CN109257743B - Method for constructing WTC-I through stable BSBC (binary-coded binary-block-code) without channel state information - Google Patents

Method for constructing WTC-I through stable BSBC (binary-coded binary-block-code) without channel state information Download PDF

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CN109257743B
CN109257743B CN201811392196.8A CN201811392196A CN109257743B CN 109257743 B CN109257743 B CN 109257743B CN 201811392196 A CN201811392196 A CN 201811392196A CN 109257743 B CN109257743 B CN 109257743B
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sequence set
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CN109257743A (en
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张高远
韩瑽琤
师聪雨
谢萍
王斐
吴红海
冀保峰
邢玲
常莉莉
王喜月
张萌
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Henan University of Science and Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K1/00—Secret communication
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L1/00—Arrangements for detecting or preventing errors in the information received
    • H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
    • H04L1/0009—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the channel coding
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/02—Protecting privacy or anonymity, e.g. protecting personally identifiable information [PII]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

The method for constructing the first type of eavesdropping channel through the BSBC when no channel state information exists comprises the following steps: step 1, establishing communication connection; step 2, the legal receiver randomly generates a feedback verification sequence set and broadcasts and sends the feedback verification sequence set; step 3, a legal sender randomly generates a standby sequence set; step 4, the legal sender encodes the secret information to be sent to obtain an information sequence; step 5, the legal sender generates a complete standby sequence set; step 6, a legal sender generates a sending sequence set and broadcasts and sends the sending sequence set without errors; step 7, fusing the received feedback check sequence set and the transmission sequence by a legal receiver and an eavesdropper to obtain a sequence to be decrypted; step 8, a legal receiver and an eavesdropper calculate a bit log-likelihood ratio; and 9, decrypting the sequence to be decrypted by the legal receiver and the eavesdropper by using the bit log-likelihood ratio based on a soft-decision algorithm. The invention has lower complexity, smaller transmission time delay and lower energy consumption on the premise of ensuring the communication safety.

Description

Method for constructing WTC-I through stable BSBC (binary-coded binary-block-code) without channel state information
Technical Field
The invention relates to the technical field of communication safety, in particular to a method for constructing WTC-I through stable BSBC when no channel state information exists.
Background
With the rapid development of information technology, the dependence of private information and commercial information transmission on wireless communication networks is increasing dramatically, and the concern of the derived security problems of the communication systems themselves is also increasing rapidly. Based on the open system interconnection 7-layer protocol, the information security mechanism of the traditional communication system is established at the network layer and above, the core technology is the key encryption mechanism, the premise is that the physical layer at the bottom of the protocol provides a smooth and error-free transmission link, and the information security problem of the physical layer does not draw enough attention. However, due to the openness and universality of the electromagnetic signal transmission environment, any third party with appropriate equipment can secretly access the network to steal information of others within the effective coverage range of the transmission power, and great threats are brought to the privacy and security of wireless communication. With the high speed of wireless data transmission and the diversification of wireless services, especially in the fifth generation mobile communication system scenario with the requirements of "high conversion, high density and high speed", the damage and loss caused by information stealing is difficult to measure. Therefore, compared to a wired network in which the physical transmission medium is relatively closed, the physical layer information security problem of the wireless communication network is more serious, and research on the physical layer information security problem is urgent.
Referring to fig. 1, Wyner proposes a WTC-I (wireless Channel-I, first type of eavesdropping Channel) model in 1975, in which a legitimate receiver and an eavesdropper simultaneously receive data transmitted by a transmitter. Under the assumption that the quality of an eavesdropper channel is inferior to that of a main channel, namely, the channels of both sides of legal communication have superiority in quality, perfect secret communication can be realized through a reasonable safe encoding scheme on the premise that the transmission rate does not exceed the safe capacity without depending on a shared key. However, the assumed condition that the channel quality of the eavesdropper is inferior to that of the main channel is difficult to guarantee in practice, for example, the eavesdropper is very close to the private information sender, and the power of the receiving antenna is very high, so that the receiving error rate can be easily guaranteed to be lower than that of a legal receiver. The model only proves the realizability of unconditional safe communication, and does not suggest how to construct the WTC-I and a reasonable safe coding scheme. It can be seen that the construction of the WTC-I and the security coding are two key technologies for unconditional secure communication.
