CN102111178A - Synchronous capturing based on sequence correlation property under very low signal-to-noise ratio - Google Patents

Abstract

The invention provides a novel long sequence capturing method based on sequence fast correlation attacks. The target of the sequence capturing is to find an initial state of the current sequence from a receiving signal; in most actual solutions, only the long sequences are visible; therefore, the sequence capturing problem can be described as follows: under the condition that the visible sequence Z of a given M-length and noise is {zi} (t=0, 1,..., M-1), the initial state of the sequence is estimated and generated; the traditional sequence capturing technology uses self-correlation characteristics of pseudo codes to locally generate a pseudo code copy and receive the pseudo code to perform correlation operation; if a threshold detection identifies the correlation peak, the capturing is finished. The novel long sequence capturing method based on sequence fast correlation attack provided by the invention has the following fundamental principle: the key information is used as the initial state of a linear feedback shifting register; an output sequence of the linear feedback shifting register is taken as output for encoding a code word; the output code word is decoded by the fast correlation attack algorithm at a receiving end via a channel; and the key information is recovered as the initial state of the linear feedback shifting register so as to realize the sequence capturing. The method is low in complicatedness and fast in capturing speed; moreover, the method not only can be used for capturing linear sequences but also can be used for capturing nonlinear sequences.

Description

Under the utmost point low signal-to-noise ratio based on the synchronization acquistion of sequence dependent features

Technical field

The invention belongs to electronic technology field,, particularly adopt simultaneous techniques to improve the mobile radio system that communication reliability communicates as fields such as radio communication, mobile communication, deep space communications.

Background technology

Simultaneous techniques is an important problem in the communication, in communication system, the transmitting terminal of signal and receiving terminal will reach temporal acting in agreement, often relate to synchronously for reaching this purpose of acting in agreement, the reduction of synchro system performance, the reduction that can directly cause communication system performance for the reliable transmission of guarantee information, requires synchro system that higher reliability should be arranged Just because of this.In direct sequence spread spectrum communication,, must make that at first (PN, Pseudo-noise) sequence and received signal PN sequence realize regularly synchronous for local pseudorandom in the receiver for realizing communication.Two steps that generally were divided into synchronously of direct sequence realize, promptly catch synchronously and follow the tracks of synchronously, and the pseudo random sequence of communication starting stage to catch be the top priority of spread spectrum communication.The attack of stream cipher is exactly to obtain the initial condition that it respectively generates feedback shift register (LFSR) by the sequence flows of intercepting and capturing, and it is the most effective a kind of in the Sequence Cipher Attack method that fast correlation is attacked.Recovery initial information algorithm during fast correlation is attacked has shown the good performance that restPoses under low signal-to-noise ratio.And the pseudo random sequence of communication starting stage is caught the initial condition of seeking communication sequence just.

This patent provides a kind of long sequence capturing new method of attacking based on fast correlation.Traditional sequence capturing technology is all utilized the autocorrelation performance of pseudo-code, produces a pseudo-code copy by this locality and carries out related operation with the reception pseudo-code, if Threshold detection identifies relevant peaks then catches and finish.The basic thought of the long sequence capturing method of attacking based on fast correlation is the initial information of searching formation sequence from the sequence flows that receives, with the initial state of key message as linear feedback shift register, the output sequence of linear feedback shift register is regarded the output of coding codeword as, the output code word is through channel, decipher with the fast correlation attack algorithm at receiving terminal, recover key message, i.e. the initial state of linear feedback shift register realizes sequence capturing thus.This method complexity is low, acquisition speed is fast, and both can be used for catching of linear order, can be used for catching of non-linear sequence again.

