CN102904715A - Parallel pseudorandom bit generator based on coupling chaotic mapping system - Google Patents
Parallel pseudorandom bit generator based on coupling chaotic mapping system Download PDFInfo
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- CN102904715A CN102904715A CN2012103648411A CN201210364841A CN102904715A CN 102904715 A CN102904715 A CN 102904715A CN 2012103648411 A CN2012103648411 A CN 2012103648411A CN 201210364841 A CN201210364841 A CN 201210364841A CN 102904715 A CN102904715 A CN 102904715A
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Abstract
The invention aims at designing a pseudorandom bit generator which is efficient and can be used for hardware implementation and parallel operation and particularly relates to a parallel pseudorandom bit generator based on a coupling chaotic mapping system. According to the parallel pseudorandom bit generator, by means of an initialization module, initial values (also called seeds) of a random bit generator are subjected to nonlinear transformation expansion to generate initial values of the coupling chaotic mapping system; the initial values of the coupling chaotic mapping system, which are generated by expanding, are input into the coupling chaotic mapping system, and multi-path chaotic sequences are parallelly output by means of actions of the coupling chaotic mapping system; and the output chaotic sequences are processed by an output module, and pseudorandom bit sequences which meet an NIST SP800-22 revise testing standard are parallelly output.
Description
Technical field
The present invention relates to field of information security technology, be based on the parallel Pseudo-random bit generator of coupled chaotic mapping system.
Technical background
Pseudo random number has a wide range of applications in Monte Carlo Calculation, text encryption, image encryption and video-encryption and the key in cipher protocol, initializing variable, so the research of randomizer has consequence in Statistical Physics and modern password.The sequence that pseudorandom number generator produces requires to have large as far as possible cycle and good randomness.
Because chaotic orbit is to initial value and sensitiveness of parameters, and the pseudo-randomness of chaotic signal, in recent years, many researcher's application of chaos dynamics make up pseudorandom number generator.From existing achievement in research, a more competitive class is take the chaos pseudo random number generator of space-time coupling chaotic mapping grid as the basis.Compare with low-dimensional system, Spatiotemporal Chaotic Systems has a plurality of positive Liapunov exponents, has increased complexity and the cycle of system.Therefore chaotic computing is based on real number field, and the design of existing randomizer based on chaos is applicable to software operating environment mostly, is used for moving to that to exist the operation cost on the hardware platform high, the shortcoming that operational efficiency is low.
The present invention is special completely newly, based on the parallel Pseudo-random bit generator of chaos coupling mapping, its main feature is to adopt the one dimension coupled chaotic mapping system, by selecting effective parameter, guaranteed the space-time chaos complexity of system, also not only make the sequence of output have good statistical property, and be applicable to hardware platform by limited, easily shifting function; Can be used for simultaneously the parallel output random bit sequence.
Summary of the invention
The objective of the invention is design can be used for the hardware realization, is applicable to parallel work-flow, high efficiency Pseudo-random bit generator.Based on the parallel Pseudo-random bit generator of coupled chaotic mapping system, its process feature is following treatment step:
A1) by initialization module, the initial value of Pseudo-random bit generator (being also referred to as seed) is produced the initial value of coupled chaotic mapping system by the nonlinear transformation expansion;
A2) the initial value input coupled chaotic mapping system of the coupled chaotic mapping system of expansion generation, through the effect of coupled chaotic mapping system, parallel output multichannel chaos sequence;
A3) the processing of the chaos sequence of output by output module, parallel output satisfies the random bit sequence of testing standard.
In A1, the initial value of 64 bits is extended to the 32N bit by nonlinear transformation, produces N initial value x of coupled chaotic mapping system
0(i), i=1,2 ..., N, N is the number of coupling mapping, N 〉=4, each x
0(i) all be to belong to [0,2
32) integer on the interval; If the initial value that all equates is arranged, i.e. x
0(i)=x
0(1), i=2,3 ..., N, the initial value of output is changed to x
0(i)=x
0(1)+and 10000 * i, i=2,3 ..., N, wherein symbol+be mould 2
32Addition.
