CN102684871A - Quick parallel generating method for multidimensional pseudo-random sequence with uniform distribution characteristics - Google Patents
Quick parallel generating method for multidimensional pseudo-random sequence with uniform distribution characteristics Download PDFInfo
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Abstract
The invention discloses a quick parallel generating method for a multidimensional pseudo-random sequence with uniform distribution characteristics, wherein the quick parallel generating method improves a classic coupled map lattice (CML) model according to the security requirement of the cryptography, cancels diffusion coefficients thereof, increases constant terms, limits the grid value to be within [0, 1] through modular operation, and achieves a novel coupled tent map lattice system with the uniform distribution characteristics; and in addition, the pseudo-random sequence is generated through user key conversion and initial vector conversion by utilizing a coupled tent map lattice system model with the uniform distribution characteristics. The quick parallel generating method inherits the coupling diffusion mechanism and the parallel iteration characteristics of the CML model, leads system state tendency to achieve ergodicity through the stretching and folding of the local grid tent map as well as the double nonlinear action of the modular operation, overcomes the defect of the CML model on security, and can generate the multidimensional pseudo-random sequence with the uniform distribution characteristics in a parallel and quick manner.
Description
Technical field
The invention belongs to network, command, control, communications, and information safe practice field, especially disclose a kind of method that obtains equally distributed multidimensional pseudo random sequence based on coupling tent image system fast.
Background technology
Pseudorandom number generator is a kind of important password source, is the widely used cryptographic techniques in field such as various countries' military affairs, politics and diplomacy.Utilize pseudorandom number generator to encrypt again expressly converting successive bits stream to, the production with key use and manage simplifications, advantage such as encryption/decryption speed is fast, and error diffusion is little, hardware is realized simply and real-time is good, thereby be widely used in cryptographic system.
In today that computer technology develops rapidly, the defective that traditional pseudorandom number generator exists is also more and more obvious, and shorter like the cycle of key, correlation is bigger etc.Traditional pseudorandom number generator extensively adopts is m-sequence and the improvement sequence that is the basis with the m-sequence; But the linear complexity of m-sequence is lower; There is the possibility that is decrypted, verified in theory, can confirm whole m-sequence as long as know any 2n position in the m-sequence.Occur in the conventional sequence cryptographic system under the situation of all defectives that is difficult to remedy and deficiency, the chaos pseudo random number generator arises at the historic moment as a kind of novel stream cipher system.
Chaotic signal has height unpredictability and pseudo-random characteristics, and this is to confirm the most attractive characteristic of opinion chaos system, and it can cause the application of up-to-date engineering aspect.Because chaos system has many characteristics that meet the cryptography requirement such as the variation sensitivities of variable and parameter, using it for information encryption has in recent years become password educational circles question of common concern.An important difference of chaos system and traditional cryptographic algorithm is that chaos system is defined on the real number field.Under the situation that limited precision realizes, there is serious degeneration in the relative continuous system of the dynamics of digitlization chaos system.For making AES really move towards practical application based on chaos, will examine the fail safe of digitlization chaos system with cryptographic viewpoint closely, design meets the safe chaos system that cryptography requires fully.
In some typical chaos systems of being studied at present; The one type of piecewise linear maps that is mapped as representative with tent has even distribution character; But has very strong correlation between the consecutive value of the truncation chaos sequence that produces by this type low-dimensional chaos system; The low bit of initial state is little to the influence of some output signals; Utilize this characteristic to cut apart attack to chaos cipher, in addition, also exist key space little and under some initial value output sequence have only very short safety defects such as cycle.
Coupling tent map grid pattern (Coupled Tent Map Lattices; CML) be the exemplary of higher-dimension space-time chaos system; It is realized through the coupling to the tent mapping, can improve the complexity of system greatly, thus the fail safe that helps improving system.Yet regrettably, it but no longer has the even distribution character of tent mapping with the nonlinear function of tent mapping as lattice point, and in addition, it still can not satisfy the designing requirement of cryptographic algorithm fully.Pseudorandom number generator with TD-ERCS chaos system structure need just have equally distributed characteristic through an inverse cosine function and an arctan function conversion, has influenced computational speed.The sequence homogenizing being carried out in the output of existing pseudo-random generator handle, also be a kind of effective ways that generate equally distributed pseudo random sequence, but this processing method has increased operand undoubtedly.
Summary of the invention
According to background technology, the purpose of this invention is to provide a kind of method based on the equally distributed pseudo random sequence of the coupling fast parallel generation of tent image system.
Method of the present invention is according to cryptographic security requirement; Coupling map grid pattern (CML) to classics improves; Cancel its diffusion coefficient, increase constant term, its lattice values is limited to [0 through modulo operation; 1] in, realized a novel coupling tent map trellis system with even distribution characteristics.It has inherited the coupling diffusion mechanism and the parallel iteration characteristic of CML model; Through the stretching of local lattice point tent mapping and the Double Nonlinear effect of folding and modulo operation; Make system mode move towards each attitude traversal; Overcome the deficiency in the fail safe of CML model, can walking abreast fast, the generation multidimensional has the pseudo random sequence of even distribution character.