Summary of the invention

This patent provides a kind of long sequence capturing new method of attacking based on fast correlation.For sequence generator shown in Figure 1, (u ₁, u ₂... u _i... u _s) be the output sequence of linear shift register (LFSR), z _iBe the output after comprehensive through function f (f can be that linear function also can be a nonlinear function); The model attacked of fast correlation as shown in Figure 2, sequence (u ₁, u ₂... u _i... u _s) by bit be the BSC channel of 1-p by error probability, obtain sequence z=(z ₁... z _i, z _I+1... z _N), the dependent probability p of definition channel output sequence and list entries is p=P (u _i=z _i), the thought that fast correlation is attacked is exactly the sequence z in the length N of known channel output, and recovers original sequence (u under the situation of dependent probability p ₁, u ₂... u _i, u _s), thereby recover initial condition (a ₁, a ₂... a _k).

With the basic principle of the PN sequence capturing of lucid and lively fast correlation attack algorithm as the linear feedback shift register of Fig. 3, the linear feedback shift register of Fig. 3 is the linear feedback shift register on binary system r rank, establishes u _t=a _tBe the output of moment t, then a _T+i, 0≤i≤r-1 is the value of i register, and constraints is

$g_0{a}_{t+r}\⊕g_1{a}_{t+r-1}\⊕\·\·\·\⊕g_{r-1}{a}_{t+1}\⊕g_r{a}_t=0---\left(1\right)$

Wherein

Expression mould 2 adds g _i∈ 0, and 1}, 0≤i≤r is a feedback factor.Generator polynomial is g (x)=g ₀+ g ₁X+ ... + g _R-1x ^R-1+ g _rx ^rAs g (x) is the initial condition a=(a of primitive polynomial and register ₀, a ₁..., a _R-1), a _i{ 0, when 1} was not zero entirely, the maximum cycle of the linear feedback shift register on r rank was N=2 to ∈ ^r-1.

The target of sequence capturing is to find the initial condition a of current sequence from received signal z.In most practical solution, the part of having only long sequence as seen, so the problem of sequence capturing can be described as: at the visible sequence Z={z of the long band of given M noise _t, t=0,1 ..., under the M-1 situation, estimate formation sequence initial condition a, acquisition procedure is:

The naive model that step 1 is set up acquisition sequence is

$z=\sqrt{E_c}{y}_t\left(u\right)+n_t---\left(2\right)$

E wherein _cBe every chip signal energy, n _tBe that average is that zero variance is N ₀/ 2 additive white Gaussian noise (AWGN).A formula mistake! Do not find Reference source.In model be expressed as with vector form

$Z=\sqrt{E_c}Y\left(u\right)+n---\left(3\right)$

N=(n wherein ₀, n ₁..., n _M-1) ^TBe that average is that null covariance matrix is N ₀/ 2I _MGauss's vector, I _MIt is the unit matrix of M * M.

The step 2 iteration probability calculation stage

(1) establishes proper polynomial g (x)=1+g of LFSR ₁X+g ₂x ²+ ... + g _rx ^rTap number be t, weight is t+1.Because

Repetition power by g (x) can obtain the check polynomial that new weight is t+1, and each check polynomial is again corresponding to a verification equation.

(2) be provided with one about u _iWeight be the verification equation of t+1

$u_i=u_{i-{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="H2009102650037E00013.png,H2009102650037E00021.png"\; state="\{\{state\}\}">j</figure-callout>}}_1}+u_{i-j_2}+\&CenterDot;\&CenterDot;\&CenterDot;+u_{i-j_t---\left(4\right)}$

Translation feature by LFSR can obtain other t about u _iDifferent verification equatioies:

$u_{i+{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="H2009102650037E00013.png,H2009102650037E00021.png"\; state="\{\{state\}\}">j</figure-callout>}}_1}=u_i+u_{i+j_1-j_2}+\&CenterDot;\&CenterDot;\&CenterDot;+u_{i+j_1-j_t}$

.

. (5)

.