At present, the research of building WTC-I based on a single-antenna communication system is not a lot, and as the first single-antenna WTC-I model in China, the WTC-I model based on interactive communication provided by the invention patent of 'building wire-tapI by feedback and LDPC codes' disclosed by the Chinese patent 'CN 200910058796.5' is widely concerned, and the implementation process has two significant characteristics: the method comprises the following steps that (1) noise of a main channel is transferred to an eavesdropper channel in an interaction process through reasonable algorithm design, and the quality advantage of the main channel is fundamentally established; (2) the threshold effect of the hard decision decoding algorithm is utilized to realize the improvement and optimization of the main channel quality and the degradation and maintenance of the eavesdropper channel quality, thereby amplifying the established channel quality advantage. However, this solution has some disadvantages: (1) a legal sender needs to send information by means of a noisy common channel, so that the common channel is completely reliable by reducing the information transmission rate and combining technical means such as a powerful error correcting code and the like, and the complexity of system implementation is additionally increased; (2) the weak error correction capability of the hard decision decoding algorithm results in low reliability of the main channel, so that the expansion effect on the established channel quality advantage is not obvious, and the maximum safe transmission rate upper limit of subsequent safe and reliable coding is also low.
Aiming at the above disadvantages of the solution disclosed in chinese patent "CN 200910058796.5", the solution of "a method for constructing a first type eavesdropping channel through BSBC" disclosed in chinese patent "CN 201610586991.5" is improved. The key point of the scheme is to disclose a bit log-likelihood ratio extraction method, and then the safety capacity is improved through soft-decision decoding. However, the scheme still has the following defects: first, the disclosed bit log-likelihood ratio extraction method involves a large number of exponential and logarithmic operations, and the resource consumption (implementation complexity, storage space, energy consumption and time delay) is large. In particular, as the number of feedback sequences increases, resource consumption also increases. Secondly, the soft-decision decoding adopts a sum-product algorithm, which also involves a large number of exponential and logarithmic operations, and the resource consumption is also large. Third, to obtain the bit log-likelihood ratio information, the scheme requires an accurate estimation of the channel state information (i.e., the channel false transition probability) at the receiving end. The inaccuracy of estimation will seriously reduce the reliability of both legal communication parties, and further reduce the security capacity, i.e. the robustness to the channel state information is insufficient. These three disadvantages make this solution unsuitable for systems with limited energy supply and computing power, which require high transmission delays.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides a method for constructing the WTC-I through the stable BSBC when no channel state information exists, and the method has the advantages of lower complexity, smaller transmission time delay and lower energy consumption on the premise of ensuring the communication safety.
In order to achieve the purpose, the invention adopts the specific scheme that: the method for constructing the WTC-I through the stable BSBC when no channel state information exists comprises the following steps:
step 1, a legal sender and a legal receiver are in bidirectional communication connection through a stable BSBC (binary symmetric broadcast channel), a channel between the legal sender and the legal receiver is a main channel, an eavesdropper is in one-way communication connection with the legal sender or the legal receiver through the stable BSBC, and a channel between the eavesdropper and the legal sender or the legal receiver is an eavesdropper channel;
step 2, a legal receiver randomly generates a feedback check sequence set and transmits the feedback check sequence set through stable BSBC broadcasting, the legal transmitter receives the feedback check sequence set interfered by the master channel error vector set, and an eavesdropper receives the feedback check sequence set interfered by the eavesdropping channel error vector set;
step 3, a legal sender randomly generates a default standby sequence set, wherein the length of each standby sequence in the default standby sequence set is equal to the length of the feedback check sequence;
step 4, a legal sender encodes the secret information to be sent by using a binary (N, K) linear block code approaching to the Shannon limit to obtain an information sequence, wherein the length of the information sequence is equal to that of the feedback check sequence;
step 5, the legal sender utilizes the existing default standby sequence set and information sequence to generate an extended standby sequence, and the default standby sequence set and the extended standby sequence form a complete standby sequence set;
step 6, the legal sender fuses the complete standby sequence set and the feedback check sequence set interfered by the main channel error vector set into a sending sequence set, and broadcasts and sends the sending sequence set through an error-free public channel, and both the legal receiver and the eavesdropper receive the error-free sending sequence;
step 7, fusing the feedback check sequence set and the sending sequence set by a legal receiver to obtain a main channel sequence to be decrypted, and fusing the feedback check sequence set interfered by the eavesdropping channel error vector set and the sending sequence set by an eavesdropping receiver to obtain a sequence to be decrypted of the eavesdropping channel;
step 8, the legal receiver calculates the bit log-likelihood ratio of the main channel by using the sequence to be decrypted of the main channel, and the eavesdropper calculates the bit log-likelihood ratio of the eavesdropping channel by using the sequence to be decrypted of the eavesdropping channel;
and 9, the legal receiver decrypts the sequence to be decrypted of the main channel based on the soft decision algorithm by utilizing the bit log-likelihood ratio of the main channel to obtain secret information, and the eavesdropper decrypts the sequence to be decrypted of the eavesdropping channel based on the soft decision algorithm by utilizing the bit log-likelihood ratio of the eavesdropping channel to obtain error information.