In A2, the initial value input coupled chaotic mapping system of the coupled chaotic mapping system of expansion generation among the A1, described coupled chaotic mapping system satisfies
x
n+1(i)＝(1-ε
1-ε
2)f(x
n(i))+ε
1f(x
n(i+1))+ε
2f(x
n(i-1))，i＝1，2，...，N，
N=0 wherein, 1,2 ... be the discrete time step number; I is coupling mapping position coordinate, and N is the length of coupled map lattices; Adopt periodic boundary condition x
n(0)=x
n(N), x
n(N+1)=x
n(1); F (x)=ax mod 2
32The displacement mapping, a ∈ (1,2]; ε
1And ε
2Be stiffness of coupling, satisfy ε
1＞0, ε
2＞0, and ε
1≠ ε
2, 1-ε
1-ε
2＞0;
And described coupled chaotic mapping system requires parameter a, ε
1And ε
2Selection so that coupled system is Spatiotemporal Chaotic Systems, simultaneously in order to make complicated multiplying be converted into simple shifting function, getting parameter is following form
And described coupled chaotic mapping system requires discrete time n greater than just beginning the parallel output chaos time sequence at 100 o'clock.
In A3, the chaos time sequence value of A2 output is converted into 32 bits
Wherein
The lower partial bit position of output sensitiveness
J 〉=17, the bit sequence of output adopt NIST SP800-22 revised edition as testing standard, guarantee that each sequence has good statistical property, and are separate between the different sequences.
The present invention has following technique effect:
1. the randomizer based on Time Chaotic Dynamical Systems generally is only applicable to software operating environment, and the present invention is by selecting parameter a, ε
1And ε
2, make the random bit generator based on Time Chaotic Dynamical Systems can conveniently be used for the hardware realization with less cost.
2. this Pseudo-random bit generator can the parallel output bit sequence.
Description of drawings
Fig. 1 is structural representation of the present invention.
Fig. 2 is embodiment of the invention f (x)=2x mod 2
32Displacement map operation schematic diagram.
Fig. 3 is the embodiment of the invention
Displacement map operation schematic diagram.
Fig. 4 is the schematic diagram of the coupling chaotic mapping of the embodiment of the invention.
Fig. 5 is the output module schematic diagram of the embodiment of the invention.
Embodiment
Further describe technical scheme of the present invention below in conjunction with accompanying drawing and example: A1) by initialization module, the initial value of Pseudo-random bit generator (being also referred to as seed) expansion is produced the initial value of coupled chaotic mapping system; A2) the initial value input coupled chaotic mapping system of the coupled chaotic mapping system of expansion generation, through the effect of coupled chaotic mapping system, parallel output multichannel chaos sequence; A3) the processing of the chaos sequence of output by output module, parallel output satisfies the random bit sequence of testing standard.
In A1, initialization module is that the initial value of 64 bits is extended to the 32N bit by nonlinear transformation, produces N initial value x of coupled chaotic mapping system
0(i), N is the number of coupling mapping, N 〉=4, each x
0(i) all be to belong to [0,2
32) integer on the interval.If all initial value all equates, i.e. x
0(i)=x
0(1), i=2,3 ..., N, then the initial value of output is x
0(i)=x
0(1)+and 10000 * i, i=2,3 ..., N.
Above-mentioned nonlinear transformation can adopt hash function method, for example SHA-1.The initial value of 64 bits is carried out the SHA-1 hash transformation as information, obtain the hashed value of 160 bits, the expansion of 160 bits is whenever got 32 bit values as the initializaing variable x of a mapping of coupled chaotic mapping system corresponding to the coupling mapped system of N=5
0(i), i=1,2,3,4,5.If the coupling mapped system of N＞5 then continues 160 bit values of output are carried out the SHA-1 hash transformation as new information, whenever get the hashed value continuation of 32 bits output as the initializaing variable x of the remaining mapping of coupled chaotic mapping system
0(i), i=6,7,8,9,10.By that analogy, if the coupling mapped system of N＞10 then continues 160 bit values of output are carried out the SHA-1 hash transformation as new information, whenever get the hashed value of 32 bits output as the initializaing variable x of coupled chaotic mapping system
0(i), i=11,12... is until obtain all initializaing variable x of the coupled chaotic mapping system of needs
0(i), i=1,2 ..., N.