To achieve these goals, the present invention is achieved through the following technical solutions:
A kind of fast parallel generation method of multidimensional pseudo random sequence with even distribution characteristics is characterized in that:
(1) user key and key conversion:
User key length is 128bits, and it is decomposed into four isometric parts, every part 32bits, and the key after the decomposition is with the key vector
K Expression,
K =
k 1 ,
k 2 ,
k 3 ,
k 4 , with component
k 1 ,
k 2 ,
k 3 ,
k 4 16 of each bit ring shift lefts, the result of generation is designated as
,
,
,
, and then the key vector that is expanded
=
k 1 ,
k 2 ,
k 3 ,
k 4 , 
,
,
,
, and each component linearity is transformed to [0,1] real number in interval, be designated as:
α 1 , α 2 , α 3 , α 4 , α 5 , α 6 , α 7 , α 8 }
(2) initial value vector and conversion:
The initial value vector that to set 8 length be 52bits,
0x01234567d807a, 0x89abcdef72be5, 0x3210fedc428a2, 0xba9876543956c,
0x02468acee49b6, 0xfdb975312de92, 0x456789ab983e5, 0xfedcba98c6e00
With its respectively as [0,1] interval in the mantissa of double precision real number, and then be transformed to [0,1] double precision real number in interval;
(3) have the coupling tent map trellis system of even distribution character:
The form of coupling tent map grid (CML) model is:
Wherein, nonlinear function
fBe the tent mapping:
<i >n</i>Be the discrete time step number;<i >i</i>=1,2 ...,<i >L</i>Be discrete lattice point coordinate,<i >L</i>Be the grid size;<i >ε</i>Be coupling coefficient, and satisfy 0<i ><ε<</i>Boundary condition by<i >x</i><sub ><i >n</i></sub><i >(0)</i>=<i >x</i><sub ><i >n</i></sub><i >(L), x</i><sub ><i >n</i></sub><i >(L+</i>1<i >)</i>=<i >x</i><sub ><i >n</i></sub><i >(</i>1<i >)</i>Realize that initial condition is the random number in [0,1],<i >k</i><sub ><i >i</i></sub>Be constant term, get<i >k</i><sub ><i >i</i></sub>=sin (<i >i</i>),<i >i</i>It is radian;
(4) pseudo random sequence generates:
Use the sequence of real numbers that obtains by user key mapping
α 1 ..., α i ,,
α 8 }As the tent mapping parameters
α(promptly use
α i As
iThe tent mapping parameters of lattice point
α), use the double precision real number that obtains by the initial value DUAL PROBLEMS OF VECTOR MAPPING as initial value, formula (3) is carried out interative computation, after iteration 30 is taken turns, at the lattice point vector
X n Each component in, preceding 48 bits of its mantissa of intercepting, and every intercepting result who takes turns iteration carried out cascade just obtain 8 pseudo random sequences (PRBS) that independently have even distribution characteristics.
Because adopt technique scheme, the present invention has following advantage and effect:
1, method of the present invention utilizes this novel coupling tent map trellis system to generate pseudo random sequence; Eliminated the relevance that reaches between the adjacent lattice point of CML model between the sequence consecutive value; Suppressed the short period phenomenon that is easy to generate in the digitlization chaos system effectively; Be a universe property zero correlation system, have cryptographic applications and be worth with comparatively stable big positive Lyapunov index.
2, method of the present invention has good statistical property and security feature, and the speed of service is fast, and also line output multidimensional pseudo random sequence is easy to use, and has extensibility preferably.
3, method of the present invention adopts the parallel iteration structure, but thereby the software and hardware Parallel Implementation, the pseudo random sequence formation speed is fast.
4, method of the present invention is easy to use flexibly, and upgrading can produce more multidimensional pseudo random sequence easily, and key length can further increase, and is simple in structure, understands easily, is convenient to statistical analysis and safety analysis, and the transparency of algorithm is high, and the user can relievedly use.
Description of drawings
Fig. 1 is that the present invention utilizes the parallel multidimensional pseudo random sequence structure chart that generates of coupling tent image system;
Fig. 2 is the test result of pseudo random sequence distribution character of the present invention;
Fig. 3 is the test result of time series Invariant Distribution characteristic of the present invention;
Fig. 4 is the test result that time series 1 jump value of the present invention distributes;
Fig. 5 is the test result of maximum Lyapunov exponent of the present invention;
Fig. 6 is the test result of initial value sensitiveness of the present invention;
Fig. 7 is the test result of autocorrelation performance of the present invention and their cross correlation;
Fig. 8 is a binary sequence degree of balance test result of the present invention;
Fig. 9 utilizes the present invention to carry out the structured flowchart of data encryption.
Embodiment
Below in conjunction with accompanying drawing the present invention is done further detailed description.
