CN101702117A - Method for generating random pseudorandom sequence based on discrete progressive determinacy - Google Patents
Method for generating random pseudorandom sequence based on discrete progressive determinacy Download PDFInfo
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Abstract
The invention provides a method for generating a random pseudorandom sequence based on a discrete progressive determinacy, which comprises the steps of: (1) selecting a discrete or chaotic map Xn+1=aXnmod2N, setting an initial value X0 and a chaotic control parameter a, and performing iterative operation with an input value Xn at the time of n, namely, the current time, so as to obtain output Xn+1 of a chaotic system at the time of Xn+1, namely, the next time; (2) nonlinearly changing the Xn into Yn=bXnmod2N to obtain the corresponding random pseudorandom Yn of the discrete progressive determinacy, wherein the nonlinear control parameter b=2k, and k is a positive integer; and (3) building a discrete progressive determinacy random system from step (1) to step (2), and changing an integer sequence Y two value into 0-1 sequence Z with a coupling method to obtain a random sequence output Z. The method has good balance, ideal run distribution, and the statistical characteristic of self correlation and mutual correlation similar to white noise, and can be taken as the pseudorandom sequence with high safety.
Description
Technical field
The invention belongs to password generating technique in the information security, particularly, he is a method of utilizing a kind of pseudo-random sequence of electronic computer technology, information coding technique and discrete progressive determinacy stochastic system generation.
Background technology
On the ordinary meaning, exist between chaos and the cryptography to be closely connected, ocular connection is carried out in obscuring with the diffusion notion in all can learning with conventional cipher such as the fundamental characteristics of Time Chaotic Dynamical Systems such as initial value susceptibility, ergodicity.1948, Shannon has just proposed to use basic " Rolled-out and folded-over " operation to carry out the design of secrecy system mixing transformation in its paper " Communication Theory of Secrecy Systems ", and this has similarity with the folding reason that causes chaos that stretches.Nineteen ninety, Ott, Grebogi, Yoke propose the OGY chaotic control method, and Pecora and Carroll propose the chaos method for synchronous.Simultaneously, Matthews and Habutsu propose respectively again based on modification Logistic sequence of mapping password and based on Tent mapping block cipher.With above-mentioned work is theory and technical foundation, and chaotic secret communication and chaos cipher research in recent years is rapidly developed.Further, again because computing power improves rapidly and new computation schema constantly occurs, conventional cipher based on complex problem solving is on the hazard day by day, all chaotic secret communication and chaos cipher is supported as the information security new technology both at home and abroad, tries hard to realize on cipher system the source innovation.
Chaos cipher mainly comprises chaos sequence password, chaos block cipher, chaos public key cryptography three aspect contents.The chaos sequence cipher core is a pseudorandom number generator.Logistic mapping, Chebyshev mapping, piecewise linearity/Nonlinear Mapping, the discrete chaotic maps of p-adic, ICMIC mapping and Henon mapping etc. have been used to design pseudorandom number generator, and further utilize combination chaotic maps, m sequence disturbance chaotic maps etc. to enhance security features.Simultaneously, Kolmogorov stream, two-dimentional Cat/Baker/ block Baker mapping, three-dimensional Cat/Baker mapping, time-varying parameter chaotic maps etc. and are used to the designed image cryptographic algorithm.In addition, utilize chaos traversal character, formed stream cipher structure mechanism again, occur random perturbation subsequently in succession, dynamically update look-up table, multiple improvement projects such as circulation chaos, coupling piecewise linear maps/network based on search mechanisms.But follow-up study shows that such scheme is attacked, cut apart attack, selects under the plaintext attack at one-time pad attack, entropy attack, key recovery respectively is unsafe.Chaos block cipher aspect mainly comprises fixing and the design of dynamic chaos S box.Fixedly chaos S box just utilizes S box or the non-linear round function in the chaos system generation conventional cryptography algorithm, and S box may be than a little less than the well-designed S boxes such as DES at random to the analysis showed that this type of.The dynamic S-box aspect mainly comprises based on chaotic maps generation dynamic pseudo-random vector and S cassette method, and the block cipher of constructing the chaos displacement based on chaos coarse track.Studies show that recently this type of scheme is dangerous on the one hand, also be subjected to the influence of coarse track periodicity, complicacy etc. on the other hand.Chaos public key cryptography aspect mainly utilizes the multiple integer/real number class RSA and the class EIGamal algorithm of the design of the oval Chebyshev mark mapping of Chebyshev/Jacobian semigroup character, and is used for key agreement, digital signature, Hash chain, deniable authentication design of protocol etc.But studies show that above-mentioned algorithm both can't resist the statistical attack based on Chebyshev mapping resonance characteristics, can not satisfy anti-impact conditions.