Above-mentioned nonlinear transformation also can be in the following way: at first the initial value with 64 bits is defined as w (1) || w (2) || ... || w (7) || w (8), each w (i) is [0,2
8) integer, i=1,2 ..., 8.Definition w (i+8)=S (w (i)+w (i+4)+i), i=1,2 ..., 4N-8.Symbol+be mould 2 wherein
8Addition, S be 8 bits to the non-linear S box conversion of 8 bits, can select the S box conversion of AES.The w that makes up in order 48 bits forms the integer of 32 bits, such as x
0(1)=and w (1) || w (2) || w (3) || w (4), x
0(2)=and w (5) || w (6) || w (7) || w (8) ..., x
0(N)=and w (4N-3) || w (4N-2) || w (4N-1) || w (4N).
In A2, the initial value input coupled chaotic mapping system of the coupled chaotic mapping system of expansion generation, through the effect of coupled chaotic mapping system, parallel output multichannel chaos sequence.Described coupled chaotic mapping system satisfies:
x
n+1(i)＝(1-ε
1-ε
2)f(x
n(i))+ε
1f(x
n(i+1))+ε
2f(x
n(i-1))，i＝1，2，...，N
Wherein f (x)=ax mod 2 is shone upon in displacement
32, a ∈ (1,2]; ε
1And ε
2Be stiffness of coupling, satisfy ε
1＞0, ε
2＞0, and ε
1≠ ε
2, 1-ε
1-ε
2＞0.Described coupled chaotic mapping system requires parameter a, ε
1And ε
2Selection so that coupled system is Spatiotemporal Chaotic Systems, and require discrete time n greater than just beginning the parallel output chaos time sequence at 100 o'clock.
Fig. 2 is displacement mapping f (the x)=ax mod 2 of the embodiment of the invention
32Operation chart.If get a=2, then f (x)=2x mod2 is shone upon in displacement
32Be converted into f (x)=(x＜＜＜1) mod2
32, wherein x＜＜＜1 represents to move to left 1 bit manipulation.
Fig. 3 is the embodiment of the invention
Displacement map operation schematic diagram.
Can be decomposed into
Then displacement mapping
Be converted into f (x)=x+ (x＞＞＞1)+(x＞＞＞2) mod 2
32, wherein x＞＞＞1 and x＞＞＞2 represent respectively to move to right 1 and 2 bit manipulations that move to right.
Fig. 4 is the schematic diagram of the coupling chaotic mapping of the embodiment of the invention.If get
Then parameter can be decomposed into
ε
2＝2
-5，
The coupling mapped system further is expressed as:
x
n+1(i)＝(1-ε
1-ε
2)f(x
n(i))+ε
1f(x
n(i+1))+ε
2f(x
n(i-1))
＝(1-ε
1-ε
2)X
n(i)+ε
1X
n(i+1)+ε
2X
n(i-1)
＝(X
n(i)＞＞＞1)+(X
n(i)＞＞＞2)+(X
n(i)＞＞＞3)
+(X
n(i+1)＞＞＞4)+(X
n(i+1)＞＞＞5)+(X
n(i-1)＞＞＞5).
Among Fig. 2, the 3 and 4 shown embodiment, having guaranteed that the multiplying of displacement mapping and coupling chaotic mapping is converted into shifting function, being conducive to the design of hardware operation.Under above-mentioned parameter, system is Spatiotemporal Chaotic Systems simultaneously.Require the running time just can the parallel output chaos time sequence greater than 100 o'clock, the initial value that has guaranteed input be fully mixed and is spread.
