CN101854242B - Method for constructing wire-tap channel I by using feedback and LDPC codes - Google Patents

Abstract

The invention provides a method for constructing a wire-tap channel I by using feedback and low-density parity-check (LDPC) codes, which is characterized in that the wire-tap channel I is a binary symmetric channel, the error probability of a listener-in channel is p, and the main channel is error-free. In the invention, the error probability of the listener-in channel is p and the main channel is error-free through one or more error corrections of the interactive communication and the LDPC codes. The basic principle of the invention is that: in the interactive communication, a random noise vector which cannot be known by the listener-in is adopted in the main channel, and the error probability of a listener-in channel is enlarged, so that no matter the error probability of the listener-in channel is larger than that of the main channel in the process of initialization, the main channel has a better communication condition through the interactive communication, the errors of the main channel are corrected by the ultra error correcting capability and threshold effect of the LDPC code, and part of the errors of the listener-in channel are remained; and therefore, the wire-tap channel I which can realize unconditional secret transmission is obtained.

Description

Method based on feedback and LDPC sign indicating number structure wire-tap channel I

Technical field

The invention belongs to the information technology security fields, like the information security technology in fields such as radio communication, mobile communication, deep space communication.

Background technology

Because the broadcast characteristic of radio communication makes wireless network lack the physical boundary, not having the physical connection radio communication is open for external listener-in, and the safety of radio communication has become a key issue of physical layer.The safe practice of physical layer is based on the security model of Shannon, and it is the theoretical model that solves radio communication border, validity and reliability.The safe practice of physical layer is defined as: based on the physical layer low probability of intercept characteristic like the transmission characteristic of modulation, coding and channel, the safe and secret transmission of its system does not need the cryptography of information source, before transmission, does not have secret key need transmit both sides and shares in advance.The wire-tap channel model that Wyner equals proposition in 1975 is the safe transmission basic model of physical layer; In the wire-tap channel model; If main channel has better channel condition than tapping channel; The safe transmission of then carrying out physical layer is possible, and how reality is constructed the wire-tap channel model effectively but is a matter of opening always.

This patent provides a kind of method of utilizing feedback and loe-density parity-check code structure wire-tap channel I, and wire-tap channel I is a kind of binary symmetric channel, and listener-in's channel error probability is p, and main channel is error-free.This patent realize that listener-in's channel error probability is p, and main channel is error-free wire-tap channel I through the interactive communication of one or many and the error correction of loe-density parity-check code.Its basic principle is: in interactive communication, and the random noise vector that main channel has adopted the listener-in to learn, listener-in's channel error probability is strengthened; Make the channel error probability of listener-in's channel when no matter initial whether greater than main channel; Through interactive communication, main channel all has better channel condition, through the super error ability and the threshold effect of LDPC sign indicating number; Make the mistake of main channel all obtain correcting, and listener-in's channel error has partly remained.Obtained to realize the wire-tap channel I of unconditional secret transmission thus.

Summary of the invention

This patent provides a kind of method of utilizing feedback and loe-density parity-check code structure wire-tap channel I.Model such as the figure one of wire-tap channel I show.An our interactive communication model is as shown in Figure 2.Suppose that Alice and Bob are the both sides of legitimate correspondence, Alice thinks carry information M={m ₀, m ₁..., m _N-1Give Bob, one time the interactive communication process is following:

Step 1 Bob send a random sequence Q={q ₀, q ₁..., q _N-1Give Alice, and Pr (q _i=0)=Pr (q _i=1)=0.5.Let E={e ₀, e ₁..., e _N-1And EA={ea ₀, ea ₁..., ea _N-1Represent Alice and listener-in's channel error probability respectively.Alice and listener-in's reception signal is:

$T=\{t_0,t_1,\·\·\·,t_{n-1}\},t_i=q_i\⊕e_i---\left(1a\right)$

With

$\mathrm{TE}=\{{\mathrm{te}}_0,{\mathrm{te}}_1,\·\·\·,{\mathrm{te}}_{n-1}\},{\mathrm{te}}_i=q_i\⊕{\mathrm{ea}}_i,---\left(1b\right)$

Pr (e here _i=1)=α and Pr (ea _i=1)=β

Step 2 Alice calculates with the sequence T that receives:

$U=\{u_0,u_1,\·\·\·,u_{n-1}\},u_i=t_i\⊕m_i---\left(2\right)$

And coding U is:

W＝φ(U) (3)

φ is a coding function.

