CN101645772A - Pseudo random sequence generation method based on t semi-order and sequence generator - Google Patents

Abstract

The invention discloses a pseudo random sequence generation method based on t semi-order and a sequence generator. The method comprises the following steps: (S1) setting parameters p, q and r; (S2) setting a semi-order control secret key; (S3) setting an initial seed secret key; (S4) setting an initial number of iterations; (S5) establishing non-linear functional semi-order iteration; (S6) encoding in accordance with a compared semi-order result of a front iteration sequence and a back iteration sequence; and (S7) repeating the procedure (S5) to obtain a long enough sequence. The generator comprises a clock generator, a register for parameters p, q and r, a register for m namely the number of iterations, a register for the initial seed secret key and a register for the semi-order control secret key are connected with a non-linear iteration functional circuit by a data bus of the system; the non-linear iteration functional circuit has two outputs, wherein feeds back an intermediate iteration result into the register for the initial seed secret key, the other generates binary output which is input to an xor gate circuit with a binary flow required for encryption, and the xor gate circuit outputs the encrypted binary flow. The sequence of the invention has high degree of randomness, fast speed, relative simple operation, convenient hardware realization, consistent encryption/description devices and relatively low cost.

Description

Pseudo random sequence generation method and sequencer based on the t semi-order

Technical field

The stream cipher that the invention belongs in the information security cryptography is learned the field.

Background technology

Stream cipher claims stream cipher again.Ciphering process is at first being injected into specific seed key (session key) the stream cipher generator, and carrying out by turn with the PRBS pseudo-random bit sequence of stream cipher generator generation with the plaintext bit stream then, XOR obtains ciphertext.Be not subjected to expressly length restriction when using stream cipher to encrypt,, can encrypt the file of any length as long as the cycle of the stream cipher that produces is enough big, very flexible.Compare with encryption method of block cipher, the stream cipher enciphering rate is the fastest.Therefore, be particularly suitable for the encryption occasion that big data quantity, real-time are had relatively high expectations.The fail safe that stream cipher is encrypted depends on the internal mechanism of key stream generator.If output is a row true random number sequence, rather than pseudo-random number sequence, then this password has the same perfectly fail safe of One-time pad.The true random sequence is difficult to be realized, the still pseudo random sequence that mainly is to use but in actual applications.Therefore the groundwork of implementation sequence password is to obtain to have pseudo random sequence.

In cryptographic system, whether its fail safe depends on to a great extent can generate some uncertain numbers randomly, and these uncertain numbers comprise private key among key, the prime P in the RSA cryptographic algorithms, Q and the DSA in the des encryption algorithm or the like.In these cases, the number that requires to produce must be enough big, and be at random, that is to say that the probability that produces any particular random number all must be enough little, utilizes rule to break a code to prevent the adversary.With generating number or binary digit arbitrarily, the generation that makes these numbers is without any specific prerequisite and rule exactly for random number and random order maker.

Random order maker (random bit generator) is the bit string that is used for exporting a series of independent random.In actual applications, there are many physical factors to consider.In the ideal case, secret number need produce by the random order maker in cryptographic algorithm and the agreement.But in some cases, want to guarantee that access safely and very large random bit sequences of transmission are unpractical, therefore, often replace the random order maker with the pseudo-random bit maker.

The pseudo-random bit maker (Pseudorandom bit generator PRBG) adopts deterministic algorithm, and promptly importing length is the binary system random sequence of k, output length be l (l＞＞k) binary system random sequence.The input of PRBG is called seed number, and output is called pseudo random sequence.Pseudo-random generator is not that its possible output only accounts for sub-fraction wherein at random in fact entirely.It is the fewer random sequence of a units to be expanded by certain method become the long random sequence of a units, and the other side just can not distinguish the pseudorandom output sequence and real length is the random sequence of l effectively like this.The Ad-hoc method is exactly to be used for producing such pseudo random sequence.In order to ensure pseudo-random generator is reliably, necessary through a large amount of tests, but can only illustrate it is reliably local by the maker of test, can not guarantee it is cocksure.

