CN1921376A - Fake random number generator based on parallel TD-ERCS chaos system - Google Patents

Abstract

The invention relates to a false random number generator of chaotic system, which comprises user key, password converter and seed distributor, parallel TD-ERCS, state sequence mixer modules. Wherein, user key is 16-mode character string, while the output is false random binary sequence; shifting leftwards for b bits, to convert the user key into seed parameter of TD-ERCS chaotic system, shifting rightwards for b bits, to convert the state sequence of TD-ERCS chaotic system into binary false random sequence. The invention uses TD-ERCS chaotic system as core algorism, with transparent design and better statistic property. And it uses parallel structure, while the user key is between 264 and 2672, with better expandable function and compatibility.

Description

Pseudorandom number generator based on parallel TD-ERCS chaos system

[technical field] the invention belongs to network and field of information security technology, is a kind of pseudorandom number generator of chaos system.

[background technology] pseudorandom number generator PRNG (Pseudo-Random Number Generator) is a kind of important password source and cryptographic algorithm.Pseudo random number claims pseudo-random number sequence again, and the algorithm that produces this pseudo random number is called pseudorandom number generator, can realize by software or hardware.There are many methods to produce pseudo random number, machine word calls the turn the common RAND of having table, linear congruence generator LCG (Linear Congruential Generators), linear feedback shift register LFSR (LinearFeed-back Shift Register), ANSI X9.17 pseudorandom number generator; Study often to have randomizer at present based on chaos system.

With constructing pseudorandom number generator after the chaotic signal discretization and forming new cryptographic algorithm is the new direction that chaology is applied to information security field.These algorithms adopt several famous chaos systems, as Logistic mapping, tent mapping.People such as Jakimoski have done analysis to this class algorithm, think that these algorithms compare with DES and also do not have competitiveness, have proposed serial corrective measure.People such as Wong improve algorithm structure by introducing the Hash function, and people such as Li have also proposed remedial measure.In addition, also have based on the circle mapping, based on the index mapping, based on piecewise linear maps, based on compound discrete chaotic system or the like.These algorithms improve in any case, but analyze from the angle of cryptosecurity and statistical property, and all there is fatal defective in they, are unsafe.Chaos system only is necessary condition rather than the adequate condition of the PRNG of safety on its structure cryptography to the sensitiveness of initial condition.

Along with the computer simulation technique based on Monte Carlo method is used to handle increasing physics and engineering problem, and the fail safe of information encryption is more and more higher to the requirement of pseudorandom number generator, and existing method more and more is difficult to adapt to new operational environment and engineering demand.

Sheng Liyuan etc. deliver " based on elliptical reflecting chamber discrete chaotic system and the performance study thereof of cutting delay " literary composition " Acta Physica Sinica " the 53rd phase in 2004, have constructed the new chaos system of a class for designing novel PRNG---cut delay elliptical reflecting chamber mapped system TD-ERCS (Tangent-DelayEllipse Reflecting Cavity map System).Theoretical research shows, TD-ERCS be universe chaos, universe zero correlation, stable even distribution arranged, huge parameter and initial value space are arranged, extremely strong degeneration ability is arranged, have and the various one to one features of conventional cipher algorithm, be a kind of chaos system with good statistical property and security feature.

[summary of the invention] the purpose of this invention is to provide a kind of is core algorithm with the TD-ERCS chaos system, has the pseudorandom number generator of parallel organization.

8. the objective of the invention is to realize with the following methods: on the theoretical research basis of TD-ERCS chaos system, with TD-ERCS is the algorithm that core develops a kind of pseudorandom number generator, comprise user key, password conversion and seed dispenser, parallel TD-ERCS, four parts such as status switch blender.The canonical form of user key is 16 system digit collection; Password conversion and seed dispenser convert user key to the initial condition and the parameter of TD-ERCS chaos system; Parallel TD-ERCS 1～4 TD-ERCS independently arranged side by side, iteration produces 1～4 group of independently status switch under the driving of 1～4 group of different initial condition and parameter respectively, with the original series of these status switches as pseudo random number stream, the password conversion determines that with seed dispenser the parallel counting method of TD-ERCS is: user key length is 16～42 16 system characters, adopts 1 TD-ERCS; User key length is 43～84 16 system characters, adopts 2 TD-ERCS; User key length is 85～126 16 system characters, adopts 3 TD-ERCS; User key length is 127～168 16 system characters, adopts 4 TD-ERCS; The status switch blender with 1～4 group independently status switch become one or two separate pseudorandom binary sequence by certain principle combinations, the pseudorandom binary sequence can further convert numeral, printable character or directly binary sequence output to.This organization plan, provide huge free key space to the user, had good statistical property and security feature, the speed of service is fast, simple in structure, easy to use, and make PRNG have compatibility, extensibility, be used for information encryption and also have upgradability.