To see noise vector that W.Bob and listener-in receive W off be W ' to step 3 Alice and decipher W ' and do through wireless channel

$\hat{U}=\mathrm{\ψ}\left(W^{\′}\right)---\left(4\right)$

Ψ is the decoding function.We suppose that the decoding error probability all receives almost error-free U for

Bob and assailant.Bob knows random sequence Q, so he adds sequence Q and to U is:

$Y=U\⊕Q=M+E---\left(5\right)$

Y＝{y ₀，y ₁，…，y _n-1}。The listener-in only knows that the reception vector T E of Q band noise can only obtain:

$Z=U\⊕\mathrm{TE}=M\⊕E\⊕\mathrm{EA}---\left(6\right)$

Z＝{z ₀，z ₁，…，z _n-1}。

Calculation equation (5) and equality (6), EA becomes extra noise.Therefore, after a two-way communication, main channel necessarily has than the better channel quality of listener-in channel.

Further repeatedly two-way communication can be arranged, can further increase the channel error probability of listener-in's channel, repeatedly two-way communication is as shown in Figure 3, and the step of I of setting up the wire-tap channel is following:

Step 1 is for transmitting the information M of k bit, we at first select (n, k) linear binary code C and satisfying:

C＝χ(M)， (7)

χ is a coding function.

Step 2 is selected C at random ₀, C ₁, C ₂..., C _T-2, wherein 0≤i＜t-1.Our compute vector then:

$C_{t-1}=C_0\⊕C_2\⊕C_3\⊕\·\·\·\⊕C_{t-2}\⊕C.---\left(8\right)$

Step 3 Bob send t random sequence i=0 through t independent parallel channel or t different time slot; 1; 2 ... T-1 gives Alice.

and

denote Alice and eavesdropper channel error probability.Alice and listener-in's reception signal is: T _iAnd TE _i

Step 4 Alice uses and receives signal T _iCalculate by formula (2) And by formula (3) coding U _iObtain W _iAlice sees W off by wireless channel _iBob and listener-in receive W _iNoise vector be W ' _iAnd decoding W ' _iBe W _iBob and listener-in can obtain

With

Our Y that sues for peace respectively of step 5 _i, i=1,2 ..., t and Z _i:

$Y=\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{Y}_i=\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{C}_i\⊕\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{E}_i---\left(9a\right)$

With

$Z=\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{Z}_i=\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{C}_i\⊕\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{E}_i\⊕\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{\mathrm{EA}}_i---\left(9b\right)$

Press equality (8), equality (9a) and (9b) become

$Y=C\⊕\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{E}_i---\left(10a\right)$

With

$Z=C\⊕\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{E}_i\⊕\underset{i=0}{\overset{t-1}{\mathrm{\Σ}}}{\mathrm{EA}}_i---\left(10b\right)$

item in the equality (10b) becomes extra mistake.

Therefore step 6 obtains correct information M from Y through decoding, and can not obtain correct information M to the decoding of Z.

In interactive communication, the random noise vector that main channel has adopted the listener-in to learn, listener-in's channel error probability is strengthened; Make the channel error probability of listener-in's channel when no matter initial whether greater than main channel; Through interactive communication, main channel all has better channel condition, if in the coding of formula (7), use super error ability and the threshold effect of LDPC sign indicating number through the LDPC sign indicating number; Make the mistake of main channel all obtain correcting, and listener-in's channel error has partly remained.Obtained to realize the wire-tap channel I of unconditional secret transmission thus.

Accompanying drawing and description of drawings

The model of Fig. 1 wire-tap channel I

The channel of sender (sender) and legitimate receiver (intended receiver) is called main channel (Main channel), and sender and listener-in's (Eavesdropper) channel is called tapping channel (Eavesdropper channel).

Interactive communication process of Fig. 2

Alice and Bob are the both sides of legitimate correspondence, M={m ₀, m ₁..., m _N-1Be the information that Alice wants to give Bob, Q={q ₀, q ₁..., q _N-1It is the random sequence of giving Alice that Bob produces.E={e ₀, e ₁..., e _N-1And EA={ea ₀, ea ₁..., ea _N-1Represent Alice and listener-in's channel error probability respectively.