A kind of fast parallel generation method of multidimensional pseudo random sequence with even distribution characteristics, its implementation procedure is:
(1) user key and key conversion: user key length is 128bits, and it is decomposed into four isometric parts, every part 32bits, and the key after the decomposition is with the key vector
K Expression,
K =
k 1 ,
k 2 ,
k 3 ,
k 4 , with component
k 1 ,
k 2 ,
k 3 ,
k 4 16 of each bit ring shift lefts, the result of generation is designated as
,
,
,
, and then the key vector that is expanded
=
k 1 ,
k 2 ,
k 3 ,
k 4 ,
,
,
,
, and each component linearity is transformed to [0,1] real number in interval, be designated as:
α 1 , α 2 , α 3 , α 4 , α 5 , α 6 , α 7 , α 8 }
(2) initial value vector and conversion: the initial value that to set 8 length be 52bits is vectorial:
0x01234567d807a, 0x89abcdef72be5, 0x3210fedc428a2, 0xba9876543956c,
0x02468acee49b6, 0xfdb975312de92, 0x456789ab983e5, 0xfedcba98c6e00
With its respectively as [0,1] interval in the mantissa of double precision real number, and then be transformed to [0,1] double precision real number in interval.
(3) have the coupling tent map trellis system of even distribution character:
The form of coupling tent map grid (CML) model does
Wherein, nonlinear function
fBe the tent mapping:
This mapping has uniform distribution function, and different control parameters is all had near consistent Invariant Distribution density, helps satisfying the balance requirement of cryptographic system.<i >n</i>Be the discrete time step number;<i >i</i>=1,2 ...,<i >L</i>Be discrete lattice point coordinate,<i >L</i>Be the grid size;<i >ε</i>Be coupling coefficient, and satisfy 0<i ><ε<</i>Boundary condition by<i >x</i><sub ><i >n</i></sub><i >(0)</i>=<i >x</i><sub ><i >n</i></sub><i >(L), x</i><sub ><i >n</i></sub><i >(L+</i>1<i >)</i>=<i >x</i><sub ><i >n</i></sub><i >(</i>1<i >)</i>Realize that initial condition is the random number in [0,1].
CML model model has the space-time chaos behavior, and a plurality of positivity Lyapunov indexes are arranged, and all is chaos on time and direction in space, and its dynamic behavior is rich and complex very, can eliminate the influence of the limited precision of computer to a certain extent.Compare with unlined tent mapping (formula (2)), the security performance of CML model has had large increase.Yet in view of the cryptography meaning, the CML model is still perfect inadequately.In the CML model, the effect of diffusion has been played in the coupling between lattice point, and it can spread apart the variation of a lattice point, influences other all lattice points.But the coupling between lattice point produces very big influence to the seasonal effect in time series distribution character, has the unlined tent mapping of even distribution character originally, and after being coupled by formula (2) mode, evenly distributivity but has been destroyed.
Coupling tent map grid pattern (formula (1)) is improved, cancel its diffusion coefficient
ε, increase constant term
k i , through modulo operation its lattice values is limited in [0,1], had the coupling tent map trellis system model of even distribution character as follows:
x n+1
(
i)=
f(
x n (
i))+
f(
x n (
i-1))+
f(
x n (
i+1)) +
k i (mod 1) (3)
In the formula,
n,
i,
LImplication and formula (1) in identical, here
L=8. nonlinear function
fStill be the tent mapping
F α . boundary condition still by
x n (0)=
x n (L), x n (L+1
)=
x n (1
)Realize that initial condition is the random number in [0,1],
k i Be constant term, get
k i =sin (
i),
iIt is radian.Model after the improvement (formula (3)) has very superior cryptography attribute.
(4) pseudo random sequence generates: use the sequence of real numbers that obtains by the user key mapping
α 1 ..., α i ,,
α 8 }As the tent mapping parameters
α(promptly use
α i As
iThe tent mapping parameters of lattice point
α), use the double precision real number that obtains by the initial value DUAL PROBLEMS OF VECTOR MAPPING as initial value, formula (3) is carried out interative computation, after iteration 30 is taken turns, at the lattice point vector
X n Each component in, preceding 48 bits of its mantissa of intercepting, and every intercepting result who takes turns iteration carried out cascade just obtain 8 pseudo random sequences (PRBS) that independently have even distribution characteristics.
But the coupling tent map trellis system (formula (3)) that is had even distribution character by the invention of Fig. 1 knowledge capital is core algorithm, and its character has determined the performance of pseudorandom number generator, and it has good statistical property.
Provide the seasonal effect in time series distribution map that formula (3) iteration generates by Fig. 2, the result shows that its rise time sequence has highly desirable even distribution character.
Provide by Fig. 3
L=8,
αWhen getting different values, by the seasonal effect in time series Invariant Distribution probability curve of formula (3) iteration generation.Because each lattice point structure of formula (3) has symmetry characteristic, thereby each lattice point has identical statistical property.One group of initial value of picked at random makes α=0.61, appoints to get a lattice point and analyze, and codomain [0,1] is divided into 10
4Individual interval is 5% o'clock in significance level, and the number that falls into each minizone is carried out χ
2Even distribution inspection is at iterations
N=10
5The time, the test value that obtains is:
χ
2=
10110.6
N=10
6When inferior, test value χ
2=9930.3
N=10
7When inferior, test value χ
2=9923.2
When significance level is 5%, table look-up
u 0.95=1.645.But approximate calculation gets:
Can find out that the pseudo random sequence of generation can be through the even distributional assumption check under the level of signifiance 5%.
