CN111314325B - Physical layer network coding encryption transceiving system and method based on relay control - Google Patents

Physical layer network coding encryption transceiving system and method based on relay control Download PDF

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CN111314325B
CN111314325B CN202010076379.XA CN202010076379A CN111314325B CN 111314325 B CN111314325 B CN 111314325B CN 202010076379 A CN202010076379 A CN 202010076379A CN 111314325 B CN111314325 B CN 111314325B
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plaintext
information
beta
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CN111314325A (en
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王雪松
展月英
张春晖
孙扬
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CETC 54 Research Institute
Technology and Engineering Center for Space Utilization of CAS
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04B10/00—Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
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Abstract

The invention relates to a physical layer network coding encryption transceiving system and method based on relay control, wherein a relay node and each source node encrypt a sent plaintext in an aliasing mode, and specifically, the relay node and each source node encrypt any data to be sent: the first sending information, the second sending information, the superposed sending information and the like are all operation results, any first plaintext and any second plaintext which originally participate in the operation cannot be deduced only from the operation results, and in the data transmission process, the information received by a malicious third party is the operation result, namely aliasing information which does not have recovery value, so that each source node completes the secret transmission of the plaintext; compared with the common TWRC scene brought by PNC, the method has the advantages that the throughput can be doubled, any data sent at any moment is realized by simple XOR operation defined by plaintext and key text and carried out in G (2), real-time communication is not influenced, and the transmission efficiency is guaranteed.