[description of drawings]

Fig. 1. pseudorandom number generator algorithm structure schematic diagram of the present invention;

Fig. 2 .IEEE754 standard real number representation method.

The present invention is described in further detail below in conjunction with accompanying drawing.

Execution mode

Among Fig. 1, at first determine password as requested by the user.Again by password conversion and seed dispenser, according to definite parameter μ (0＜μ≤1), the initial value x that uses 1～4 TD-ERCS and user key difference assignment is given each TD-ERCS through the b operation of shifting left of the length of user key ₀(1≤x ₀≤ 1) and α (0＜α＜π), cut postpone m (m=2,4,5,6 ...).Claim (μ, x ₀, α m) is the kind subparameter of TD-ERCS.Each TD-ERCS is under given kind subparameter, by the generation status switch (x separately independently that iterates _Ij, k _Ij).The status switch blender is earlier with (x _Ij, k _Ij) normalization, convert standard binary sequence (θ to through dextroposition b operation _Ij, β _Ij), because θ _IjAnd β _IjAlso be separate, can be combined into pseudo random streams output by different way.Respectively each part is done detailed explanation below.

(1) user key

User key is represented with K, 16 system digit collection

H＝{0，1，2，3，4，5，6，7，8，9，a，b，c，d，e，f} (1)

Be the user key significant character, be called for short the H character.

The H character number of K is called the 16 system length of K, uses L _(h)Expression.The number of 2 system digits of K correspondence is called the 2 system length of K, represents with L.

The space size of K is [2 ⁶⁴, 2 ⁶⁷²].In this space, desirable any one integer of K, so K is not a regular length, but one long be 16～168 H symbol strings, corresponding binary number symbol string is 64～672bit.

(2) password conversion and seed dispenser

Transformation rule must meet number representation and the TD-ERCS character of C++ simultaneously.

According to the IEEE754 standard code, the double precision binary representation of the real number of C++ is made up of three parts, and as shown in Figure 2: represent the 1-bit sign bit with s, the 11-bit that represents with e has inclined to one side exponent bits, and the 52-bit mantissa position of representing with f is by following formula

(-1) ^S×2 ^e-1023×1.f 0＜e＜2047 (2)

Be converted to decimal number and binary number.Make b=1023-e,, b 〉=1 should be arranged according to the kind subparameter of TD-ERCS chaos system and the domain of definition and the normalization requirement of status switch.The position of establishing the f of mantissa again is b ₁, b ₂, b ₃..., b ₅₂, b wherein _i=0 or 1.Therefore, one is shown greater than 0 C++ floating decimal numerical table less than 1

$2^{-b}\·(1+\frac{b_1}{2}+\frac{b_2}{2}+\frac{b_3}{2}+\mathrm{\Λ}+\frac{b_{52}}{2})---\left(3\right)$

Promptly

$\frac{1}{2^b}+\frac{b_1}{2^{1+b}}+\frac{b_2}{2^{2+b}}+\frac{b_3}{2^{3+b}}+\mathrm{\Λ}+\frac{b_{52}}{2^{52+b}}---\left(4\right)$

A Here it is decimal number that the double-precision floating points correspondence of 53 precision is arranged.So the position that can establish the limited precision binary number of a reality again is B ₁, B ₂, B ₂..., B ₅₃, B wherein _i=0 or 1, this corresponding binary number is

0.B ₁B ₂ΛB ₅₃， (5)

Compare with formula (4), have

B ₁＝0，B ₂＝0，…，B _b＝1，

B _b+1＝b ₁，B _b+2＝b ₂，…，B ₅₃＝b _53-b (6)

And b _53-b+1, b ₅₂All be omitted.Formula (6) is the technical foundation that user key is converted to the kind subparameter of TD-ERCS, also is the technical foundation that the TD-ERCS status switch is converted to binary sequence.For explaining conveniently, claim B ₁, B ₂, B ₂... be the standard binary sequence.In order to realize conversion, introduce " b that shifts left operation " and " dextroposition b operation ".