Chaos sequence is generated by the deterministic system iteration, thereby between the chaos sequence consecutive points correlation is arranged.In order to show this restriction, the absolute value of the difference of adjacent two states of definition sequence of iterations does
d 1, promptly
d 1=|
x n+ 1
-
x n |, claim
d 1Be 1 jump value, definition similarly
d k =|
x n+
k -
x n |, claim
d k For
kThe jump value.For the true random sequence that each element occurrence probability equates, the probability distribution of the absolute value of its difference is a linear decrease from big to small, until being 0.
Provide by Fig. 4
αWhen getting different values, the experimental result that the seasonal effect in time series 1 jump value that formula (3) generates distributes.Can find out that the time series that is generated by formula (3) has the identical difference characteristic of true random sequence that equates with each element occurrence probability.When
k>=1 o'clock, difference distributed and just demonstrates the linear decrease characteristic.Can't distinguish mutually with the true random sequence that each element occurrence probability equates.
The limited precision of the computer of chaos system realizes, must generate periodic orbit.In the formula (3),, make system mode move towards each attitude traversal, and then the cycle of system is increased through the stretching of local lattice point tent mapping and the Double Nonlinear effect of folding and modulo operation.Table 1 provides computational accuracy
(
h 10=2,3) under, 100 groups of initial values of picked at random, under different grid numbers, different accuracy, the minimum period and the average period of formula that calculates (1) and formula (3).Find out from table 1, in the formula (1),
h 10=2 o'clock,
LValue between 4 ~ 7, the minimum period is 1, promptly converges on fixed point after the limited number of time iteration.Compare with formula (1), formula (3) is under limited precision, and the seasonal effect in time series periodic problem of generation has clear improvement.
Minimum period and average period under the limited precision of table 1
Maximum Lyapunov exponent is the quantification index of the average index diverging rate of expression phase space neighbour track, and it has been described track the small situation about retrodeviating from being exaggerated that departs from takes place, and can quantitatively delineate the diversity of describing neighbour's track.The maximum Lyapunov exponent value is big more, and this diversity can be strong more, and the confusion degree of system is high more.From the cryptographic algorithm design point of view, always hope that the maximum Lyapunov exponent of chaotic maps can be bigger.
Can calculate the maximum Lyapunov exponent of coupling map trellis system by following formula, use λ
Max Expression, promptly
In the formula,
.
The test result of the maximum Lyapunov exponent of formula (1) and formula (3) is shown by Fig. 5.The method that is adopted is one group of initial value of picked at random, order
Dx 0=10
-8, remove 1000 step transient processes, calculate the 3000 later steps, calculate when system's dimension respectively
LThe maximum Lyapunov exponent value of system during with variable element α independent variation.
Fig. 5 (a): the maximum Lyapunov exponent of formula (1) (parameter alpha from 0.01 to 0.99 changes, step-length 0.01 (coupling coefficient ε=0.01,
L=8)); Fig. 5 (b): the maximum Lyapunov exponent (system dimension of formula (1)
LFrom 4 to 100, step-length 1 (coupling coefficient ε=0.01, α=0.61)); Fig. 5 (c): the maximum Lyapunov exponent of formula (3) (parameter alpha from 0.01 to 0.99 changes, step-length 0.01 (
L=8)); Fig. 5 (d): the maximum Lyapunov exponent (system dimension of formula (3)
LFrom 4 to 100, step-length 1 (α=0.61)).
Find out moulded dimension from result of calculation
LVariation all very little to the influence of the maximum Lyapunov exponent of two kinds of models; In the formula (1), the variation of parameter alpha is bigger to the influence of maximum Lyapunov exponent, and in the formula (3), parameter alpha obviously reduces the influence of maximum Lyapunov exponent, and the maximum Lyapunov exponent value is very big.This explanation formula (3) is a space-time chaos system with comparatively stable big positive Lyapunov index.
Can know the test result of initial value sensitiveness by Fig. 6.In order to test initial value sensitiveness, 100 groups of initial value vectors of picked at random
X 0 =[
x 0 (1)
, x 0 (2)
... X 0 (
L)] test definition
δBe the initial value component
x 0 (1) variable quantity, process
nAfter the wheel iteration, by the initial value vector
X 0 =[
x 0 (1)
, x 0 (2)
... X 0 (L)] iteration generates the lattice point vector
X n =[
x n (1)
, x n (2)
... X n (
L)], and by the initial value vector
=[
x 0 (1)+
δ, x 0 (2)
... X 0 (L)] iteration generates the lattice point vector
=[
].Get
L=8, at the lattice point vector
X n And
Each component in, preceding 50 bits of its mantissa of intercepting generate a sequence of being made up of 400 bit values respectively
B And
, definition
For
δCorresponding
B With
The mean change bit number.If
Value is then claimed system's warp near 200
nIt is repeatedly right to take turns
δExtremely sensitive.Fig. 6 abscissa is that the negative logarithm of initial value component variation amount is represented, ordinate is corresponding
Value,
rExpression iteration wheel number.Fig. 6 (a) is the test result of formula (1), iteration wheel number
rBeing respectively 5,30,60,80 takes turns; Fig. 6 (b) is the test result of formula (3), iteration wheel number
rBe respectively 5,10,20,30 and take turns, in order to make model component
δ (x0 (1
)) Susceptibility reach 10
-16The order of magnitude (according to the IEEE-754 standard, this is the high sensitive that following of double precision condition can reach), formula (1) needs iteration 80 to take turns, and formula (3) only needs iteration 30 to take turns.