Description

Physical layer network coding encryption transceiving system and method based on relay control
Technical Field
The invention relates to the field of laser communication, in particular to a physical layer network coding encryption transceiving system and method based on relay control.
Background
Physical-layer Network Coding (PNC) is a communication means for applying Network Coding to a Physical layer, a relay node performs Network Coding mapping on plaintext from different source nodes and forwards the plaintext to corresponding source nodes, and a source node receiving the plaintext recovers the plaintext of the corresponding source node, so that throughput can be doubled.
In order to avoid cracking, the current adopted method is as follows: in a multi-source node system, selecting an information source node, a legal user node and a cooperative user node, wherein the information source node and the legal user node send information and artificial noise to a relay, and the cooperative user node sends the artificial noise to the relay; the relay amplifies, forwards and broadcasts the mixed signal, meanwhile, the cooperative user node broadcasts artificial noise, the legal user node carries out self-interference elimination on the received signal and completes estimation of sufficient statistics of received symbols to obtain information symbols. But noise is artificially added in the system, and amplification of the noise exists; the method solves the problem that noise needs to be matched among a plurality of nodes back and forth, has large calculation amount, wastes transmission time slots and reduces the system efficiency.
Therefore, how to improve the transmission efficiency while ensuring the confidentiality of plaintext transmission between different source nodes is an urgent technical problem to be solved in the industry.
Disclosure of Invention
The invention aims to solve the technical problem of the prior art and provides a physical layer network coding encryption transceiving system and method based on relay control.
The invention discloses a technical scheme of a physical layer network coding encryption transceiving system based on relay control, which comprises the following steps:
selecting two source nodes from the plurality of source nodes at will, and respectively recording the two source nodes as a first source node and a second source node;
the relay node, the first source node and the second source node all store the same key F;
by means of XOR operations
Figure GDA0003349126200000028
The first source node stationFirst plaintext a to be transmitted and the key F generate first transmission information betaA(ii) a By said XOR operation
Figure GDA0003349126200000029
Generating second sending information beta by using a second plaintext b to be sent by the second source node and the key text FBWherein, in the step (A),
Figure GDA00033491262000000210
the first source node and the second source node respectively transmit the first transmission information betaAAnd the second transmission information betaBSending the information to the relay node;
the first plaintext a, the second plaintext b, the first transmission information βAAnd the second transmission information betaBBelonging to a Galois field G (2) in which an XOR operation is defined in said Galois field G (2)
Figure GDA00033491262000000211
Comprises the following steps:
Figure GDA0003349126200000021
the XOR operation satisfies the commutative, associative, and distributive laws in the Galois field G (2), and
Figure GDA00033491262000000212
and
Figure GDA0003349126200000022
the total data information received by the relay node is betaABThe total data information betaABMapping physical layer network coding (PNC) to obtain a mapping signal betaRWherein, in the step (A),
Figure GDA0003349126200000023
Figure GDA0003349126200000024
the relay node maps the mapping signal betaRObtaining the superposition information beta by a first formulacomThe first formula is:
Figure GDA0003349126200000025
the relay node then couples the superposition information betacomAfter the XOR operation is carried out, the superposed sending information is obtained
Figure GDA0003349126200000026
The relay node sends the superposition sending information
Figure GDA0003349126200000027
Respectively sending the data to the first source node and the second source node;
the first source node and the second source node use the respective key text F to send information to the superposition through a second formula
Figure GDA0003349126200000031
Respectively obtaining the superposition information beta after processingcomThe second formula is:
Figure GDA0003349126200000032
the first source node uses the first plaintext a to superimpose the information beta by a third formulacomProcessing the first plaintext b to obtain a second plaintext b, and using the second plaintext b by the second source node to obtain the superposition information beta through a fourth formulacomAnd obtaining the first plaintext a after processing, wherein a third formula is as follows:
Figure GDA0003349126200000033
the fourth formula is:
Figure GDA0003349126200000034
the physical layer network coding encryption transceiving system based on relay control has the following beneficial effects:
the relay node and each source node encrypt the transmitted plaintext in an aliasing form, and specifically, the relay node and each source node encrypt any data to be transmitted: first transmission information betaASecond transmission information betaBThe superposition sending information and the like are all operation results, any first plaintext a and any second plaintext b which originally participate in the operation cannot be deduced only from the operation results, and in the data transmission process, the information received by a malicious third party is the operation result, namely aliasing information which has no recovery value, so that each source node completes the secret transmission of the plaintext; compared with the common Two-Way Relay Channel (TWRC) scene brought by PNC, the throughput of the PNC can be doubled, any data sent at any time is realized by simple XOR operation which is defined by plaintext and key and carried out in G (2), the calculation amount is small, the real-time communication is not influenced, and the transmission efficiency is ensured. And because no other factors are involved except for increasing codes and no limitation is given to other parts involved in communication, the physical layer network coding encryption transceiving system based on relay control can be matched with any other communication technology in theory to realize a more complex communication system.
The invention discloses a technical scheme of a physical layer network coding encryption transceiving system based on relay control, which comprises the following steps:
s1, randomly selecting two of the source nodes, and respectively recording the two as a first source node and a second source node; respectively storing the same key text F in a relay node, the first source node and the second source node;
s2, generating a first sending message β from the first plaintext a to be sent by the first source node and the key F by exclusive-or operationA，
Figure GDA0003349126200000041
By said XOR operationGenerating second transmission information beta from a second plaintext b to be transmitted by the second source node and the key FB，
Figure GDA0003349126200000042
And respectively transmitting the first transmission information beta through the first source node and the second source nodeAAnd the second transmission information betaBSending the information to the relay node;
the first plaintext a, the second plaintext b, the first transmission information, and the second transmission information belong to a galois field G (2), and an exclusive or operation is defined in the galois field G (2) as:
Figure GDA0003349126200000043
the XOR operation satisfies the commutative, associative, and distributive laws in the Galois field G (2), and
Figure GDA0003349126200000044
and
Figure GDA0003349126200000045