Obviously, chaos cipher research with relatively do not obtain to break through progress, particularly chaos sequence password the beginning of the nineties even be difficult to exceed Lehmer in the 40-50 age conventional cipher field about linear congruence generator (LCG) and Ulam and Von Neumann category about Ulam conversion and linear feedback shift register (LFSR).From the nonlinear kinetics angle, Bernoulli Jacob mapping has consistance in essence with the linear congruence algorithm, and has equivalence with Logistic mapping, Chebyshev mapping etc., and the LFSR sequence may be interpreted as and is forced to pseudo-chaos symbol sebolic addressing.Aspect cryptographic applications, the linear conguential sequences performance is than better (the error free accumulation of this sequence of chaos pseudo random sequence, and guaranteeing to have ripe theory and experimental result aspect the maximum cycle), chaos cipher enhanced form based on the disturbance of m sequence also is equal to LFSR, and has proved that LCG and LFSR can not be directly used in the implementation sequence password in the conventional cipher scientific principle opinion.Lack rigorous nonlinear kinetics supporting theory just because of present chaos cipher research, be fruitful in a large number so be difficult to surmount the conventional sequence password.
Explore a kind of key means that new Nonlinear Dynamical Mechanism breaks through chaos cipher research bottleneck beyond doubt.1997, discover: explicit expression x during non-integer
n=sin
2(π θ z
n) sequence that produces has the short-term unpredictability.For being different from chaos and stochastic process, claim this phenomenon that produces unpredictable sequence by the determinacy equation be determinacy at random, and think and can produce " true random sequence ".Obviously, determinacy at random for research by provide certain function served as bridge of chaos to stochastic process, not only Research on Nonlinear Dynamics and much research field have vital role, and studies show that determinacy studies some with number theory at random and open problem and be associated.Asymptotic certainty with the unpredictable character of short-term has connected chaos and stochastic process at random, is the development to dissipating and guarding System Dynamics Theory, has vital role aspect the breakthrough chaos cipher security bottleneck.Learn the field at conventional cipher, the design concept of a class counter auxiliary mode pseudo-random generator and Li Shayu mapping are much at one.Promptly also adopt a kind of iteration pseudorandom number generator to drive a non-linear output function form.This generator adopts the low-risk principle of design, utilizes DES and RC5 algorithm respectively as iteration pseudorandom number generator and non-linear output function, and has further designed cascade and the two step counter auxiliary mode pseudo-random generators that have than the Vernonia parishii Hook degree.
Paper " Discrete Asymptotic Deterministic Randomness for the Generation ofPseudorandom Bits " (Kai Wang, Wenjiang Pei, Xubo Hou, Song Hong, Zhenya He, PhysicsLetters A, 373:653-660,2009) proposition is a kind of based on discrete progressive determinacy pseudorandom sequence generating method at random, the result shows that above-mentioned pseudo-random sequence has good balance, and the desirable distance of swimming distributes, have the auto-correlation of similar white noise and the statistical property of simple crosscorrelation, can be used as pseudo-random sequence with high security.
Summary of the invention
The present invention seeks to provides a kind of based on discrete progressive determinacy pseudorandom sequence generating method at random at the defective that prior art exists.
The present invention adopts following technical scheme for achieving the above object:
The present invention is a kind of based on discrete progressive determinacy pseudorandom sequence generating method at random, it is characterized in that comprising the steps:
(1) selects discrete domain chaotic maps X
N+1=aX
nMod2
N, and set its initial value X
0With chaos controlling parameter a, be current time input value X constantly by n
nCarry out interative computation, obtaining chaos system n+1 is next output X constantly constantly
N+1
(2) to X
nCarry out nonlinear transformation Y
n=bX
nMod2
N, obtain discrete accordingly progressive determinacy random series Y
n, nonlinear Control parameter b=2 wherein
k, k is a positive integer;
(3) step 1 to step 2 is set up discrete progressive determinacy stochastic system, by coupling process integer sequence Y two-value is turned to 0-1 sequence Z, promptly obtains pseudo-random sequence output Z.