By Fig. 7 the seasonal effect in time series correlation properties that formula (3) iteration generates are shown.The seasonal effect in time series normalized autocorrelation functions that coupling map grid pattern generates is defined as
Cross-correlation function is defined as
Wherein, | τ | ∈ [0,
N],
NBe sequence length,
The expression sequence
x n (
i) mean value,
iThe representation space lattice point,
nExpression iteration step number.
Get
N=999, parameter alpha from 0.51 to 0.99, step-length 0.01 is calculated the seasonal effect in time series correlation properties that generated by formula (3) iteration.The test result explanation, the seasonal effect in time series auto-correlation function that is generated by formula (3) iteration is similar to
δFunction, adjacent lattice point cross correlation are approximately zero, are universe zero correlation systems.
Table 2 is parameter alpha when getting different value, the seasonal effect in time series auto-correlation secondary lobe maximum, auto-correlation secondary lobe root mean square, maximum cross-correlation value and the cross-correlation root mean square that are generated by formula (3) iteration.
The analysis of table 2 sequence dependent features
| α | Auto-correlation secondary lobe maximum | Auto-correlation secondary lobe root mean square | Maximum cross-correlation value | Cross-correlation root mean square |
| 0.61 | 0.0320 | 0.0098 | 0.0366 | 0.0101 |
| 0.71 | 0.0338 | 0.0099 | 0.0315 | 0.0100 |
| 0.91 | 0.0370 | 0.0101 | 0.0308 | 0.0098 |
| 0.99 | 0.0375 | 0.0102 | 0.0351 | 0.0101 |
By Fig. 8 the binary sequence degree of balance test result that formula (3) iteration generates is shown.System dimension does
LCoupling map trellis system, the process
NAfter the wheel iteration, the parallel generation
LIndividual length does
NChaos sequence
x n (i),
i=1,2 ...,
L, and
x n (i)∈ [0,1).According to standard IEEE 75-1985, the mantissa position of the double-precision floating points of binary representation is 52-
Bit, promptly
x n (i)=
×2
-1+
×2
-2+…
×2
-52
So exportable bit sequence
,
j=1,2 ..., 52.
If bit sequence
Have even probability distribution, promptly
P{
=0}=
P{
=1}, then claim binary sequence
Has a desirable harmony.If
N 1With
N 0Represent in the sequence respectively " 1 " with " 0 " number,
NThe length of expression sequence, the degree of balance of binary sequence is defined as:
E=
The degree of balance
EMore little, harmony is good more.Get
N=999, calculate the degree of balance of bit sequence.Among Fig. 8 (a), parameter alpha from 0.51 to 0.99, step-length are 0.01, the lattice point coordinate
I=8; Among Fig. 8 (b), the lattice point coordinate
iFrom 8 to 64, step-length is 1, parameter alpha
=0.61.Find out from test result, bit sequence
, at j=1 ...,, good harmony is arranged, last 1-at 51 o'clock
BitHarmonious very poor, this is by due to the carry mechanism of real number in the Computing.
The distance of swimming characteristic of test bit sequence.The phenomenon that several same code elements (0 or 1) occur is continuously claimed the distance of swimming, and contained 1 or 0 number is called the length of this distance of swimming in the distance of swimming.For binary sequence at random, the number of the number of 1 distance of swimming and 0 distance of swimming respectively accounts for half the, and length does
iDistance of swimming probability of occurrence be 2
-
i Table 3 provides the distance of swimming distribution proportion mean value of the bit sequence that is generated by formula (3) iteration.In the test, sequence length is got 2048bits, system dimension
L=8, parameter alpha=0.61.
Table 3 distance of swimming distribution proportion mean value
Present invention is described with concrete data below.