Tradition our tectonic sequence passwords needed pseudo random sequence all is based on number theory and Boolean algebra, and commonly used have Brent sequence, clock controlled sequence and some correlation immunite functions.The present invention utilizes the nonlinear iteration of the partially ordered space to construct the pseudo-random bit maker, produces binary pseudo-random sequence.

Summary of the invention

The purpose of this invention is to provide a kind of pseudo random sequence generation method and sequencer based on the t semi-order.

The present invention has introduced a kind of new semi-order "≤t ", and we are called the t semi-order.In real Hilbert Space H, get certain initial x ₀∈ H chooses a nonlinear operator A as iteration operator as seed, sets up an iteration system:

x _n+1＝Ax _n，n＝0，1，2，…(*)

The thought of semi-order pseudo random sequence and cryptographic system thereof is: with certain t ∈ H and certain seed x ₀∈ H utilizes (*) to obtain a sequence, if x as key _n≤ t x _N+1, then record coding is " 0 "; If x _nWith x _N+1Can not compare, skip not record; If x _n〉= _tx _N+1, then record coding is " 1 ".By this method, as long as we carry out enough iteration repeatedly, we just can obtain sufficiently long binary sequence.

At R ⁿThe inner product of middle definition standard, { e _i} _I=1 ⁿFor its unit vector, establish $x=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i{e}_i(x_i\≥0),$ Get $t=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{t}_i{e}_i,(t_i\≥1),$ Obviously＜and x, t〉〉=0, because t _i〉=1, so:

${<x,t>}^2={\left(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i{t}_i\right)}^2\&GreaterEqual;{\left(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i\right)}^2\&GreaterEqual;\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{x}_i^2,$ <x，x>≤<x，t> ²，‖x‖≤<x，t>

So when getting $t=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{t}_i{e}_i,(t_i\&GreaterEqual;1),$ Awl $P=\left\{x\right|x=\mathrm{\&Sigma;}{x}_i{e}_i,x_i\&GreaterEqual;0\}$ Be a R _nIn P _tAwl.Like this, we are as long as restriction operator A is boring P _tIn carried out iteration just, make things convenient for the foundation and the realization of algorithm.

In order to make iteration have sufficiently high randomness, we can introduce chaos system in setting up nonlinear operator A, and the space that we choose is R ^u, wherein u be one more than or equal to 8 positive integer, establish:

x(n)＝(x _n，1，x _n，2，x _n，3，x _n，4，x _n，5，x _n，6，x _n，7，...，x _n，u)，x _n，j∈R ⁺.

Set up following nonlinear operator iteration: x (n+1)=A (x (n)), wherein:

x _n+1，1＝|p.sin ²(qx _n，8x _n，1-rx _n，2x _n，2)| (1)

x _n+1，2＝|p.sin ²(qx _n，1x _n，2-rx _n，3x _n，3)| (2)

x _n+1，3＝|p.sin ²(qx _n，2x _n，3-rx _n，4x _n，4)| (3)

x _n+1，4＝|p.sin ²(qx _n，3x _n，4-rx _n，5x _n，5)| (4)

x _n+1，5＝|p.sin ²(qx _n，4x _n，5-rx _n，6x _n，6)| (5)

x _n+1，6＝|p.sin ²(qx _n，5x _n，6-rx _n，7x _n，7)| (6)

……

x _n+1，u-1＝|p.sin ²(qx _n，u-2x _n，u-1-rx _n，ux _n，u)| (7)

x _n+1，u＝|p.sin ²(qx _n，u-1x _n，u-rx _n，1x _n，1)| (8)

(p wherein, q, r＞0, wherein q generally gets bigger number)

The operator of getting this form mainly is to consider will be absorbed in chaos state after each operator chooses parameter after the several times iteration.The semi-order control key is:

T=(t ₁, t ₂, t ₃, t ₄, t ₅, t ₆, t ₇..., t _u), t wherein _i〉=1, i=1,2 ..., u (10)

The initial seed key is:

x(n)＝(x _0，1，x _0，2，x _0，3，x _0，4，x _0，5，x _0，6，x _0，7，…，x _0，u)，x _0，i∈R ⁺ (11)

The primary iteration number of times is m (m is an integer).