According to the thought of the One-time pad that Shannon proposed, the key length of stream cipher must be longer than the length of encrypted information, and this is nonsensical in actual use.Therefore problem just is transformed into the key of seeking weak point, produces to have the enough macrocyclic problem of random series that is.Must encrypt needs to determine whether to satisfy by standard N IST 800-22 test based on discrete progressive determinacy pseudorandom sequence generating method PRBG at random for above-mentioned two groups.The NIST800-22 test of mark comprises the various statistical properties of 17 basic tests with analytical sequence, comprise: the Frequency test, the blockfrequency test, the runs test, longest runs test, matrix rank test, spectral test, nonoverlappingtemplate (NOT) matching test, overlapping template (OT) matching test, the universal test, Lempel-Ziv test, linear complexity test, the serial test, approximate entropy test, cumulativesums test, random excursions test and random excursion variant test.An input length is after the sequence to be measured of L, and each testing algorithm will return real number value a: P-value on [0, a 1] interval.As P-value during, can think the test that this sequence is passed through greater than threshold value 0.01.For serial combination PRBG, we have carried out 2000 tests altogether to above-mentioned 16 kinds of tests to select seed at random.The result shows that above-mentioned pseudo-random sequence has good balance, and the desirable distance of swimming distributes, and has the auto-correlation of similar white noise and the statistical property of simple crosscorrelation, can be used as the pseudo-random sequence with high security.
Description of drawings
Fig. 1 progressive determinacy stochastic system block diagram that disperses.
The discrete progressive determinacy that Fig. 2 utilizes coupling function pseudo-random sequence at random produces block diagram.
The parallel discrete progressive determinacy random series production method of Fig. 3.
The progressive determinacy of Fig. 4 pseudo-random sequence at random is applied to the theory diagram of image encryption.
The progressive determinacy of Fig. 5 pseudo-random sequence at random is applied to the theory diagram of frequency-hopping communication system.
The progressive determinacy of Fig. 6 pseudo-random sequence at random is applied to the theory diagram (radiating portion) of pulse-position modulation communication system.
The progressive determinacy of Fig. 7 pseudo-random sequence at random is applied to the theory diagram (receiving unit) of pulse-position modulation communication system.
Embodiment
Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:
As shown in Figure 1, a kind ofly comprise the steps: based on discrete progressive determinacy pseudorandom sequence generating method at random
(1) selects discrete domain chaotic maps X
N+1=aX
nMod2
N, and set its initial value X
0With controlled variable a.By by n input value X constantly
nCarry out interative computation, obtain chaos system n+1 output X constantly
N+1
(2) to X
nCarry out nonlinear transformation Y
n=bX
nMod2
N, obtain discrete accordingly progressive determinacy random series Y
n, b=2 wherein
k, k is a positive integer.
(3) according to the process of step 1-step 2, set up discrete progressive determinacy stochastic system, by coupling process integer sequence Y two-value is turned to 0-1 sequence Z, promptly obtain pseudo-random sequence output Z.
In step 1, selected discrete domain chaotic maps satisfies the maximum cycle principle, promptly discrete chaos sequence X
nIn positive integer interval [1,2
N-1] goes up traversal, must guarantee that for this reason controlled variable a satisfies: a=q2
N-i+ 2
-j, i wherein, j is a positive integer, q is strange positive integer.As shown in Figure 1, discrete progressive determinacy is equivalent at random non-linear congruence generator is carried out once non-linear non-reversible static conversion.
In step 2, must guarantee that controlled variable b satisfies: b=2
k, wherein k is a positive integer, thereby makes calling sequence Y
nHas many-valued corresponding relation, that is: known m≤M step observation sequence Y
0, Y
1... Y
M-1, next step observed reading Y then
mHave Q kind possibility, the possibility Q of wherein maximum unpredictable step number M and observed reading is by controlled variable a, and b determines.Positive integer sequence Y with above-mentioned many-valued corresponding relation
n, then be referred to as discrete progressive determinacy random series.
The discrete progressive determinacy random series of utilizing step 1-step 2 to be set up, in step 3, we are by selecting different initial value X
0 1And X
0 2, and different controlled variable a
1, b
1And a
2, b
2, produce two groups and different advance determinacy random series { Y
n 1And { Y
n 2.As shown in Figure 2, n utilizes composite function constantly:
Produce 0-1 sequence Z, promptly obtain pseudo-random sequence output Z.