Fig. 5 is the output module schematic diagram of the embodiment of the invention.In order to guarantee that sequence has preferably statistical property, select 32 bit x
N+1(i) the low partial bit of the sensitivity in is namely selected as output
(
) in 16 low bits
Adopt the statistical method of NIST SP800-22 revised edition to detect, testing result shows N sequence of parallel output
(i=1,2 ..., N) all having good statistical property, adjacent sequence has good cross-correlation statistical property, i.e. sequence simultaneously
Also be satisfied with the detection of NIST SP800-22 revised edition, i=1 wherein, 2 ..., N-1.
Claims (7)
1. based on the parallel Pseudo-random bit generator of coupled chaotic mapping system, its process feature is following treatment step:
A1) by initialization module, the initial value of the initial value of Pseudo-random bit generator (being also referred to as seed) by nonlinear transformation expansion and generation coupled chaotic mapping system;
A2) the initial value input coupled chaotic mapping system of the coupled chaotic mapping system of expansion generation, through the effect of coupled chaotic mapping system, parallel output multichannel chaos sequence;
A3) the processing of the chaos sequence of output by output module, parallel output satisfies the PRBS pseudo-random bit sequence of testing standard.
2. the parallel Pseudo-random bit generator based on coupled chaotic mapping system according to claim 1, it is characterized in that described steps A 1 is extended to the 32N bit to the initial value of 64 bits by nonlinear transformation, produce N initial value x of coupled chaotic mapping system
0(i), i=1,2 ..., N, N is the number of coupling mapping, N 〉=4, each x
0(i) all be to belong to [0,2
32) integer on the interval; If the initial value that all equates is arranged, i.e. x
0(i)=x
0(1), i=2,3 ..., N, the initial value of output is changed to x
0(i)=x
0(1)+and 10000 * i, i=2,3 ..., N.
3. described according to claim 2, nonlinear transformation can be in the following way: at first the initial value with 64 bits is defined as w (1) || w (2) || ... ‖ w (7) || w (8), each w (i) is [0,2
8) integer, i=1,2 ..., 8.Definition w (i+8)=S (w (i)+w (i+4)+i), i=1,2 ..., 4N-8.Symbol+be mould 2 wherein
8Addition, S be 8 bits to the non-linear S box conversion of 8 bits, can select the S box conversion of AES; Make up in order the integer that 4 w form 32 bits, such as x
0(1)=and w (1) || w (2) || w (3) || w (4), x
0(2)=and w (5) || w (6) || w (7) || w (8) ..., x
0(N)=and w (4N-3) || w (4N-2) || w (4N-1) || w (4N).
4. the parallel Pseudo-random bit generator based on coupled chaotic mapping system according to claim 1, it is characterized in that described steps A 2 the initial value input coupled chaotic mapping system of the coupled chaotic mapping system of expansion generation, described coupled chaotic mapping system satisfies
x
n+1(i)＝(1-ε
1-ε
2)f(x
n(i))+ε
1f(x
n(i+1))+ε
2f(x
n(i-1))，i＝1，2，...，N，
N=0 wherein, 1,2 ... be the discrete time step number; I is coupling mapping position coordinate, and N is the length of coupled map lattices; Adopt periodic boundary condition x
n(0)=x
n(N), x
n(N+1)=x
n(1); F (x)=ax mod2
32The displacement mapping, a ∈ (1,2]; ε
1And ε
2Be stiffness of coupling, satisfy ε
1＞0, ε
2＞0, and ε
1≠ ε
2, 1-ε
1-ε
2＞0.
5. coupled chaotic mapping system according to claim 3 requires parameter a, ε
1And ε
2Selection so that coupled system is Spatiotemporal Chaotic Systems, and satisfy following form:
a
1∈ { 0,1};
b
1∈ { 0,1};
c
1∈ { 0,1}.
6. coupled chaotic mapping system according to claim 3 requires discrete time n greater than just beginning the parallel output chaos time sequence at 100 o'clock.
7. the parallel Pseudo-random bit generator based on coupled chaotic mapping system according to claim 1 is characterized in that in the described steps A 3, and the chaos time sequence value of A2 output is converted into 32 bits
(
), the lower partial bit position of output sensitiveness
J 〉=17, the bit sequence of output adopt NIST SP800-22 revised edition as testing standard, guarantee that each sequence has good statistical property, and are separate between the different sequences.
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