Utilize above principle, can realize a cryptographic algorithm and a device based on the t semi-order.

Specifically, method of the present invention realizes by following steps:

(S1), parameter p is set, q, r, p wherein, q, r＞0, wherein q generally gets bigger number;

(S2), semi-order control key t=(t is set ₁, t ₂, t ₃, t ₄, t ₅, t ₆, t ₇..., t _u), t _i〉=1, i=1,2 ..., u;

(S3), the initial seed key being set is:

x(0)＝(x _0，1，x _0，2，x _0，3，x _0，4，x _0，5，x _0，6，x _0，7，…，x _0，u)，x _0，i∈R ⁺；

(S4), the primary iteration number of times being set is m (m is an integer);

(S5), set up nonlinear operator iteration: x (n+1)=A (x (n)), by x (n) calculating x (n+1), wherein x _n=x (n), x _N+1=x (n+1), n=0,1,2 ..., this iteration is non-linear functional semi-order iteration;

(S6), if x _n≤ _tx _N+1, then record coding is a binary zero; If x _nWith x _N+1Can not compare, skip not record; If x _n〉= _tx _N+1, then record coding be binary system " 1 ", wherein the comparison procedure method is as follows:

Calculate $s_1=\sqrt{\underset{i=1}{\overset{u}{\mathrm{\&Sigma;}}}{(x_{n+1,i}-x_{n,i})}^2},$ $s_2=\underset{i=1}{\overset{u}{\mathrm{\&Sigma;}}}{t}_i*(x_{n+1,i}-x_{n,i}),$ s ₃=| s ₂|, if s ₁＜s ₃, then explanation can be compared, if s wherein ₂〉=0, record coding is a binary zero, otherwise note is encoded to binary one, can not be record more not;

(S7), repetitive process (S5), up to obtaining the long enough binary sequence.

Sequencer of the present invention is achieved through the following technical solutions (referring to accompanying drawing 4):

By clock generator, parameter p, q, r register, iterations m register, initial seed cipher key register, semi-order control key register, nonlinear iteration functional circuit, NOR gate circuit are formed, clock generator, parameter p, q, r register, iterations m register, initial seed cipher key register, semi-order control key register link to each other with the nonlinear iteration functional circuit by system data bus, the nonlinear iteration functional circuit has two outputs, and one is that the iteration result preserves in the initial seed cipher key register in the middle of the feedback; Be to produce the output of 0-1 binary system in addition, input to the NOR gate circuit input, the binary stream after encrypting by NOR gate circuit output with needs ciphered data binary stream.

The clock control generator is responsible for the synchronous bus data-signal, send initialization register, remove signals such as register and termination transfer of data, parameter p, q, the r register is used to preserve parameter p, q, r, iterations m register is used to be provided with preservation primary iteration number of times m, semi-order control key register is used to be provided with preservation semi-order control key, the initial seed cipher key register is used to be provided with preserves the initial seed key, and accepts a feedback input of nonlinear operator iterative circuit, preserves each intermediate object program that generates.

The decrypting process of sequencer of the present invention (device) is referring to shown in the accompanying drawing 1, be about to plaintext preliminary treatment binary sequence and import as a NOR gate circuit, the binary stream (ciphertext binary sequence) after NOR gate circuit output is encrypted with the semi-order pseudo random sequence.

The ciphering process of sequencer of the present invention (device) is about to the ciphertext binary sequence and imports as a NOR gate circuit with the semi-order pseudo random sequence referring to shown in the accompanying drawing 2, and NOR gate circuit output is the preliminary treatment binary sequence expressly.

Because the degree of correlation is very low between non-linear functional chaos sequence, sequence degree of randomness height of the present invention, speed is fast, and the computing of Cai Yonging is simple relatively in addition, be convenient to realize with hardware, the ciphering and deciphering device unanimity, cost is cheap relatively.Can be widely used in real-time requires in high safety communication, the data encryption.