(1) user key and key conversion: (hexadecimal number is represented)
Selected user key
K =afce234789236abd9485727892358934
Then
k 1 =Afce2347,
k 2 =89236abd
,
k 3 =94857278
,
k 4 =92358934;
And then the key that is expanded
=2347afce,
=6abd8923,
=72789485,
=89349235
(2) initial value vector:
0x01234567d807a, 0x89abcdef72be5, 0x3210fedc428a2, 0xba9876543956c,
0x02468acee49b6, 0xfdb975312de92, 0x456789ab983e5, 0xfedcba98c6e00；
(3) to coupling tent map grid mapping carry out 30 take turns preparatory iteration after, the lattice point state value (decimal representation) that obtains:
x 30 (1
)= 0.602615371812239;
x 30 (2
)= 0.607771262934258;
x 30 (3
)= 0.115757471624734 ;
x 30 (4
)= 0.329314182694977 ;
x 30 (5
)= 0.255977911557113;
x 30 (6
)= 0.828701702728407;
x 30 (7
)= 0.556950630124935;
x 30 (8
)= 0.723374972040466
；
(4) 8 pseudo random sequences that independently have even distribution characteristics that generate:
1)28ecc90e197aee6ade906fa71e6b9cef41af766dabbe29ec4e187b5a085b6ca7cbd72e30d205a0a6c3cb00fef78a9781286e60a5ef9a69aec10f6404fdd462927eef9638bbc555ba94d7792dde89cb73e4e01517c7abcd28035455a1d942d64904eb38d041369abbc14c0af92527eaa175d8bc15b2e3f4ea……
2)d4c29ebece11129d2aa19d7bd302d647391a4eb4e0edb1ea73b0f02341b82954d0dbd22fff0dba21eef20fc50a3d036fde7f4161b0e880bfc34abf721227f7a7c3a0ee24356936b260603a49d601e16578c7e6c02b6ab710b690343d0dc9dd4db7d5291f672abb25b507e3886a6dd88d16e81b5a1863a89e…… 3)c31381b0183dc3d03f2cd6137dbd9ea760542bd2d7fae435985af8bb919eedfd3018028254ceaf7ee34f7ca2ab9db87ef735aba6a667bd2f31b0c9d3a368988053e3ce4bfbfe79543ea41bcd84f8339f8a606c5c28f50987d1148bba62a36aa51bb7527eb3fa06fc3d5aae2f1f355f3e0ba3a8b28d076288……
4)65583cd8572f5fab9102c4ba75b0eb2b62b5558970f4c2b98f5ef7976eb5b0d1b0507497701b9ad4eb9da070ced2aa0be648a14b3c5b88f46afdfa7f621588661e9547c558270050993c3a2fe3b23c80e83177b9a6d024bf655e5e5e40caa7860d826f7f7e0a33d4536f6396c5a10b4833ad90c902c362f8…… 5)b138c1ae536b9427b943592d20a928589197343e6f24115025b6452bba0f511d25394f6a8a8b96155424a062cdac216299fdf1afe5a2f0ff66858d572537e3c2b1753be6de7af94ae51f73e63a3fe28d7e2f86fb8c67716de6bf63588f4e1d6805e11330f1cc788d3f7f51e4f137468ee0691b4043f3b603…… 6)3cd0880986a9fc2973642a0bb336d2807f3f9a78b489230329740de2fae5f5bdec5d48eac8f8b73d2c5524306d7754eed54ca5d9e13713676096a2dba480f3f749e6ace5e83a800a5cae036e25bf0483da0cba1d09efb4da98309631da6f5b34da3f1959c0d3019e93441c95ae12b7c845608a27f2cff4cd……
7)592a54e1cef07fbab537a41182eb2fa28d7b1ff481200c9ed51786430697a4c6b6cff7d66e0578ee4b8291632c105464f92fe831e2a80cfbc87e8bdc8ff1d46de198a5c9df9a9d04961c6e1596dfad6449aa08684f09fb2ac6bcea223262c81ed4811216d6e75856f0a68a0749c37d56a5d4c18e662e07e9…… 8)43ae3883b3047e8e2f8f6d39098ced6baa3c1da423cbaba9287e9c8d31400829ded60d9c4fbbe06c1b2a1adda3053c83f8ee36f02eea53b526a0adbd5062a207501064e03532be7f3769e511f4a6fcf01f1766aa410a59756505db3462e6551ff0d0b50112b073d64a273cd97c486fbe0595c03b991786de……
(5) key in the above-mentioned instance is changed a bit, regenerate pseudo random sequence.
As key is changed into:
K = afce234789236abd9485727892358932
To coupling tent map grid mapping carry out 30 take turns preparatory iteration after, the lattice point state value that obtains:
x 30 (1
)=0.520456123745309;
x 30 (2
)= 0.883242801481582;
x 30 (3
)= 0.145212665711578;
x 30 (4
)= 0.049349587422868;
x 30 (5
)= 0.229196247563788;
x 30 (6
)= 0.838745499910412 ;
x 30 (7
)= 0.988412441016985;
x 30 (8
)=0.724627585793497
.