There are two kinds of multi-form production methods of serial combination PRBG and The parallel combined PRBG to produce determinacy random series Y respectively
n i, i=1,2.Wherein:
Serial combination PRBG: in the serial combination form, we utilize X under the different parameters form
N+1=aX
nMod2
NAnd Y
n=bX
nMod2
NThe Y that conversion produces
n iSequence is according to producing the 0-1 pseudo-random sequence by composite function g ().For example, we select N=25 to design this system, this time series { X
nCycle Length be 2
25-1=33554431.Two groups of discrete progressive determinacy stochastic systems are selected controlled variable respectively:
b
1=2, q wherein
1=9, i
1=j
1=4;
b
2=23, q wherein
2=2049, i
1=j
1=12.We select composite function:
The parallel combined PRBG: the discrete progressive determinacy random series multistep of serial is measurable.We can increase the unpredictability of sequence by parallel method: utilize any pseudo-random sequence generator to produce kind of a subsequence { X
0 h.Suppose that discrete progressive determinacy produces sequence M at random and goes on foot unpredictable.At h constantly, utilize seed X
0 hGenerate the progressive determinacy random series { Y of length M
n h}
N=0 M-1Each moment formation sequence is spliced from beginning to end, obtain required sequence { Y}.Parallel discrete progressive determinacy design frame chart at random as shown in Figure 3.The Y that is produced
n iSequence is according to producing the 0-1 pseudo-random sequence by composite function g ().We select N=25 to design this system, and this up-to-date style (5.7a) produces sequence { X
nCycle Length be 2
25-1=33554431.Two groups of discrete progressive determinacy stochastic systems are selected controlled variable respectively:
b
1=2, q wherein
1=9, i
1=j
1=4;
b
2=23, q wherein
2=2049, i
1=j
1=12.We select composite function:
For example the present invention is done more detailed description below.
Example 1: we are used for the image encryption aspect with above-mentioned PRBG is example.View data is not stolen in transmission course in order to protect, bootlegging and propagation etc., and people propose various encipherment scheme incoming wave love view data safety.It is exactly that data encrypted has been converted into one group of skimble-skamble code that these enciphered datas have a common feature.In case the interceptor has found such code, they just know that they have had the information that has very much value.In order to protect view data safety and the value of avoiding exposing view data, can utilize the information redundancy characteristic of image, a sub-picture is hidden in another width of cloth image.For image encryption, possible human observer or illicit interception person can be by the intercepting ciphertexts, and it is decoded, or send after ciphertext destroyed again, thereby influence the safety of confidential information; But image information is hidden, and possible human observer or illicit interception person are difficult to then judge whether secret image information exists, and is difficult to intercept and capture secret image information from public image information, thereby can guarantee the safety of secret image information.Because pseudo-random sequence generator of the present invention has good randomness, unpredictability, higher security is fit to be applied to image information and hides, its application principle block diagram is seen Fig. 4 at encryption section, and PRBG encrypts the plaintext image with certain image and cryptographic algorithm; In decryption portion, adopt corresponding decipherment algorithm, ciphertext graph is looked like to be decrypted, recover expressly image.
Example 2: the key areas that random series is used is exactly a frequency hopping communications, and the carrier frequency of frequency-hopping communication system is controlled by a group code sequence, in much wide frequency band than information band, and random jump according to certain rules, this saltus step rule is called frequency hopping pattern.The sign indicating number sequence of control frequency hopping pattern is called frequency hop sequences.Frequency hop sequences is generally produced by pseudo-random sequence.The frequency hop sequences of a function admirable must have randomness preferably, and Chang cycle as far as possible, performance such as evenly distribute in working band and non-linear preferably.
PRBG is applied in the frequency-hopping communication system, and synoptic diagram as shown in Figure 5.Produce the carrier frequency of saltus step with PRBG control frequency hopping frequency meter.Here, the effect of PRBG time control frequency hopping is to realize frequency expansion.Transmitter and receiver changes in the scope of broad with identical rule controlled frequency, though the momentary signal bandwidth is narrower, macroscopical signal bandwidth is very wide.For receiving-transmitting sides, after synchronously, can realize perfect reception; For illegal receiver,, be difficult to realize effectively disturbing because therefore frequency hop sequences the unknown can't intercept effective information.
Example 3: a kind of novel short distance high-speed radiocommunication technology that receives much concern at present during ultra broadband (UWB) technology.UWB communicates by direct emission burst pulse, in view of system to the having relatively high expectations of power validity, the modulation system of impulse radio is general to adopt binary impulse phase modulation (PPM).In order to improve the confidentiality of communication, adopt chaos impulse phase modulation (CPPM).This communication plan is based on chaos pulse sequence, and the interpulse time interval is controlled by PRBG.This pulse train that has the chaos recurrent interval can be used as carrier wave.Method with pulse position modulation (PPM) is modulated to binary message on the carrier wave, and the left side of each pulse is along constant in certain moment or what postpone to depend on emission respectively is " 0 " or " 1 ".By receiving system and chaos pulse sequence synchronously, can predict burst length, the recovery emission information of therefore can decoding corresponding to " 0 " and " 1 ".Fig. 6 and Fig. 7 represent respectively with PRBG be used for the pulse-position modulation communication system theory diagram transmit and receive part.