Description of drawings

Fig. 1 is a semi-order pseudo random sequence ciphering process.

Fig. 2 is a semi-order pseudo random sequence decrypting process.

Fig. 3 is the pseudorandom number generator algorithm flow chart based on t semi-order nonlinear iteration.

Fig. 4 is the pseudo-random sequence generator based on the t semi-order.

Specific implementation method

The present invention will be described further by following examples.

Embodiment 1.

Below we provide a concrete example.The space that we choose is R ⁸, when promptly getting u=8, establish:

x(n)＝(x _n，1，x _n，2，x _n，3，x _n，4，x _n，5，x _n，6，x _n，7，x _n，8)，x _n，i∈R ⁺.

Set up following nonlinear operator iteration: x (n+1)=A (x (n)), wherein:

x _n+1，1＝|p.sin ²(qx _n，8x _n，1-rx _n，2x _n，2)| (1.1)

x _n+1，2＝|p.sin ²(qx _n，1x _n，2-rx _n，3x _n，3)| (1.2)

x _n+1，3＝|p.sin ²(qx _n，2x _n，3-rx _n，4x _n，4)| (1.3)

x _n+1，4＝|p.sin ²(qx _n，3x _n，3-rx _n，5x _n，5)| (1.4)

x _n+1，5＝|p.sin ²(qx _n，4x _n，5-rx _n，6x _n，6)| (1.5)

x _n+1，6＝|p.sin ²(qx _n，5x _n，6-rx _n，7x _n，7)| (1.6)

x _n+1，7＝|p.sin ²(qx _n，6x _n，7-rx _n，8x _n，8)| (1.7)

x _n+1，8＝|p.sin ²(qx _n，7x _n，8-rx _n，1x _n，1)| (1.8)

(p wherein, q, r＞0, wherein q generally gets bigger number)

The operator of getting this form mainly is to consider will be absorbed in chaos state after each operator chooses parameter after the several times iteration.The semi-order control key is:

T=(t ₁, t ₂, t ₃, t ₄, t ₅, t ₆, t ₇, t ₈), t wherein _i〉=1, i=1,2 ..., 8 (1.9)

The initial seed key is:

x(n)＝{x _0，1，x _0，2，x _0，3，x _0，4，x _0，5，x _0，6，x _0，7，x _0，8)，x _0，i∈R ⁺ (1.10)

The primary iteration number of times is m (m is an integer).

Utilize above principle, can realize a cryptographic algorithm and a device based on the t semi-order.

Specifically, method of the present invention realizes (flow chart is seen accompanying drawing 3) by following steps:

(S1), parameter p is set, q, r, p wherein, q, r＞0, wherein q generally gets bigger number;

(S2), semi-order control key t=(t is set ₁, t ₂, t ₃, t ₄, t ₅, t ₆, t ₇, t ₈), ti 〉=1 wherein, i=1,2 ..., 8;

(S3), the initial seed key being set is: x (0)=(x _0,1, x _0,2, x _0,3, x _0,4, x _0,5, x _0,6, x _0,7, x _0,8), x _{0, i}∈ R ⁺

(S4), the primary iteration number of times being set is m (m is an integer);

(S5), set up nonlinear operator iteration: x (n+1)=A (x (n)), by x (n) calculating x (n+1), wherein x _n=x (n), x _N+1=x (n+1), n=0,1,2 ..., this iteration is non-linear functional semi-order iteration;

(S6), if x _n≤ _tx _N+1, then record coding is a binary zero; If x _nWith x _N+1Can not compare, skip not record; If x _n〉= _tx _N+1, then record coding be binary system " 1 ", wherein the comparison procedure method is as follows:

Calculate $s_1=\sqrt{\underset{i=1}{\overset{8}{\mathrm{\&Sigma;}}}{(x_{n+1,i}-x_{n,i})}^2},$ $s_2=\underset{i=1}{\overset{8}{\mathrm{\&Sigma;}}}{t}_i*(x_{n+1,i}-x_{n,i}),$ s ₃=| s ₂|, if s ₁＜s ₃, then explanation can be compared, if s wherein ₂〉=0, record coding is a binary zero, otherwise note is encoded to binary one, can not be record more not;

(S7), repetitive process (S5), up to obtaining the long enough binary sequence.