Repeatedly two-way communication process of Fig. 3

Alice and Bob are the both sides of legitimate correspondence, M={m ₀, m ₁..., m _N-1Be the information that Alice wants to give Bob, Bob selects t random sequence at first at random

I=0,1,2 ... T-1, and send to Alice,

With

The channel error probability of representing Bob and Alice and listener-in (attacker) and Alice respectively; Alice receives t the random sequence Q that Bob sends _iThe noise version

I=0,1 ..., (listener-in also receives Q to t-1 simultaneously _iThe noise version

I=0,1 ..., t-1), Alice selects C at random then ₀, C ₁, C ₂..., C _T-2, wherein

0≤i＜t-1, and satisfy:

C=χ (M) is the coding of k bit information M here, and Alice calculates I=0,1 ..., t-1 also sends to Bob; Bob receives

I=0,1 ..., calculate behind the t-1

I=0,1 ..., t-1, decoding obtains information M then.

Claims (2)

1. method of utilizing feedback and loe-density parity-check code to construct wire-tap channel I, wire-tap channel I is a kind of binary symmetric channel, listener-in's channel error probability is p, and main channel is error-free; Realize that through the interactive communication of one or many and the error correction of loe-density parity-check code listener-in's channel error probability is p; And main channel is error-free wire-tap channel I, step below when adopting the method for interactive communication and loe-density parity-check code realization wire-tap channel, comprising:

Step 1 Alice and Bob are the both sides of legitimate correspondence, and Alice thinks carry information M={m ₀, m ₁..., m _N-1Giving Bob, Bob send a random sequence Q={q ₀, q ₁..., q _N-1Give Alice, and Pr (q _i=0)=Pr (q _i=1)=0.5, lets E={e ₀, e ₁..., e _N-1And EA={ea ₀, ea ₁..., ea _N-1Represent Alice and listener-in's channel error probability respectively; Alice and listener-in's reception signal is:

With

Pr (e _i=1)=α and Pr (ea _i=1)=β.

Step 2 Alice calculates with the sequence T that receives:

And coding U is:

W＝φ(U) (3)

φ is a coding function;

Step 3 Alice sees W off through wireless channel, and the noise vector that Bob and listener-in receive W is W ' and deciphers W ' and do

Ψ is the decoding function; We suppose that the decoding error probability is

; Bob and assailant receive almost error-free U; Bob knows random sequence Q, so he adds sequence Q and to U is:

Y={y ₀, y ₁..., y _N-1, the listener-in only knows that the reception vector T E of Q band noise can only obtain:

Z＝{z ₀，z ₁，…，z _n-1}；

Calculation equation (5) and equality (6), EA becomes extra noise, and therefore, after a two-way communication, main channel necessarily has than the better channel quality of listener-in channel.

2. a kind of method of utilizing feedback and loe-density parity-check code structure wire-tap channel I according to claim 1, when the step below the method that adopts repeatedly interactive communication and loe-density parity-check code realization wire-tap channel comprises:

Step 1 is for transmitting the information M of k bit, we at first select (n, k) linear binary code C and satisfying:

C＝χ(M)， (7)

χ is a coding function;

Step 2 is selected C at random ₀, C ₁, C ₂..., C _T-2, wherein

0≤i＜t-1, our compute vector then:

Step 3 Bob send t random sequence through t independent parallel channel or t different time slot

I=0,1,2 ... T-1 gives Alice,

With

The channel error probability of representing Alice and listener-in respectively, Alice and listener-in's reception signal is: T _iAnd TE _i

Step 4 Alice uses and receives signal T _iCalculate And press W _i=φ (U _i), φ is a coding function, coding U _iObtain W _i, Alice sees W off by wireless channel _i, Bob and listener-in receive W _iNoise vector be W ' _iAnd decoding W ' _iBe W _i, Bob and listener-in can obtain

With

Our Y that sues for peace respectively of step 5 _i, i=1,2 ..., t and Z _i:

With

Press equality (8), equality (9a) and (9b) become

With

item in the equality (10b) becomes extra mistake;

Step 6 obtains correct information M from Y through decoding, and can not obtain correct information M to the decoding of Z.

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