Definition 1: if 51-bit among the f of mantissa, 50-bit ..., (51-b+1)-bit is " 0 ", and (51-b)-bit is " 1 ", the right that then the preceding b position of f is moved on to successively f constitutes the new f of mantissa, and such operation is called the b operation of shifting left.

For example

F:000001010100001111 before the displacement ... 10,

Displacement back f:010100001111 ... 10000001,

Here b=6.

The purpose of the b that shifts left operation is the kind subparameter that the user key with binary code representation is converted to the TD-ERCS chaos system that double-precision floating points represents expediently.

Definition 2: 0-bit is set to " 1 " among the f of mantissa, 1-bit, and 2-bit ..., (b-1)-bit all is set to " 0 ", the left side that then the back b position of f is moved on to successively f constitutes the new f of mantissa, and such operation is called dextroposition b operation.

For example

F:010100001111 before the displacement ... 10011000,

Reset and put f:010100001111 ... 10000001,

Displacement back f:000001010100001111 ... 10,

Here b=6.

The purpose of dextroposition b operation is that the status switch of TD-ERCS chaos system that double-precision floating points is represented is converted to the standard binary sequence expediently.

TD-ERCS and line number are by the user key length L _(h)Determine regulation: L _(h)=16～42,1 TD-ERCS; L _(h)=43～84,2 TD-ERCS; L _(h)=85～126,3 TD-ERCS; L _(h)=127～168,4 TD-ERCS.

Use K _i, i=1,2,3,4 represent to distribute among the K codon piece of i TD-ERCS, then K can be expressed as the serial connection of 4 codon pieces, is defined as

K＝K ₁K ₂K ₃K ₄， (7)

Here, K ₁K ₂Expression K ₁With K ₂Serial connection, non-multiplying each other.

In like manner, use K _Ij, j=1,2,3,4 expression K _iIn distribute to the codon piece of the kind subparameter of j TD-ERCS, K then _iCan be expressed as the serial connection of 4 codon pieces, be defined as

K _i＝K _i1K _i2K _i3K _i4，i＝1，2，3，4， (8)

K _IjAs follows with the corresponding relation and the assignment method of kind of subparameter:

K _I1Get 13 H symbols, long 52bit composes to parameter μ as binary code.

The first step is given the f of μ mantissa assignment, i.e. K _I1→ f; Second step, 0 → s; The 3rd step is to shift left b operation of f; The 4th step is if b＞30 then make b=30; The 5th step, (1023-b) → e.

K _I2Get 13 H symbols, long 52bit composes to initial value α as binary code.

The first step is given the f of α mantissa assignment, i.e. K _I2→ f; Second step, 0 → s; The 3rd step is to shift left b operation of f; The 4th step, (1023-b) → e; If K _I2=0, then the 0-bit of f composes " 1 ", and " 0 " is composed in all the other positions, again according to the operation of the 3rd step.After assignment finished, it was on duty with π doubly.

K _I3Get 13 H symbols, long 52bit composes to initial value x as binary code ₀

The first step is given x ₀The f of mantissa assignment, i.e. K _I3→ f; In second step, give sign bit s with the value of the 0-bit among the f; The 3rd step is to shift left b operation of f; The 4th step, (1023-b) → e; If K _I3=0, f=+0 then.