As a preferable scheme, the specific method of step 2 comprises:
step 2.1, the legal receiver randomly generates a feedback check sequence set, wherein the feedback check sequence set comprises t t or more than 1 mutually independent N-length binary sequences with each bit being equal in outline, and the N-length binary sequences are expressed as
Figure BDA0001874328670000035
Step 2.2, the legal receiver sends the feedback check sequence through stable BSBC broadcasting;
step 2.3, the receiver received by the legal senderThe set of feedback check sequences for the interference of the set of main channel error vectors is represented as
Figure BDA0001874328670000031
Wherein the content of the first and second substances,
Figure BDA0001874328670000032
denotes the modulo-2 sum operation, { ej＝[ej，i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to N is taken as a main channel error vector set, and a feedback check sequence set which is received by an eavesdropper and is interfered by the eavesdropper and is represented as
Figure BDA0001874328670000033
Wherein { eaj＝[eaj，i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to N, and the j is an error vector set of the eavesdropping channel.
As a preferred scheme, the set of primary channel error vectors { e }j＝[ej，i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to Nj，iThe probability of 1 does not vary with i and j, and the set of eavesdropping channel error vectors { ea }j＝[eaj，i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to Nj，iThe probability of 1 does not change with i and j.
Preferably, in step 3, the default spare sequence set is denoted as { cj＝[cj，i]，1≤j≤t-1，1≤i≤N}；
In step 4, the secret information is represented by x, and the encoded information sequence is represented by { c ═ ci，1≤i≤N}；
In the step 5, the method for generating the extended standby sequence by the legal sender is that
Figure BDA0001874328670000034
As a preferable scheme, in step 6, the method for generating the transmission sequence by the legitimate sender includes:
step 6.1, mixing { cj＝[cj，i]J is 1. ltoreq. t-1, i is 1. ltoreq. N } and
Figure BDA0001874328670000041
combined into a complete set of spare sequences cj，1≤j≤t}；
Step 6.2, mixing { cjJ is more than or equal to 1 and less than or equal to t
Figure BDA0001874328670000042
The middle elements are subjected to modulo-2 sum operation in a one-to-one correspondence mode according to subscripts to obtain a sending sequence set
Figure BDA0001874328670000043
As a preferable scheme, in the step 7,
the legitimate receiver will y'jAnd
Figure BDA0001874328670000044
carrying out integral modulo 2 sum operation to obtain a main channel to-be-decrypted sequence
Figure BDA0001874328670000045
Namely, it is
Figure BDA0001874328670000046
An eavesdropper will
Figure BDA0001874328670000047
And
Figure BDA0001874328670000048
integral modulo-2 sum operation is carried out to obtain a to-be-decrypted sequence of the eavesdropping channel
Figure BDA0001874328670000049
Namely, it is
Figure BDA00018743286700000410
As a preferable scheme, in the step 8,
the method for the legal receiver to calculate the bit log-likelihood ratio of the main channel is
Figure BDA00018743286700000411
The method for calculating the bit log-likelihood ratio of the eavesdropping channel by the eavesdropper is that
Figure BDA00018743286700000412
As a preferred scheme, in the step 4, a binary (N, K) linear block code approaching to the shannon limit is a low density parity check code.