Embodiment 2.

The MATLAB realization example of algorithm

According to method of the present invention, present embodiment illustrates the foundation and the work of algorithm in conjunction with a MATLAB example program that generates semi-order pseudo random sequence binary stream:

% program 1: generate semi-order stream cipher binary stream demonstration program 1.0

T=[2.5,3.2,4,1.2,3,5,2.5,4]; % semi-order control key

Q=2137; The % parameter q

P=3.7; The % parameter p

R=7; % parameter r

M=43; % primary iteration number of times

MAXSIZE=512; The binary sequence length that % will produce

% definition initial seed key

x(1)＝0.43；

x(2)＝2.3；

x(3)＝1.52；

x(4)＝3.4；

x(5)＝2.78；

x(6)＝5.34；

x(7)＝7.42；

x(8)＝4.51；

Y=[0,0,0,0,0,0,0,0]; % defines an interim array, preserves the iteration result

Z=[0,0,0,0,0,0,0,0]; % defines an interim array, preserves the iteration result

K=1; % binary sequence counting variable

% carries out primary iteration, enters chaos state

for?i＝1:m

y(1)＝abs(p*sin(q*x(8)*x(1)-r*x(2)*x(2))*sin(q*x(8)*x(1)-r*x(2)*x(2)))；

y(2)＝abs(p*sin(q*x(1)*x(2)-r*x(3)*x(3))*sin(q*x(1)*x(2)-r*x(3)*x(3)))；

y(3)＝abs(p*sin(q*x(2)*x(3)-r*x(4)*x(4))*sin(q*x(2)*x(3)-r*x(4)*x(4)))；

y(4)＝abs(p*sin(q*x(3)*x(4)-r*x(5)*x(5))*sin(q*x(3)*x(4)-r*x(5)*x(5)))；

y(5)＝abs(p*sin(q*x(4)*x(5)-r*x(6)*x(6))*sin(q*x(4)*x(5)-r*x(6)*x(6)))；

y(6)＝abs(p*sin(q*x(5)*x(6)-r*x(7)*x(7))*sin(q*x(5)*x(6)-r*x(7)*x(7)))；

y(7)＝abs(p*sin(q*x(6)*x(7)-r*x(8)*x(8))*sin(q*x(6)*x(7)-r*x(8)*x(8)))；

y(8)＝abs(p*sin(q*x(7)*x(8)-r*x(1)*x(1))*sin(q*x(7)*x(8)-r*x(1)*x(1)))；

for?j＝1:8

x(j)＝y(j)；

end

end

while?k＜＝MAXSIZE

y(1)＝abs(p*sin(q*x(8)*x(1)-r*x(2)*x(2))*sin(q*x(8)*x(1)-r*x(2)*x(2)))；

y(2)＝abs(p*sin(q*x(1)*x(2)-r*x(3)*x(3))*sin(q*x(1)*x(2)-r*x(3)*x(3)))；

y(3)＝abs(p*sin(q*x(2)*x(3)-r*x(4)*x(4))*sin(q*x(2)*x(3)-r*x(4)*x(4)))；

y(4)＝abs(p*sin(q*x(3)*x(4)-r*x(5)*x(5))*sin(q*x(3)*x(4)-r*x(5)*x(5)))；

y(5)＝abs(p*sin(q*x(4)*x(5)-r*x(6)*x(6))*sin(q*x(4)*x(5)-r*x(6)*x(6)))；

y(6)＝abs(p*sin(q*x(5)*x(6)-r*x(7)*x(7))*sin(q*x(5)*x(6)-r*x(7)*x(7)))；

y(7)＝abs(p*sin(q*x(6)*x(7)-r*x(8)*x(8))*sin(q*x(6)*x(7)-r*x(8)*x(8)))；

y(8)＝abs(p*sin(q*x(7)*x(8)-r*x(1)*x(1))*sin(q*x(7)*x(8)-r*x(1)*x(1)))；

% carries out the t semi-order relatively, and wherein y is x (n+1) vector, and x is x (n) vector