K _I4Get 3 H symbols, long 12bit composes to cutting delay m according to following formula with integer form

$m=\left\{\begin{array}{cc}2& K_{i4}=0\\ 4& K_{i4}=1\\ K_{i4}+3& 2\≤K_{i4}\≤4095\end{array}\right.,---\left(9\right)$

Like this, K can be write as and 4 corresponding forms that are connected in series of TD-ERCS seed

K=K ₁₁K ₁₂K ₁₃K ₁₄K ₂₁K ₂₂K ₂₃K ₂₄K ₃₁K ₃₂K ₃₃K ₃₄K ₄₁K ₄₂K ₄₃K ₄₄. (10) are giving x ₀, when α and μ assignment, because b 〉=1, so follow the b that shifts left to operate always.The regulation key block distributes the back if insufficient section occurs successively, then uses " 0 " to replenish, and promptly the kind subparameter maximum length of each TD-ERCS is 42 H symbols, if curtailment 42 then uses " 0 " to add to 42.

(3) TD-ERCS chaos system

The iterative algorithm of TD-ERCS chaos system carries out according to following steps:

1) given parameter μ, initial value x ₀And α, and after cutting delay m, calculate other initial condition data of TD-ERCS successively

$y_0=\mathrm{\μ}\sqrt{1-x_0^2},---\left(11\right)$

$k_0^{\′}=-\frac{x_0}{y_0}{\mathrm{\μ}}^2,---\left(12\right)$

$k_0=\frac{\tan \mathrm{\α}+k_0^{\′}}{1-k_0^{\′}\tan \mathrm{\α}}.---\left(13\right)$

2) other state of calculating TD-ERCS, promptly

$x_n=-\frac{2k_{n-1}{y}_{n-1}+x_{n-1}({\mathrm{\μ}}^2-k_{n-1}^2)}{{\mathrm{\μ}}^2+k_{n-1}^2},---\left(14\right)$

$k_n=\frac{2k_{n-m}^{\′}-k_{n-1}+k_{n-1}{k}_{n-m}^{\′2}}{1+2k_{n-1}{k}_{n-m}^{\′}-k_{n-m}^{\′2}},---\left(15\right)$

n＝1，2，3，…，

Wherein

$k_{n-m}^{\&prime;}=\left\{\begin{array}{cc}-\frac{x_{n-1}}{y_{n-1}}{\mathrm{\&mu;}}^2& n<m\\ -\frac{x_{n-m}}{y_{n-m}}{\mathrm{\&mu;}}^2& n\&GreaterEqual;m\end{array}\right.---\left(13\right)$

y _n＝k _n-1(x _n-x _n-1)+y _n-1， (14)

Here, the state of n＜m is called transition state, and the state of n 〉=m is called normal condition.

3) get status switch

x _2m+1，x _2m+2，x _2m+3，…； (15)

k _2m+1，k _2m+2，k _2m+3，…. (16)

Original series as pseudo random sequence.

(4) status switch blender

Enable 4 parallel TD-ERCS, original series (15), (16) are rewritten into

{x _ij|i＝1，2，3，4；j＝1，2，Λ}， (17)

{k _ij|i＝1，2，3，4；j＝1，2，Λ}， (18)

X wherein _IjAnd k _IjX value and the k value of representing the 2m+j time iteration of i TD-ERCS.Remake conversion and normalized

${\mathrm{\&theta;}}_{\mathrm{ij}}=\frac{\arccos \left(x_{\mathrm{ij}}\right)}{\mathrm{\&pi;}},(0\&le;{\mathrm{\&theta;}}_{\mathrm{ij}}\&le;1)---\left(19\right)$

${\mathrm{\&beta;}}_{\mathrm{ij}}=0.5+\frac{\arctan \left(k_{\mathrm{ij}}\right)}{\mathrm{\&pi;}},(0<{\mathrm{\&beta;}}_{\mathrm{ij}}<1)---\left(20\right)$

θ _IjAnd β _IjBe corresponding x _IjAnd k _IjThe normalization sequence.