As a preferable scheme, in the step 9, the soft decision algorithm is a minimum sum algorithm of low density parity check codes under a binary symmetric broadcast channel.
Has the advantages that:
1. the invention does not need channel state information in the bit log-likelihood ratio calculation stage and the decoding stage, and has the advantages of low complexity, small transmission time delay and low energy consumption;
2. the bit log-likelihood ratio is calculated by adopting an approximation method, so that the reliability of the communication process can be reduced, but for an eavesdropper, the noise level of the channel is far higher than that of a legal receiver, and the decoding convergence cannot be guaranteed even if the bit log-likelihood ratio information is obtained by adopting an accurate calculation method, so that the higher noise level of the eavesdropper channel provides sufficient space and room for constructing the eavesdropping channel, and the constructed eavesdropping channel can be guaranteed to have positive safety capacity even if the reliability of a main channel is slightly reduced, so that the reliability and the safety of information transmission can be still guaranteed;
3. the invention achieves better balance matching between communication safety and resource consumption.
Drawings
FIG. 1 is a schematic diagram of WTC-I model proposed by Wyner;
FIG. 2 is a schematic representation of Φ (x) when x > 0;
fig. 3 is a flow chart of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 2 and 3, fig. 2 is a schematic view of Φ (x) when x > 0, and fig. 3 is a flowchart of the present invention.
The method for constructing the WTC-I through the stable BSBC when no channel state information exists comprises steps 1 to 9.
Step 1, a legal sender and a legal receiver are connected through stable BSBC two-way communication, a channel between the legal sender and the legal receiver is a main channel, an eavesdropper is connected with the legal sender or the legal receiver through stable BSBC one-way communication, and a channel between the eavesdropper and the legal sender or the legal receiver is an eavesdropping channel.
And 2, the legal receiver randomly generates a feedback check sequence set and transmits the feedback check sequence set through stable BSBC broadcasting, the legal transmitter receives the feedback check sequence set interfered by the master channel error vector set, and the eavesdropper receives the feedback check sequence set interfered by the eavesdropping channel error vector set.
Step 2.1, the legal receiver randomly generates a feedback check sequence set, wherein the feedback check sequence set comprises t t or more than 1 mutually independent N-length binary sequences with each bit being equal in outline, and the N-length binary sequences are expressed as
Figure BDA0001874328670000051
And 2.2, the legal receiver sends the feedback check sequence through stable BSBC broadcasting.
Step 2.3, the feedback check sequence set interfered by the master channel error vector set and received by the legal sender is expressed as
Figure BDA0001874328670000052
Wherein the content of the first and second substances,
Figure BDA0001874328670000053
denotes the modulo-2 sum operation, { ej＝[ej，i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to N is taken as a main channel error vector set, and a feedback check sequence set which is received by an eavesdropper and is interfered by the eavesdropper and is represented as
Figure BDA0001874328670000054
Wherein { eaj＝[eaj，i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to N, and the j is an error vector set of the eavesdropping channel. And, the primary channel error vector set ej＝[ej，i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to Nj，iThe probability of 1 does not vary with i and j, and the set of eavesdropping channel error vectors { ea }j＝[eaj，i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to Nj，iThe probability of 1 does not change with i and j.
And 3, randomly generating a default spare sequence set by a legal sender, wherein the length of each spare sequence in the default spare sequence set is equal to that of the feedback check sequence, and the default spare sequence set is expressed as
{cj＝[cj，i]，1≤j≤t-1，1≤i≤N}。
And 4, a legal sender encodes the secret information x to be sent by using a binary (N, K) linear block code approaching to the Shannon limit to obtain an information sequence, wherein the length of the information sequence is equal to that of the feedback check sequence, and the information sequence is expressed as { c ═ ciAnd i is more than or equal to 1 and less than or equal to N }. Wherein, the binary (N, K) linear block code approaching to the Shannon limit is the low density parity check code.
Step 5, the legal sender uses the existing default standby sequence set and information sequence to generate an extended standby sequence, and the default standby sequence set and the extended standby sequence form a complete standby sequence set, and the method for generating the extended standby sequence comprises the following steps of
Figure BDA0001874328670000061
And 6, fusing the complete spare sequence set and the feedback check sequence set interfered by the main channel error vector set into a transmission sequence set by the legal sender, and broadcasting and transmitting the transmission sequence set through an error-free public channel, wherein both the legal receiver and the eavesdropper receive the error-free transmission sequence. . The method of generating a set of transmission sequences by a legitimate sender comprises steps 6.1 and 6.2.