$u_{i+j_t}=u_i+u_{i+j_t-j_2}+\&CenterDot;\&CenterDot;\&CenterDot;+u_i$

Obtain M altogether about u by last method _iThe verification equation, the element substitution of correspondence position among the z is had:

z _i+y ₁＝L ₁

z _i+y ₂＝L ₂ (6)

.

.

.

z _i+y _M＝L _M

y _jThe value correct probability of middle t diverse location is respectively p ₁, p ₂..., p _t,

$S_j({\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="H2009102650037E00013.png,H2009102650037E00021.png"\; state="\{\{state\}\}">p</figure-callout>}}_1,p_2,\&CenterDot;\&CenterDot;\&CenterDot;,p_t,t)=P(u_{j_k+i}-u_i=y_k),---\left(7\right)$

So, z _iTotal h the establishment of total M verification equation, Probability p ^*=P (u _i=z _i| u _i) following calculating:

$p_i^{*}=\frac{Y}{(Y+(1-p_i)\&times;(1-S_{j1})\&times;\&CenterDot;\&CenterDot;\&CenterDot;\&times;(1-S_{\mathrm{jh}})\&times;S_{j(h+1)}\&times;\&CenterDot;\&CenterDot;\&CenterDot;\&times;S_{\mathrm{jM}}}---\left(8\right)$

The step 3 verification stage in stage

Work as p ^*These new probability are less than given thresholding p _ThrNumber N _wSurpass another set-point N _Thr, the iterations that perhaps calculates new probability surpasses certain value, just new probability is got benefit less than the bit of set-point, then replaces former sequence with new sequence, and the probability of each bit is changed to former dependent probability p again, obtains (u ₁, u ₂... u _i... u _s) ^*

The iteration capture of step 4 sequence

(u with step 3 output ₁, u ₂... u _i... u _s) ^*Recover initial information (a ₁, a ₂... a _k) ^*, catching of verification sequence if realize catching, stops; Otherwise repeat above-mentioned steps two, three, surpass certain value up to reproducing former LFSR sequence or iterations.

Accompanying drawing and description of drawings

Fig. 1 composite sequence maker

(a ₁, a ₂... u _k) be the initial condition of input, (u ₁, u ₂... u _i, u _s) be the output sequence of linear shift register (LFSR), z _iBe the output after comprehensive through function f;

The model that Fig. 2 fast correlation is attacked

Sequence (u ₁, u ₂... u _i... u _s) by bit be the BSC channel of 1-p by error probability, obtain sequence z=(z ₁, z _i, z _I+1... z _N), the dependent probability p=P (u of definition channel output sequence and list entries _i=z _i), p is the metastasis model of channel.

The generation block diagram of Fig. 3 r-rank LFSR

u _t=a _tBe the output of moment t, then a _T+i, 0≤i≤r-1 is the value of i register, and constraints is, Wherein

Expression mould 2 adds g _i∈ 0, and 1}, 0≤i≤r is a feedback factor.The initial condition of register is a=(a ₀, a ₁..., a _R-1), a _i∈ 0, when 1} is not zero entirely.

Fig. 4 sequence iteration capture

(u with step 3 output ₁, u ₂... u _i, u _s) ^*Recover initial information (a ₁, a ₂... a _k) ^*, catching of verification sequence if realize catching, changes tracking over to; Otherwise with (u ₁, u ₂... u _i... u _s) ^*Replace z _i, repeating step two, three.

The performance of each catching method relatively when Fig. 5 caught length 256

When catching length 256 constantly, iterations is that 20 times new method is being dwindled with gap parallel, the serial catching method, and new catching method performance has surpassed iterative message and transmitted catching method.

Claims (3)

1. this patent provides a kind of long sequence capturing method of attacking based on sequence fast correlation, the basic thought of this method is an initial information of seeking formation sequence from the sequence flows that receives, with the initial state of key message as linear feedback shift register, the output sequence of linear feedback shift register is regarded the output of coding codeword as, the output code word is through channel, decipher with the fast correlation attack algorithm at receiving terminal, recover key message, be the initial state of linear feedback shift register, realize sequence capturing thus.