Get θ _IjAnd β _IjFloating number in exponent e, make b=1023-e; Get θ again _IjAnd β _IjFloating number in the f of mantissa, and it is carried out dextroposition b operation, the binary code of the f of mantissa that gained is new is corresponding θ _IjAnd β _IjThe standard binary sequence, totally 52, be designated as

${\mathrm{\&theta;}}_{\mathrm{ij}}={\mathrm{\&theta;}}_{\mathrm{ij}}^1{\mathrm{\&theta;}}_{\mathrm{ij}}^2{\mathrm{\&theta;}}_{\mathrm{ij}}^3\mathrm{\&Lambda;}{\mathrm{\&theta;}}_{\mathrm{ij}}^{51}{\mathrm{\&theta;}}_{\mathrm{ij}}^{52},---\left(21\right)$

${\mathrm{\&beta;}}_{\mathrm{ij}}={\mathrm{\&beta;}}_{\mathrm{ij}}^1{\mathrm{\&beta;}}_{\mathrm{ij}}^2{\mathrm{\&beta;}}_{\mathrm{ij}}^3{\mathrm{\&Lambda;\&beta;}}_{\mathrm{ijj}}^{51}{\mathrm{\&beta;}}_{\mathrm{ij}}^{52},---\left(22\right)$

Wherein ${\mathrm{\&theta;}}_{\mathrm{ij}}^l=\left\{\mathrm{0,1}\right\},$ ${\mathrm{\&beta;}}_{\mathrm{ij}}^l=\left\{\mathrm{0,1}\right\},$ l＝1，2，Λ，52。So θ _IjAnd β _IjAvailable 13 H symbolic representations respectively.

Sequence (21) and (22) of 4 TD-ERCS are mixed, constitute new codeword block, be designated as κ _j, desirable following three kinds of plain modes (other way of output does not exemplify one by one).

First kind of mode: because θ _IjAnd β _IjBe separate, so sequence (21) and (22) can be used as two independently codeword block, promptly

κ _j=θ _1jθ _2jθ _3jθ _4j. (23) and κ _j=β _1jβ _2jβ _3jβ _4j. (24)

The second way: with the alternate serial connection of independent sequence (23) with (24)

κ _j＝θ _1jβ _1jθ _2jβ _2jθ _3jβ _3jθ _4jβ _4j. (25)

The third mode: with independent sequence (23) and (24) corresponding XOR serial connection

κ _j＝(θ _1jβ _1j)(θ _2jβ _2j)(θ _3jβ _3j)(θ _4jβ _4j). (26)

Wherein "  " is xor operator, and " () () " expression piece () is connected in series non-multiplying each other with piece ().

At last, by κ _jThe codeword block stream that produces

κ ₁κ ₂κ ₃Λκ _jΛ， (27)

Be pseudo random sequence or the pseudo random streams that pseudorandom number generator of the present invention produces, it is a pseudorandom binary sequence, abbreviates the TD-ERCS sequence as.

Obviously, analyze from security standpoint, formula (26) is the safest, and 1 sequence also is safe if only export wherein in formula (23) and the formula (24), and the fail safe of formula (25) is low slightly, but the pseudo random streams generation maximum of formula (25) is the twice of preceding two kinds of output intents.

The present invention is core algorithm with TD-ERCS, and the status switch of TD-ERCS chaos system is converted to pseudo random sequence, therefore, the performance of the determined pseudorandom number generator of character of TD-ERCS chaos system, it has following good characteristic:

1) good statistical property: as stable uniform distribution character, the universe zero correlation, independence etc. have been carried out various the analysis showed that such as harmony, distance of swimming characteristic, correlation to formula (27), and this sequence is all than aforesaid various pseudo random sequence excellences.

2) good security feature: as huge key space; Ultra-long period is not so that also test the effective ways of this sequence period at present; There is not the stable short period, just do not have consequent weak key; Extremely strong degeneration ability is arranged, and promptly the computer truncation error can not cause the short period; Good resisting differential analysis ability is arranged.

3) hardware is realized easily: as realizing that with FPGA particularly adopt parallel organization, the random number formation speed is fast, interface capability is good, and function expansibility can be good, expands to the encryption chip of other different purposes easily.

4) easy to use flexible: as easy upgrading, also can produce multiple independently random sequence, key length is fixing, can be by user's any value in the domain of definition, simple in structure, understand easily, be convenient to statistical analysis and safety analysis, thereby the transparency height of algorithm, the user can relievedly use.

Present invention is described with concrete data below.

(1) user key

Get K=7654321fedcba12345678900983456789fedcba012cba987654321 00000abcdeffed, then L _(h)=68, the pairing binary system code length of K L=272.

(2) password conversion and seed dispenser

1) that determine TD-ERCS and line number

Because of 43＜L _h＜84, then adopt two TD-ERCS.