Step 6.1, mixing { cj＝[cj，i]J is 1. ltoreq. t-1, i is 1. ltoreq. N } and
Figure BDA0001874328670000062
combined into a complete set of spare sequences cj，1≤j≤t}。
Step 6.2, mixing { cjJ is more than or equal to 1 and less than or equal to t
Figure BDA0001874328670000063
The middle elements are subjected to modulo-2 sum operation in a one-to-one correspondence mode according to subscripts to obtain a sending sequence set
Figure BDA0001874328670000064
And 7, fusing the feedback check sequence set and the sending sequence set by the legal receiver to obtain a main channel sequence to be decrypted, and fusing the feedback check sequence set interfered by the eavesdropping channel error vector set and the sending sequence set by the eavesdropping receiver to obtain a sequence to be decrypted of the eavesdropping channel.
The legitimate receiver will y'jAnd
Figure BDA0001874328670000065
carrying out integral modulo 2 sum operation to obtain a main channel to-be-decrypted sequence
Figure BDA0001874328670000066
Namely, it is
Figure BDA0001874328670000067
An eavesdropper will { y'jAnd
Figure BDA0001874328670000068
integral modulo-2 sum operation is carried out to obtain a to-be-decrypted sequence of the eavesdropping channel
Figure BDA0001874328670000069
Namely, it is
Figure BDA00018743286700000610
And 8, calculating the bit log-likelihood ratio of the main channel by the legal receiver by using the sequence to be decrypted of the main channel, and calculating the bit log-likelihood ratio of the wiretap channel by the wiretap receiver by using the sequence to be decrypted of the wiretap channel.
The method for the legal receiver to calculate the bit log-likelihood ratio of the main channel is
Figure BDA0001874328670000071
The method for calculating the bit log-likelihood ratio of the eavesdropping channel by the eavesdropper is that
Figure BDA0001874328670000072
And 9, the legal receiver decrypts the sequence to be decrypted of the main channel based on the soft decision algorithm by utilizing the bit log-likelihood ratio of the main channel to obtain secret information, and the eavesdropper decrypts the sequence to be decrypted of the eavesdropping channel based on the soft decision algorithm by utilizing the bit log-likelihood ratio of the eavesdropping channel to obtain error information.
In step 8, the theoretical basis for calculating the bit log-likelihood ratio is as follows.
First, it is known that the hyperbolic tangent function is defined as
Figure BDA0001874328670000073
And the relation between tanhx and its inverse function arc tanh x is
Figure BDA0001874328670000074
Then there are:
Figure BDA0001874328670000075
Figure BDA0001874328670000076
wherein alpha isj，iAnd betaj，iRepresenting the probability of a BSBC's error transition between a legitimate sender (Alice) and a legitimate receiver (Bob) and between an eavesdropper (Eve) and Bob, i.e.
