ 0.4, order
Restart iteration, till satisfying condition.
Essence of the present invention is: by adopting two Logistic mapping coupled structures, a mapping is as the disturbance parameter generator, and another is as chaos sequence generator.As disturbance output valve x '
N+1Satisfy 0.357≤x '
N+1≤ 0.4 and cnt 〉=200 o'clock, the disturbance parameter that uses the disturbance parameter generator to produce, go to upgrade the Control Parameter of chaos sequence generator, thereby make track constantly transition on the chaotic maps collection of chaos sequence generator output sequence, promptly reach the length that prolongs chaos sequence output track, the purpose that the uniformity that output sequence is distributed is strengthened.Avoid influencing the fail safe of chaos cipher, advance the real world applications of chaos cipher because of chaos system enters the short period track,
Specific embodiment described herein only is that the present invention's spirit is illustrated.The technical staff of the technical field of the invention can make various modifications or replenishes or adopt similar mode to substitute described specific embodiment, but can't depart from spirit of the present invention or surmount the defined scope of appended claims.
Although this paper has used terms such as iteration, track, feedback, sequencer, mapping morely, do not get rid of the possibility of using other term.Using these terms only is in order to describe and explain essence of the present invention more easily; They are construed to any additional restriction all is contrary with spirit of the present invention.
Claims (2)
1. a method for generating chaos sequence based on the Logistic mapping, is characterized in that, may further comprise the steps:
Step 1 is provided with a disturbance parameter generator and a chaos sequence generator respectively, and chaos sequence generator is Logistic mapping x
N+1=b
mx
n(1-x
n), wherein, x
nBe the feedback input value of chaos sequence generator, b
mBe the chaos sequence Control Parameter of chaos sequence generator, x
N+1Be the chaos sequence output valve; The disturbance parameter generator is Logistic mapping x '
N+1=b ' x '
n(1-x '
n), wherein, x '
nBe the feedback input value of disturbance parameter generator, b ' is the disturbance Control Parameter of disturbance parameter generator, x '
N+1Be the disturbance output valve, said n and m are positive integer;
Step 2, it is (x that the chaos initial key is set respectively
0, b
0), and the disturbance initial key (x '
0, b '), wherein, x
0And x '
0All at (0,1) interior value, b
0And b ' is all in [3.57,4] interior value;
Step 3 is imported chaos initial key in the step 2 and disturbance initial key respectively in chaos sequence generator and the disturbance parameter generator, begins to carry out iteration;
Step 4 writes down the input value x of the chaos sequence generator after this iteration
nWith chaos output valve x
N+1, the input value x ' of disturbance parameter generator
nWith disturbance output valve x '
N+1, and iterations cnt,
Except that iteration first, after later each iteration, all chaos is exported x
N+1Feed back to the input value x of chaos sequence generator
n, feed back to the input value x ' of disturbance parameter generator
nValue be:
1., if as chaos output valve x
N+1With disturbance output valve x '
N+1The fractional part numerical value of addition institute value is not equal at 0 o'clock, with chaos output valve x after this iteration
N+1With disturbance output valve x '
N+1The fractional part of addition institute value feeds back to the input value x ' of disturbance parameter generator
n
2., if as chaos output valve x
N+1With disturbance output valve x '
N+1The fractional part numerical value of addition institute value equals at 0 o'clock, with the disturbance output valve x ' after this iteration
N+1Directly feed back to the input value x ' of disturbance parameter generator
n
Check disturbance output valve x ' simultaneously
N+1Whether satisfy 0.357≤x '
N+1≤ 0.4 and cnt 〉=200,
1., if satisfy 0.357≤x ' simultaneously
N+1≤ 0.4 and cnt 〉=200, then be provided with by 10x '
N+1Replace chaos sequence Control Parameter b
m, i.e. b
m=10x '
N+1, cnt is changed to 0 simultaneously, and continues repeating step 4;
2., if check disturbance output valve x '
N+1Do not satisfy 0.357≤x '
N+1≤ 0.4, during and 200≤cnt＜M, wherein, M is a set point one, writes down this iterations cnt, and continues repeating step 4;
Step 5 produces N chaos output valve x
N+1Back iteration finishes, and obtains by N chaos output valve x
N+1The chaos sequence that constitutes, wherein, N is a set point two.
2. method for generating chaos sequence according to claim 1 is characterized in that, in the described step 4, and when reaching set point one M as if cnt, disturbance output valve x '
N+1Do not have and once satisfy 0.357≤x '
N+1≤ 0.4, this season
Write down the output valve x of the chaos sequence generator after this iteration
N+1Output valve x ' with the disturbance parameter generator
N+1, cnt is changed to 0 simultaneously, and continues repeating step 4.
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| 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 |
| CN102412960A (en) * | 2011-11-21 | 2012-04-11 | 东北大学 | Chaos based Enigma encryption method |
| CN102624519A (en) * | 2012-03-12 | 2012-08-01 | 浙江工业大学 | Wireless sensor network-oriented mutual interference compound chaos stream cipher implementation method |
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| 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 |
| CN102289425B (en) * | 2011-04-28 | 2015-05-06 | 哈尔滨工业大学 | Hash algorithm based on extensible precision chaos |
| CN102412960A (en) * | 2011-11-21 | 2012-04-11 | 东北大学 | Chaos based Enigma encryption method |
| CN102412960B (en) * | 2011-11-21 | 2015-02-11 | 东北大学 | Chaos based Enigma encryption method |
| CN102624519A (en) * | 2012-03-12 | 2012-08-01 | 浙江工业大学 | Wireless sensor network-oriented mutual interference compound chaos stream cipher implementation method |
| CN102624519B (en) * | 2012-03-12 | 2014-12-17 | 浙江工业大学 | Wireless sensor network-oriented mutual interference compound chaos stream cipher implementation method |
| CN103595523A (en) * | 2012-08-15 | 2014-02-19 | 希姆通信息技术（上海）有限公司 | A file encryption method |
| CN103595523B (en) * | 2012-08-15 | 2017-02-08 | 希姆通信息技术（上海）有限公司 | A file encryption method |
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