2) determine key block

K＝K ₁₁K ₁₂K ₁₃K ₁₄K ₂₁K ₂₂K ₂₃K ₂₄，

Wherein

K ₁₁＝7654321fedcba，K ₁₂＝1234567890098，

K ₁₃＝3456789fedcba，K ₁₄＝012，

K ₂₁＝cba9876543210，K ₂₂＝0000abcdeffed，

K ₂₃＝0000000000000，K ₂₄＝000。

Here K ₂₃, K ₂₄Do not have corresponding key block, replenish with " 0 ".

3) give the μ assignment

K ₁₁Corresponding 52bit binary code is 0,111 0,110 0,101 0,100 0,011 0,010 0,001 1,111 11,101,101 1,100 1,011 1010, try to achieve b=2 thus, so s=0, (decimal system: 1021), f=1101 1,001 0,101 0,000 1,100 1,000 0,111 1,111 1,011 0,111 0,010 1,110 1001. is μ to e=01111111101 ₁=0.4622222.

K ₂₁Corresponding 52bit binary code is 1,100 1,011 1,010 1,001 1,000 0,111 0,110 0,101 01,000,011 0,010 0,001 0000, try to achieve b=1 thus, so s=0, (decimal system: 1022), f=1001 0,111 0,101 0,011 0,000 1,110 1,100 1,010 1,000 0,110 0,100 0,010 0001 is μ to e=01111111110 ₂=0.7955560.

4) give the α assignment

K ₁₂Corresponding 52bit binary code is 0,001 0,010 0,011 0,100 0,101 0,110 0,111 1,000 10,010,000 0,000 1,001 1000, try to achieve b=4 thus, so s=0, (decimal system: 1019), f=0010 0,011 0,100 0,101 0,110 0,111 1,000 1,001 0,000 0,000 1,001 10,000 001 is α to e=01111111011 ₁=0.0711111 * π.

K ₂₂Corresponding 52bit binary code is 0,000 0,000 0,000 0,000 1,010 1,011 1,100 1,101 11,101,111 1,111 1,110 1101, try to achieve b=17 thus, so s=0, (decimal system: 1006), f=0101 0,111 1,001 1,011 1,101 1,111 1,111 1,101 1,010 0,000 0,000 0,000 0001 is α to e=01111101110 ₂=1.02403 * 10 ^-5* π.

5) give x ₀Assignment

K ₁₃Corresponding 52bit binary code is 0,011 0,100 0,101 0,110 0,111 1,000 1,001 1,111 11,101,101 1,100 1,011 1010, try to achieve b=3 thus, so s=0, (decimal system: 1020), f=1010 0,010 1,011 0,011 1,100 0,100 1,111 1,111 0,110 1,110 0,101 1,101 0001 is x to e=01111111100 ₁₀=0.2044443.

K ₂₃Corresponding 52bit binary code is 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 00,000,000 0,000 0,000 0000, try to achieve b=53 thus, so s=0, (decimal system: 970) f=0000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0,000 0000 is x to e=01111001010 ₂₀=1.110223 * 10 ^-16

6) give the m assignment

K ₁₄Corresponding 12bit binary code is 0,000 0,001 0010 (decimal system is 18), so m ₁=18+3=21.

K ₂₄Corresponding 12bit binary code is 0,000 0,000 0000 (decimal system is 0), so m ₂=2.

(4) TD-ERCS chaos system status switch calculates

1) by parameter μ, initial value x ₀With α calculating formula (11), (12) and (13),

y ₁₀＝0.452459，k ₁₀′＝-0.0965378，k ₁₀＝0.127852

y ₂₀＝0.795556，k ₂₀′＝-1.76649×10 ^-16，k ₂₀＝3.2171×10 ^-5

2) computing mode sequence.

3) get the status switch of first TD-ERCS

x ₄₃，x ₄₄，x ₄₅，…；k ₄₃，k ₄₄，k ₄₅，…。

Status switch with second TD-ERCS

x ₅，x ₆，x ₇，…；k ₅，k ₆，k ₇，…。

Original series as pseudo random sequence.Preceding 20 iterative value of corresponding (15) and formula (16) are listed in table 1 and table 2.