S1=sqrt ((y-x) * (y-x) '); % calculates s1=‖ y-x ‖

S2=(y-x) * t '; % calculates s2=＜y, t 〉-＜x, t 〉

S3=abs (s2); % calculates s3=|＜y, t 〉-＜x, t〉| judge x, whether y can compare

Can if s1＜s3 % compare? can carry out the sequence value

If if were s2＞=0 % y＞x

Wts (k)=0; The % sequence gets 0

else

Wts (k)=1; The % sequence gets 1

end

k＝k+1；

end

for?j＝1:8

x(j)＝y(j)；

end

end

Wts % output sequence

Embodiment 3.

Use the stream cipher program of example 1-based on the semi-order random sequence

Use the semi-order stream cipher algorithm very easy,, carry out XOR with semi-order stream cipher binary stream and get final product (as shown in Figure 1) as long as will expressly obtain expressly binary stream earlier by the preliminary treatment ciphering process.Decrypting process is as long as carry out XOR (as shown in Figure 2) again with semi-order stream cipher binary stream.The key of algorithm is to obtain semi-order pseudo random sequence binary stream.

Claims (2)

1, a kind of pseudo random sequence generation method based on the t semi-order is characterized in that realizing by following steps:

(S1), parameter p is set, q, r, p wherein, q, r＞0, wherein q generally gets bigger number;

(S2), semi-order control key t=(t is set ₁, t ₂, t ₃, t ₄, t ₅, t ₆, t ₇..., t _u), t _i〉=1, i=1,2 ..., u;

(S3), the initial seed key being set is:

x(0)＝(x _0，1，x _0，2，x _0，3，x _0，4，x _0，5，x _0，6，x _0，7，…，x _0，u)，x _0，i∈R ⁺；

(S4), the primary iteration number of times being set is m (m is an integer);

(S5), set up nonlinear operator iteration: x (n+1)=A (x (n)), by x (n) calculating x (n+1), wherein x _n=x (n), x _N+1=x (n+1), n=0,1,2 ..., this iteration is non-linear functional semi-order iteration;

(S6), if x _n≤ _tx _N+1, then record coding is a binary zero; If x _nWith x _N+1Can not compare, skip not record; If x _n〉= _tx _N+1, then record coding is a binary one, wherein the comparison procedure method is as follows:

Calculate $s_1=\sqrt{\underset{i=1}{\overset{u}{\mathrm{\&Sigma;}}}{(x_{n+1,i}-x_{n,i})}^2},$ $s_2=\underset{i=1}{\overset{u}{\mathrm{\&Sigma;}}}{t}_i*(x_{n+1,i}-x_{n,i}),$ s ₃=| s ₂|, if s ₁＜s ₃, then explanation can be compared, if s wherein ₂〉=0, record coding is a binary zero, otherwise note is encoded to binary one, can not be record more not;

(S7), repetitive process (S5), up to obtaining the long enough binary sequence.

2, the sequencer that the described method of claim 1 realizes, it is characterized in that by clock generator, parameter p, q, the r register, iterations m register, the initial seed cipher key register, semi-order control key register, the nonlinear iteration functional circuit, NOR gate circuit is formed, clock generator, parameter p, q, the r register, iterations m register, the initial seed cipher key register, semi-order control key register links to each other with the nonlinear iteration functional circuit by system data bus, the nonlinear iteration functional circuit has two outputs, and one is that the iteration result preserves in the initial seed cipher key register in the middle of the feedback; Be to produce the output of 0-1 binary system in addition, input to the NOR gate circuit input, the binary stream after encrypting by NOR gate circuit output with needs ciphered data binary stream.

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