8 pseudo random sequences that independently have even distribution characteristics that generate:
1)71b63f2e79927a70379edc61bdd3cd5dd6ed3559f64a5cf55cfdbad9c0b87486f871b251a63508cad0a1042e0c2b2fda0c2649e92a081d532b067f7b6f0a0d6368b534dace4d4484cba5329c725a3dd8c3ca5a1c8822b577bb3895846939a491fa5b870d03a03eceb090a0a731d305aca6e88c938ac65125…… 2)2b3eda524b8a84281ec69b0dcb4b22507a305b4288c547f4429a9ed32226f6eea2b8411df4ad1c70169b7d38031a0068887adfb58bb854550e4631a2aa10a4cd609112011e40f4a4ffd5fcba89e9572a874ab7d6be59ee40be5c1d69fea68a6c5bf145885187b79c16257463cce9e89ee5d4b13e96d564cd…… 3)bab2dad941b7215f6cfbdb56eccd9f9acf2738ba2c322e70060a3a56d588def7202e41f8c60d1f8f3be2b62a61063d8b34d8b81cf2589764d4669cbca95306f9cfc961bf1f5a81057365892660627dc6fd00db0fa188816d4bddd6a1b7c6806109f87a3086e7895c9235f929f87dcc16ea18541c1f3ef091……
4)fccddb5fc9395711f5e0c24fcdab0f63e9c77a18358e77751dc0f3145f52e4ad2df1dd1f993b7bf36b17440677093a220e82b15d004b8847986643bb67feaacfd993c6e22bc65807539bf36bd4b6ff3010ed0f7326e5b2b98ee22ba2afe2c593b7c54f652f512b3a59f111f4648f27f5ce637d0393cdcd2b……
5)37461d721177ce0912bc3c45eda948648afae091551be2623b0d6301f7bac0fa2cf933c2f88e5b5e21e7df69134e7769b943ac4480d45bc502bcf48611b93842fc4c0dcf4f24e89e3b4ae9f6938b13150a6f452bc4b2ad3861bec2b442a31ec6183d29eaed8b0ea88cce0ca3290ab40c5c95a59fb8b5071c…… 6)7890ad57388ce9f9ff52bdafc7c34a675e101f6928973bd397a73e06a0a1b8b6d05739bf64c3c0e1a49f10357a6640bc68965883fb04bf32c6321fd27c721819bf08ca1d2027c9159e9955c613b31be01772c5afd828ae11ead3ac794055aba08f8bd0859b96345457111548fc104f465d56069377101dad…… 7)8c434e23346a0e89460937212be40baf00c783fa6d179830616257c41934ce505565cb2b8de7bb9385d88a958b7ee92ae85803ac771b034294bd61a8ee1e53042b99acd473bb9cc220b46ccdf21157553b58d181624c1e3631f932d32ff74212bb6c5e1485b38eda04c40d4e5565597f6b9f6c7f34ddb930…… 8)5c8fa1babf4320eac3f720680d7e88871eea4bd9725c50e9b8d3554ec61cf7d79bb573441268d90f08abe006ddfa861d1ca49bee2f2a6f33e672e298fec387fa87a6c1f97db2f4636655ad176b7eac7e1791d71dce969f8fa04c09d06a1c9f4a5af8e537bc5f3513dde06ac1886fbd1451b4036281b7375f……。
See that thus key changes 1 bit, the pseudo random sequence that generates is then different fully.
The present invention can be used for fields such as internet data encryption, spread spectrum communication, combines specific embodiment that the present invention is carried out data encryption at present and further specifies.
As shown in Figure 9, the data encryption structured flowchart is encrypted and is deciphered through the XOR computing.
The outstanding feature of " the fast parallel generation method of the multidimensional pseudo random sequence " enciphered data that provides with the present invention is: safe, speed is fast, but the Parallel Implementation multiple data stream encrypt, be particularly suitable under multi-core environment and parallel computation environment, using.Provide the example of concrete realization data encryption below: (the encryption and decryption process of single data flow)
Example 1: (expressly sequence is a text)
(1) plaintext sequence 1:
The hardware of computers has undergone revolutionary changes. The gain in the speed and function has been impressive.
(2) seed key and key conversion: (hexadecimal number is represented)
Selected seed key
K =
23984A8D FA712345CD239871B9BA7912
Then
k 1 =23984A8D,
k 2 =FA712345,
k 3 =
CD239871,
k 4 =B9BA7912;
And then the key that is expanded
=23984A8D, 
=FA712345,
=
CD239871, 
=
B9BA7912;
(3) initial value vector:
0x01234567d807a, 0x89abcdef72be5, 0x3210fedc428a2, 0xba9876543956c,
0x02468acee49b6, 0xfdb975312de92, 0x456789ab983e5, 0xfedcba98c6e00
(4) encrypted result (ciphertext sequence)
7eb9818b37f50dd51a1b35fec060be35026e057defcd18e3d4821097dad1d05a51295b16d4587fad0f6eddd67704f19ea514bdcd57aaf9f752994ae4b4964cca44724b2a2b39b230da3fa9ef5b47c53de20645b314c96a87fed448db835e6e8ca95146d2ba516058f40e8f399d03727e1401ffa34721ac32 。
Decrypted result when (5) seed key is correct:
The hardware of computers has undergone revolutionary changes. The gain in the speed and function has been impressive.