(5) status switch blender

1) the normalization sequence of corresponding (19) and formula (20) is listed in table 1 and table 2.

2) dextroposition b operation is converted to the standard binary sequence with the normalization sequence, and conversion method is with θ ₁₄₃And θ ₂₅For example is described as follows

θ ₁₄₃=0.3272315, the exponential sum mantissa of corresponding floating number is respectively e=01111111101, and (decimal system: 1021), f=0100 1,111 0,001 0,101 1,100 0,111 1,111 1,011 1,110 1,000 0,100 00110100.By index calculate b=2, after the dextroposition b operation θ ₁₄₃The standard binary sequence: θ ₁₄₃=01,010,011 1,100 0,101 0,111 0,001 1,111 1,110 1,111 1,010 0,001 0,000 1101.

θ ₂₅=0.4997168, the exponential sum mantissa of corresponding floating number is respectively e=01111111101, and (decimal system: 1021), f=1111 1,111 1,011 0,101 1,100 0,011 1,110 1,110 1,111 1,010 0,101 01011100.By index calculate b=2, after the dextroposition b operation θ ₂₅The standard binary sequence: θ ₂₅=0,111 11,111,110 1,101 0,111 0,000 1,111 1,011 1,011 1,110 1,001 0,101 0111.

In like manner can obtain the θ after the dextroposition ₁₄₄, θ ₁₄₅, β ₁₄₃, β ₁₄₄, β ₁₄₅, θ ₂₆, θ ₂₇, β ₂₅, β ₂₆, β ₂₇...

3) output pseudo random streams (first kind of pseudo random streams slightly)

Getting second kind of pseudo random streams that this example produced according to formula (25) is:

θ ₁₄₃β ₁₄₃θ ₂₅β ₂₅θ ₁₄₄β ₁₄₄θ ₂₆β ₂₆θ ₁₄₅β ₁₄₅θ ₂₇β ₂₇ΛΛ.

Corresponding binary pseudo-random is:

0101001111000101011100011111111011111010000100001101

1010001101010101000110010001101100000111110001101001

0111111111101101011100001111101110111110100101010111

1000000000001111011011111000000010010001001000110000

1101001110100001000000110111111000011010000100001001

1101011111011101111011100011000001000011101101110010

1000000000111001010111001111010110101110000001001100

0111111111110000100100000111111101101110110000010100

…………。

Getting the third pseudo random streams that this example produced according to formula (26) is:

(θ ₁₄₃β ₁₄₃)(θ ₂₅β ₂₅)(θ ₁₄₄β ₁₄₄)(θ ₂₆β ₂₆)(θ ₁₄₅β ₁₄₅)(θ ₂₇β ₂₇)ΛΛ.

Corresponding binary pseudo-random is:

1111000010010000011010001110010111111101110101100100

1111111111100010000111110111101100101111101101100111

0000010001111100111011010100111001011001101010001011

1111111111001001110011001000101010100000110001011000

…………。

Each quantity of state of first TD-ERCS of table 1

Iterations	Quantity of state
					x	k	θ	β
	43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 ……	0.5165083 -0.8554371 -0.5142549 -0.4311952 0.0338635 -0.1149288 0.4178790 -0.6744337 0.9999944 -0.8116496 -0.9997068 -0.9994556 0.3838242 0.8889620 0.5613054 0.6247357 0.9401510 0.8262750 0.9971645 0.8257646 ……	0.4629781 1.8635410 -9.7937160 1.8900870 6.1906220 1.6499190 0.6968748 0.2047368 -0.1481873 1.3762410 16.1530000 0.2975316 -1.2640270 0.5214306 11.7208900 -0.6449082 -0.9031624 -1.7270710 1.3180670 2.3858330 ……	0.3272315 0.8266756 0.6719315 0.6419080 0.4892189 0.5366640 0.3627736 0.7356122 0.0464995 0.8014243 0.9531043 0.9527591 0.3746069 0.1515691 0.3102993 0.2852067 0.1118953 0.1904664 0.0503526 0.1907544 ……					0.6380172 0.8432301 0.0323892 0.8450986 0.9490223 0.8265575 0.6937315 0.5642814 0.4531713 0.7999845 0.9803192 0.5920522 0.2130461 0.6529940 0.9729081 0.3176761 0.2661824 0.1670638 0.7934050 0.8736636 ……