Claims (6)
1. one kind based on discrete progressive determinacy pseudorandom sequence generating method at random, it is characterized in that comprising the steps:
(1) selects discrete domain chaotic maps X
N+1=aX
nMod2
N, and set its initial value X
0With chaos controlling parameter a, be current time input value X constantly by n
nCarry out interative computation, obtaining chaos system n+1 is next output X constantly constantly
N+1
(2) to X
nCarry out nonlinear transformation Y
n=bX
nMod2
N, obtain discrete accordingly progressive determinacy random series Y
n, nonlinear Control parameter b=2 wherein
k, k is a positive integer;
(3) step 1 to step 2 is set up discrete progressive determinacy stochastic system, by coupling process integer sequence Y two-value is turned to 0-1 sequence Z, promptly obtains pseudo-random sequence output Z.
2. according to claim 1 a kind ofly it is characterized in that in step 1 based on discrete progressive determinacy pseudorandom sequence generating method at random, selected discrete domain chaotic maps satisfies the maximum cycle principle, promptly discrete chaos sequence X
nIn positive integer interval [1,2
N-1] goes up traversal, must guarantee that for this reason chaos controlling parameter a satisfies: a=q2
N-i+ 2
-j, i wherein, j is a positive integer, q is strange positive integer.
3. according to claim 1 a kind of based on discrete progressive determinacy pseudorandom sequence generating method at random, it is characterized in that described discrete progressive determinacy is equivalent at random carries out once non-linear non-reversible static conversion with non-linear congruence generator.
4. according to claim 1 a kind ofly it is characterized in that in step 2, must guarantee that the nonlinear Control parameter b satisfies: b=2 based on discrete progressive determinacy pseudorandom sequence generating method at random
k, wherein k is a positive integer, thereby makes discrete progressive determinacy random series Y
nHas many-valued corresponding relation, that is: known m≤M step observation sequence Y
0, Y
1... Y
M-1, next step observed reading Y then
mHave Q kind possibility, the possibility Q of wherein maximum unpredictable step number M and observed reading is by chaos controlling parameter and nonlinear Control parameter a, and b determines.
5. according to claim 1 a kind ofly it is characterized in that in step 3 based on discrete progressive determinacy pseudorandom sequence generating method at random is by selecting different initial value X
0 1And X
0 2, and different controlled variable a
1, b
1And a
2, b
2, produce two groups and different advance determinacy random series { Y
n 1And { Y
n 2, n utilizes composite function constantly:
Produce 0-1 sequence Z, promptly obtain pseudo-random sequence output Z.
6. according to claim 1 a kind of based on discrete progressive determinacy pseudorandom sequence generating method at random, it is characterized in that comprising that serial combination produces determinacy random series Y based on discrete progressive determinacy pseudorandom sequence generating method and The parallel combined at random based on two kinds of multi-form production methods of discrete progressive determinacy pseudorandom sequence generating method at random
n i, i=1,2, wherein:
Serial combination is based on discrete progressive determinacy pseudorandom sequence generating method at random: utilize X under the different parameters form
N+1=aX
nMod 2
NAnd Y
n=bX
nMod 2
NThe Y that conversion produces
n iSequence, according to producing the 0-1 pseudo-random sequence by composite function g (), two groups of discrete progressive determinacy stochastic systems are selected controlled variable respectively:
b
1=2, q wherein
1=9, i
1=j
1=4;
b
2=23, q wherein
2=2049, i
1=j
1=12, composite function:
The parallel combined is based on discrete progressive determinacy pseudorandom sequence generating method at random: the discrete progressive determinacy random series multistep of serial is measurable, increases the unpredictability of sequence by parallel method: utilize any pseudo-random sequence generator to produce kind of a subsequence { X
0 h, it is unpredictable that discrete progressive determinacy produces the sequence M step at random, at h constantly, utilizes seed X
0 hGenerate the progressive determinacy random series { Y of length M
n h}
N=0 M-1, each moment formation sequence is spliced from beginning to end, obtain required sequence { Y}, the Y that is produced
n iSequence, according to producing the 0-1 pseudo-random sequence by composite function g (), two groups of discrete progressive determinacy stochastic systems are selected controlled variable respectively:
b
1=2, q wherein
1=9, i
1=j
1=4;
b
2=23, q wherein
2=2049, i
1=j
1=12, composite function:
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