Decrypted result when (6) seed key changes 1bit:
For example seed key is changed into
K =
22984A8D FA712345CD239871B9BA7912
Then decrypted result is:
70b8eadade4b353359ed086e6ed684899887041364480ba847e4f1a7843b495fe2e642a012ed600055e74a895be6255318d96d680c3c64d5ac7f6c012164ba3da94d91f260788fd1a4719066cee7ef587245e018208ff2e651093c6afcffaa0ce67b30a73feb5d5404953590e2b7e0331f705e0bb930033f。
Example 2: (expressly sequence is binary data (hexadecimal number is represented))
(1) plaintext sequence 1:
d76aa478e8c7b756242070dbc1bdceeef57c0faf4787c62aa8304613fd469501698098d88b44f7afffff5bb1895cd7be6b901122fd987193a679438e49b40821f61e2562c040b340265e5a51e9b6c7aad62f105d02441453d8a1e681e7d3fbc821e1cde6c33707d6f4d50d87455a14eda9e3e905fcefa3f8
(2) seed key and key conversion: (hexadecimal number is represented)
Selected seed key
K =
23984A8D FA712345CD239871B9BA7912
Then
k 1 =23984A8D,
k 2 =FA712345,
k 3 =
CD239871,
k 4 =B9BA7912;
And then the key that is expanded
=23984A8D, 
=FA712345,
=
CD239871, 
=
B9BA7912;
(3) initial value vector:
0x01234567d807a, 0x89abcdef72be5, 0x3210fedc428a2, 0xba9876543956c,
0x02468acee49b6, 0xfdb975312de92, 0x456789ab983e5, 0xfedcba98c6e00
(4) encrypted result (ciphertext sequence)
7eb9818b37f50dd51a1b35fec060be35026e057defcd18e3d4821097dad1d05a51295b16d4587fad0f6eddd67704f19ea514bdcd57aaf9f752994ae4b4964cca44724b2a2b39b230da3fa9ef5b47c53de20645b314c96a87fed448db835e6e8ca95146d2ba516058f40e8f399d03727e1401ffa34721ac32
Decrypted result when (5) seed key is correct:
d76aa478e8c7b756242070dbc1bdceeef57c0faf4787c62aa8304613fd469501698098d88b44f7afffff5bb1895cd7be6b901122fd987193a679438e49b40821f61e2562c040b340265e5a51e9b6c7aad62f105d02441453d8a1e681e7d3fbc821e1cde6c33707d6f4d50d87455a14eda9e3e905fcefa3f8
Decrypted result when (6) seed key changes 1bit:
For example seed key is changed into
K =
22984A8D FA712345CD239871B9BA7912
Then decrypted result is:
70b8eadade4b353359ed086e6ed684899887041364480ba847e4f1a7843b495fe2e642a012ed600055e74a895be6255318d96d680c3c64d5ac7f6c012164ba3da94d91f260788fd1a4719066cee7ef587245e018208ff2e651093c6afcffaa0ce67b30a73feb5d5404953590e2b7e0331f705e0bb930033f。
Above embodiment is only for reference, and protection range is not so limited.
Claims (5)
1. fast parallel generation method of multidimensional pseudo random sequence with even distribution characteristics, concrete steps are following:
(1) user key and key conversion;
(2) initial value vector and conversion;
(3) foundation has the coupling tent map trellis system of even distribution character;
(4) pseudo random sequence generates.
2. the fast parallel generation method of multidimensional pseudo random sequence with even distribution characteristics according to claim 1; It is characterized in that: described user key and key conversion; User key length is 128bits; It is decomposed into four isometric parts, every part 32bits, the key after the decomposition is with the key vector
K Expression,
K =
k 1 ,
k 2 ,
k 3 ,
k 4 , with component
k 1 ,
k 2 ,
k 3 ,
k 4 16 of each bit ring shift lefts, the result of generation is designated as
,
,
,
, and then the key vector that is expanded
=
k 1 ,
k 2 ,
k 3 ,
k 4 ,
,
,
,
, and each component linearity is transformed to [0,1] real number in interval, be designated as:
α 1 , α 2 , α 3 , α 4 , α 5 , α 6 , α 7 , α 8 }
3. the fast parallel generation method of multidimensional pseudo random sequence with even distribution characteristics according to claim 1 is characterized in that: described initial value vector and conversion, and the initial value that to set 8 length be 52bits is vectorial,
0x01234567d807a, 0x89abcdef72be5, 0x3210fedc428a2, 0xba9876543956c,
0x02468acee49b6, 0xfdb975312de92, 0x456789ab983e5, 0xfedcba98c6e00，
With its respectively as [0,1] interval in the mantissa of double precision real number, and then be transformed to [0,1] double precision real number in interval.
4. the fast parallel generation method of multidimensional pseudo random sequence with even distribution characteristics according to claim 1; It is characterized in that: described coupling tent map trellis system with even distribution character, the form of coupling tent map grid (CML) model is:
<i >n</i>Be the discrete time step number;<i >i</i>=1,2 ...,<i >L</i>Be discrete lattice point coordinate,<i >L</i>Be the grid size;<i >ε</i>Be coupling coefficient, and satisfy 0<i ><ε<</i>Boundary condition by<i >x</i><sub ><i >n</i></sub><i >(0)</i>=<i >x</i><sub ><i >n</i></sub><i >(L), x</i><sub ><i >n</i></sub><i >(L+</i>1<i >)</i>=<i >x</i><sub ><i >n</i></sub><i >(</i>1<i >)</i>Realize that initial condition is the random number in [0,1],<i >k</i><sub ><i >i</i></sub>Be constant term, get<i >k</i><sub ><i >i</i></sub>=sin (<i >i</i>),<i >i</i>It is radian.
5. the fast parallel generation method of multidimensional pseudo random sequence with even distribution characteristics according to claim 1 is characterized in that: described pseudo random sequence generates, use the sequence of real numbers that obtains by the user key mapping
α 1 ..., α i ,,
α 8 }As the tent mapping parameters
α(promptly use
α i As
iThe tent mapping parameters of lattice point
α), use the double precision real number that obtains by the initial value DUAL PROBLEMS OF VECTOR MAPPING as initial value, formula (3) is carried out interative computation, after iteration 30 is taken turns, at the lattice point vector
X n Each component in, preceding 48 bits of its mantissa of intercepting, and every intercepting result who takes turns iteration carried out cascade just obtain 8 pseudo random sequences (PRBS) that independently have even distribution characteristics.
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