αj，i＝P ej，i＝1，βj，i＝P(eaj，i＝1)；
And is provided with a plurality of groups of the following components,
Figure BDA0001874328670000077
secondly, for 1 ≦ i ≦ N, the bit log-likelihood ratio calculation methods of Bob and Eve disclosed in chinese patent "CN 201610586991.5" are known as follows:
Figure BDA0001874328670000078
Figure BDA0001874328670000079
then, as can be obtained from formulas (5) to (9), (8) and (9) can be equivalently described as:
Figure BDA0001874328670000081
Figure BDA0001874328670000082
furthermore, from the Tanh criterion:
Figure BDA0001874328670000083
wherein the content of the first and second substances,
Figure BDA0001874328670000084
Φ (x) is referred to as a Gallager function or involution transform function. Then the bit log-likelihood calculation method of Bob disclosed by chinese patent "CN 201610586991.5" can be equivalently described as follows:
Figure BDA0001874328670000085
as can be seen from fig. 2, Φ (x) is inversely proportional to x, and as x decreases, Φ (x) increases rapidly, the pair
Figure BDA0001874328670000086
Has the main functions of
Figure BDA0001874328670000087
Recombined phi-1(Φ (x)) ═ x, then in equation (12)
Figure BDA0001874328670000088
Can be approximated as:
Figure BDA0001874328670000089
then, as can be seen from equation (13), equation (8) can be simplified as:
Figure BDA0001874328670000091
similarly, equation (9) can be simplified as:
Figure BDA0001874328670000092
finally, in stationary BSBC channelUnder the condition that the transmission quality of a legal communication channel between Alice and Bob and an illegal communication channel between Alice and Eve is kept unchanged in the single information communication process, namely the probability of error transition of a main channel { alpha }j，iJ is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to N and probability of error transfer of eavesdropping channel { beta ≦j，iJ is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to N is not changed along with the change of i and j. Without loss of generality, the error transfer probabilities of the legal BSC are all made to be alpha, the error transfer of the illegal BSC is made to be beta, and j is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to N:
Figure BDA0001874328670000093
Figure BDA0001874328670000094
as can be seen from equations (16) and (17), equations (14) and (15) can be changed to:
Figure BDA0001874328670000095
Figure BDA0001874328670000096
as can be seen from equations (18) and (19), the bit log likelihood ratio includes channel state reliability information
Figure BDA0001874328670000097
And
Figure BDA0001874328670000101
but independent of i, i.e. constant.
It is well known that the min-sum algorithm of low density parity check codes does not require channel state information. Therefore, Bob can recover K-length secret information after decoding by adopting the minimum sum algorithm under BSBC
Figure BDA0001874328670000102
In this case, the following formula (18) and formula (19)
Figure BDA0001874328670000103
And
Figure BDA0001874328670000104
the omission of the items does not affect the final decoding result. Therefore, the formula (18) can be further simplified to
Figure BDA0001874328670000105
Similarly, formula (19) can be varied to
Figure BDA0001874328670000106
From the above, the invention does not need the channel state information in the bit log-likelihood ratio calculation stage and the decoding stage, i.e. the invention has stronger robustness to the channel state information, and has the advantages of low complexity, small transmission delay and low energy consumption.
On the other hand, the invention can still ensure the safe transmission of information. For the main channel, compared with the accurate calculation method, the reliability of the bit log-likelihood ratio calculated by adopting the approximate method is reduced, but for the eavesdropper, because the channel noise level is far higher than that of a legal receiver, the decoding convergence of the bit log-likelihood ratio information cannot be guaranteed even if the eavesdropper adopts the accurate calculation method, so that the higher noise level of the eavesdropper channel provides sufficient space and room for constructing the eavesdropping channel, and the constructed eavesdropping channel can be guaranteed to have positive safety capacity even if the reliability of the main channel is slightly reduced, thereby ensuring the safe transmission of the information.
In conclusion, the invention achieves better balance matching between communication safety and resource consumption.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (4)

1. The method for constructing the WTC-I through stable BSBC when no channel state information exists, wherein the WTC-I is a first type of eavesdropping channel, and is characterized in that: the method comprises the following steps:
step 1, a legal sender and a legal receiver are connected through stable BSBC two-way communication, wherein BSBC is a binary symmetric broadcast channel, a channel between the legal sender and the legal receiver is a main channel, an eavesdropper is connected with the legal sender or the legal receiver through stable BSBC in one-way communication, and a channel between the eavesdropper and the legal sender or the legal receiver is an eavesdropper channel;
step 2, the legal receiver randomly generates a feedback check sequence set and broadcasts and transmits the feedback check sequence set through stable BSBC, wherein the feedback check sequence set comprises t, t is more than or equal to 1 mutually independent N-long binary sequences with equal bit outlines, and the N-long binary sequences are expressed as