Second each quantity of state of TD-ERCS of table 2

Iterations	Quantity of state
					x	k	θ	β
	5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ……	0.0008896 -0.0027498 0.0046100 -0.0029116 -0.0097859 0.0409113 -0.0836065 0.0872325 0.0725527 -0.5347132 0.9840011 -0.9323114 0.2842229 0.3603247 -0.2745875 -0.1745816 -0.8679116 -0.9270055 -0.7670402 -0.3623885 ……	0.0007399 -0.0007399 -0.0006756 0.0050509 -0.0123865 0.0170201 -0.0014476 -0.0637645 0.1995629 -0.3493304 0.2241053 0.8634884 -0.2710813 2.3737010 15.4822300 1.6997760 -11.7362100 -5.0560920 -0.5709890 -0.4491105 ……	0.4997168 0.5008753 0.4985326 0.5009268 0.5031150 0.4869739 0.5266439 0.4721977 0.4768855 0.6795803 0.0670505 0.8813469 0.4082644 0.3826659 0.5885413 0.5558573 0.8344783 0.8769365 0.7782705 0.6180386 ……					0.5002355 0.4997645 0.4997850 0.5016077 0.4960575 0.5054171 0.4995392 0.4797306 0.5626992 0.3930230 0.5701755 0.7267235 0.4157372 0.8730841 0.9794688 0.8307286 0.0270567 0.0621536 0.3348561 0.3656369 ……

Claims (7)

1. the pseudorandom number generator of a chaos system, comprise user key, password conversion and seed dispenser, status switch blender algoritic module, it is characterized in that: user key is with 16 system character representations, password conversion and seed dispenser are determined the also line number of TD-ERCS, user key are converted to the kind subparameter of TD-ERCS; Parallel TD-ERCS is formed side by side by 1～4 TD-ERCS chaos system, produces the status switch of system under given kind subparameter by iterative computation; The status switch that the status switch blender produces TD-ERCS chaos system iteration mixes and is converted to the binary system pseudo random streams to be exported.

2. pseudorandom number generator according to claim 1 is characterized in that: the described user key of the kind subparameter space of TD-ERCS is [2 ⁶⁴, 2 ⁶⁷²], user key length is value between 64～672bit or 16～168 16 system characters.

3. pseudorandom number generator according to claim 1 is characterized in that: described TD-ERCS kind subparameter comprises parameter μ, initial condition x ₀With α, cut and postpone m, the system mode sequence that the iterative equation of the seed parameter system of TD-ERCS chaos TD-ERCS is produced is as the original series of pseudo random number stream.

4. according to claim 1 or 2 or 3 described pseudorandom number generators, it is characterized in that: password conversion and the parallel number of seed dispenser by the definite TD-ERCS of use of the length chaos system of user key, user key with 16 systems converts binary code to again, has by one then binary fraction is converted to the b operation of shifting left of floating-point system decimal function with the kind subparameter of standard binary sequence for each TD-ERCS.

5. pseudorandom number generator according to claim 1 is characterized in that: the described conversion with seed dispenser by password determines that the method for TD-ERCS arranged side by side and line number is: user key length is 16～42 16 system characters, adopts 1 TD-ERCS; User key length is 43～84 16 system characters, adopts 2 TD-ERCS; User key length is 85～126 16 system characters, adopts 3 TD-ERCS; User key length is 127～168 16 system characters, adopts 4 TD-ERCS.

6. according to claim 1 or 4 described pseudorandom number generators, it is characterized in that: the status switch blender has dextroposition b operation that the floating-point system decimal is converted to the binary fraction function by one the status switch of TD-ERCS is converted to the standard binary sequence, these standard binary sequences is arranged in order as the pseudorandom binary sequence exports again.

7. pseudorandom number generator according to claim 6 is characterized in that: three kinds of methods of described pseudorandom binary sequence output are: export two independently the pseudorandom binary sequence, with two independently the alternate serial connection output of pseudorandom binary sequence or with two independently the corresponding XOR serial connection of pseudorandom binary sequence export.

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