2. the long sequence capturing method that a kind of sequence fast correlation according to claim 1 is attacked comprises following step:

The naive model that step 1 is set up acquisition sequence is

$z_t=\sqrt{E_c}{y}_t\left(u\right)+n_t---\left(1\right)$

E wherein _cBe every chip signal energy, n _tBe that average is that zero variance is N ₀/ 2 additive white Gaussian noise (AWGN).A formula mistake! Do not find Reference source.In model be expressed as with vector form

$Z=\sqrt{E_c}Y\left(u\right)+n---\left(2\right)$

N=(n wherein ₀, n ₁..., n _M-1) ^TBe that average is that null covariance matrix is N ₀/ 2I _MGauss's vector, I _MIt is the unit matrix of M * M.

The step 2 iteration probability calculation stage

(1) establishes proper polynomial g (x)=1+g of LFSR ₁X+g ₂x ²+ ... + g _rx ^rTap number be t, weight is t+1.Because $g{\left(x\right)}^{2^i}=g\left(x^{2^i}\right),$ Repetition power by g (x) can obtain the check polynomial that new weight is t+1, and each check polynomial is again corresponding to a verification equation.

(2) be provided with one about u _iWeight be the verification equation of t+1

$u_i=u_{i-j_1}+u_{i-j_2}+\&CenterDot;\&CenterDot;\&CenterDot;+u_{i-j_t}---\left(3\right)$

Translation feature by LFSR can obtain other t about u _iDifferent verification equatioies:

$u_{i+j_1}=u_i+u_{i+j_1-j_2}+\&CenterDot;\&CenterDot;\&CenterDot;+u_{i+j_1-j_t}$

.

. (4)

.

$u_{i+j_t}=u_i+u_{i+j_t-j_2}+\&CenterDot;\&CenterDot;\&CenterDot;u_i$

Obtain M altogether about u by last method _iThe verification equation, the element substitution of correspondence position among the z is had:

z _i+y ₁＝L ₁

z _i+y ₂＝L ₂ (5)

.

.

.

z _i+y _M＝L _M

y _jThe value correct probability of middle t diverse location is respectively p ₁, p ₂..., p _t,

$S_j(p_1,p_2,\&CenterDot;\&CenterDot;\&CenterDot;p_t,t)=P(u_{j_k+i}-u_i=y_k),---\left(6\right)$

So, z _iTotal h the establishment of total M verification equation, Probability p ^*=P (u _i=z _i| u _i) following calculating:

$p_i^{*}=\frac{Y}{(Y+(1-p_i)\&times;(1-S_{j1})\&times;\&CenterDot;\&CenterDot;\&CenterDot;\&times;(1-S_{\mathrm{jh}})\&times;S_{j(h+1)}\&times;\&CenterDot;\&CenterDot;\&CenterDot;\&times;S_{\mathrm{jM}}}---\left(7\right)$

The step 3 verification stage in stage

Work as p ^*These new probability are less than given thresholding p _ThrNumber N _wSurpass another set-point N _Thr, the iterations that perhaps calculates new probability surpasses certain value, just new probability is got benefit less than the bit of set-point, then replaces former sequence with new sequence, and the probability of each bit is changed to former dependent probability p again, obtains (u ₁, u ₂... u _i... u _s) ^*

The iteration capture of step 4 sequence

(u with step 3 output ₁, u ₂... u _i... u _s) ^*Recover initial information (a ₁, a ₂... a _k) ^*, catching of verification sequence if realize catching, stops; Otherwise repeat above-mentioned steps two, three, surpass certain value up to reproducing former LFSR sequence or iterations.

3. a kind of long sequence capturing method of attacking based on sequence fast correlation according to claim 2, it is characterized in that: this method both can be used for catching of linear order, can be used for catching of non-linear sequence again.

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