Figure FDA0003207480190000011
The legal sender receives a set of feedback check sequences, denoted by
Figure FDA0003207480190000012
Wherein the content of the first and second substances,
Figure FDA0003207480190000013
denotes the modulo-2 sum operation, { ej＝[ej,i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to N is taken as a main channel error vector set; the feedback check sequence set of the eavesdropper receiving the interference of the eavesdropping channel error vector set is expressed as
Figure FDA0003207480190000014
Wherein { eaj＝[eaj,i],1≤j≤t,1≤i≤NThe symbol is an eavesdropping channel error vector set;
set of primary channel error vectors ej＝[ej,i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to Nj,iThe probability of 1 does not vary with i and j, and the set of eavesdropping channel error vectors { ea }j＝[eaj,i]J is more than or equal to 1 and less than or equal to t, i is more than or equal to 1 and less than or equal to Nj,iThe probability of 1 does not vary with i and j;
step 3, a legal sender randomly generates a default standby sequence set, wherein the length of each standby sequence in the default standby sequence set is equal to the length of the feedback check sequence;
step 4, a legal sender encodes the secret information to be sent by using a binary (N, K) linear block code approaching to the Shannon limit to obtain an information sequence, wherein the length of the information sequence is equal to that of the feedback check sequence; the binary (N, K) linear block code is a low density parity check code;
step 5, the legal sender utilizes the existing default standby sequence set and information sequence to generate an extended standby sequence, and the default standby sequence set and the extended standby sequence form a complete standby sequence set;
step 6, the legal sender fuses the complete standby sequence set and the feedback check sequence set interfered by the main channel error vector set into a sending sequence set, and broadcasts and sends the sending sequence set through an error-free public channel, and both the legal receiver and the eavesdropper receive the error-free sending sequence;
7, the legal receiver collects the feedback check sequence
Figure FDA0003207480190000015
And transmit sequence set { y'jGet the main channel to be deciphered sequence by fusion
Figure FDA0003207480190000016
Feedback check sequence set interfered by eavesdropper on eavesdropping channel error vector set
Figure FDA0003207480190000017
And transmit sequence set { y'jGet the sequence to be decrypted of the eavesdropping channel by fusion
Figure FDA0003207480190000018
Step 8, the legal receiver calculates the bit log-likelihood ratio of the main channel by using the sequence to be decrypted of the main channel, and the method is that
Figure FDA0003207480190000021
An eavesdropper calculates the bit log-likelihood ratio of the eavesdropping channel by using the sequences to be decrypted of the eavesdropping channel, and the method comprises the following steps
Figure FDA0003207480190000022
And 9, decrypting the sequence to be decrypted of the main channel by the legal receiver by using the bit log-likelihood ratio of the main channel based on the minimum sum algorithm of the low-density parity check codes under the binary symmetric broadcast channel to obtain secret information, and decrypting the sequence to be decrypted of the wiretapped channel by the wiretapped receiver by using the bit log-likelihood ratio of the wiretapped channel based on the minimum sum algorithm of the low-density parity check codes under the binary symmetric broadcast channel to obtain error information.
2. The method for constructing WTC-I by stationary BSBC without channel state information according to claim 1, wherein: in step 3, the default standby sequence set is denoted as { cj＝[cj,i],1≤j≤t-1,1≤i≤N}；
In step 4, the secret information is represented by x, and the encoded information sequence is represented by { c ═ ci],1≤i≤N}；
In the step 5, the method for generating the extended standby sequence by the legal sender is that
Figure FDA0003207480190000023
3. The method for constructing WTC-I by stationary BSBC without channel state information according to claim 2, wherein: in step 6, the method for generating the transmission sequence by the legitimate sender includes:
step 6.1, mixing { cj＝[cj,i]J is 1. ltoreq. t-1, i is 1. ltoreq. N } and
Figure FDA0003207480190000024
combined into a complete set of spare sequences cj,1≤j≤t}；
Step 6.2, mixing { cjJ is more than or equal to 1 and less than or equal to t
Figure FDA0003207480190000025
The middle elements are subjected to modulo-2 sum operation in a one-to-one correspondence mode according to subscripts to obtain a sending sequence set
Figure FDA0003207480190000026
4. The method for constructing WTC-I by stationary BSBC without channel state information according to claim 3, wherein: in the step 7, the process is carried out,
the legitimate receiver will y'jAnd
Figure FDA0003207480190000027
carrying out integral modulo 2 sum operation to obtain a main channel to-be-decrypted sequence
Figure FDA0003207480190000028
Namely, it is
Figure FDA0003207480190000029
An eavesdropper will { y'jAnd
Figure FDA00032074801900000210
integral modulo-2 sum operation is carried out to obtain a to-be-decrypted sequence of the eavesdropping channel
Figure FDA00032074801900000211
Namely, it is
Figure FDA00032074801900000212
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