s3, the total data information received by the relay node is betaABAnd converting the total data information betaABMapping physical layer network coding (PNC) to obtain a mapping signal betaRWherein, in the step (A),
Figure GDA0003349126200000046
Figure GDA0003349126200000047
the relay node maps the mapping signal betaRObtaining the superposition information beta by a first formulacomThe first formula is:
Figure GDA0003349126200000048
the relay node then couples the superposition information betacomAfter the XOR operation is carried out, the superposed sending information is obtained
Figure GDA0003349126200000049
The relay node sends the superposition sending information
Figure GDA00033491262000000410
Respectively sending the data to the first source node and the second source node;
s4, the first source node and the second source node send information to the superposition by a second formula using the respective key texts F
Figure GDA00033491262000000411
Respectively obtaining the superposition information beta after processingcomThe second formula is:
Figure GDA00033491262000000412
s5, the first source node uses the first plaintext a to overlap the information beta through a third formulacomProcessing the first plaintext b to obtain a second plaintext b, and using the second plaintext b by the second source node to obtain the superposition information beta through a fourth formulacomAnd obtaining the first plaintext a after processing, wherein a third formula is as follows:
Figure GDA0003349126200000051
the fourth formula is:
Figure GDA0003349126200000052
the physical layer network coding encryption transceiving method based on relay control has the following beneficial effects:
the relay node and each source node encrypt the transmitted plaintext in an aliasing form, and specifically, the relay node and each source node encrypt any data to be transmitted: first transmission information betaASecond sending informationβBThe superposition sending information and the like are all operation results, any first plaintext a and any second plaintext b which originally participate in the operation cannot be deduced only from the operation results, and in the data transmission process, the information received by a malicious third party is the operation result, namely aliasing information which has no recovery value, so that each source node completes the secret transmission of the plaintext; compared with the common TWRC scene brought by PNC, the method has the advantages that the throughput can be doubled, any data sent at any moment is realized by simple XOR operation defined by plaintext and key text and carried out in G (2), the calculation amount is small, real-time communication is not influenced, and the transmission efficiency is guaranteed. And because no other factors are involved except for adding codes and no limitation is made to other parts involved in communication, the relay control-based physical layer network coding encryption transceiving system can be matched with any other communication technology in theory.
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Fig. 1 is a schematic diagram of an operating principle of a relay control-based physical layer network coding encryption transceiving system according to an embodiment of the present invention;
fig. 2 is a schematic flowchart of a physical layer network coding encryption transceiving method based on relay control according to an embodiment of the present invention.
Detailed Description
In the physical layer network coding encryption transceiving system based on relay control according to the embodiment of the present invention, as shown in fig. 1, two source nodes are arbitrarily selected from a plurality of source nodes and are respectively marked as a first source node and a second source node; the number of the source nodes may be 2, 4, 6, etc., the number of the relay nodes may be 1, 2, 3, etc., and the relay nodes, the first source node, and the second source node all store the same key F;
an information sequence formed by splicing the first sequence C and the second sequence D in sequence is defined as CD, so that qm, pn and qn in the application can be more conveniently understood;
the key F comprises an operation instruction and key content, when the operation instruction is a common instruction, a sequence of the common instruction is marked as q, a sequence of the key content is marked as m, the key F is generated to be qm according to q and m, and qm represents an information sequence formed by splicing the q and the m in sequence;
generating first sending information beta by using an XOR operation between a first plaintext a to be sent by the first source node and the key FA，
Figure GDA0003349126200000061
Namely, the encryption of the first plaintext a is completed;
generating second sending information beta by using the second plaintext b to be sent by the second source node and the key F through the XOR operationB，
Figure GDA0003349126200000062
Namely, the encryption of the second plaintext b is completed;
the first source node and the source node respectively transmit the first transmission information betaAAnd the second transmission information betaBSending the information to the relay node;
the first plaintext a, the second plaintext b, the first transmission information βAAnd the second transmission information betaABelongs to a Galois field G (2), where the Galois field G (2) defines the XOR operation as:
Figure GDA0003349126200000063
the XOR operation satisfies the commutative, associative, and distributive laws in the Galois field G (2), and
Figure GDA0003349126200000067
and
Figure GDA0003349126200000064
the total data information received by the relay node is betaABThe total data information betaABMapping physical layer network coding (PNC) to obtain a mapping signal betaRWherein, in the step (A),
Figure GDA0003349126200000065
and converting the total data information betaABMapping physical layer network coding (PNC) to obtain a mapping signal betaRCan be expressed as:
Figure GDA0003349126200000066
the relay node maps the mapping signal betaRObtaining the superposition information beta by a first formulacomThe first formula is:
Figure GDA0003349126200000071
namely, it is
Figure GDA0003349126200000072
That is, the relay node is receiving the mapping signal βRWhile directly obtaining the superposed information betacom；
Then the relay node performs the superposition information beta againcomAfter the XOR operation is carried out, the superposed sending information is obtained
Figure GDA0003349126200000073
And will superimpose the transmitted information
Figure GDA0003349126200000074
Sending β to the first source node and the second source node, i.e. relay nodes, respectivelycomEncrypting to send information as superposition
Figure GDA0003349126200000075
The first source node and the second source node use the respective key text F to send information to the superposition through a second formula
Figure GDA0003349126200000076
Respectively obtaining the superposition information beta after processingcom: second maleThe formula is as follows:
Figure GDA0003349126200000077
namely, it is
Figure GDA0003349126200000078
That is, the first source node and the second source node respectively transmit information to the superposition
Figure GDA0003349126200000079
Decrypting to obtain the superposed information betacom；
The first source node uses the first plaintext a to superimpose the information beta by a third formulacomAnd obtaining the second plaintext b after processing, wherein a third formula is as follows:
Figure GDA00033491262000000710
the second source node uses the second plaintext b to add the information beta by a fourth formulacomAnd obtaining the first plaintext a after processing, wherein a fourth formula is as follows:
Figure GDA00033491262000000711
in short, the first source node obtains the second plaintext b through a third formula using the first plaintext a, and the second source node obtains the first plaintext a through a fourth formula using the second plaintext b, that is, the plaintext exchange between the first source node and the second source node is completed, and the communication between the first source node and the second source node is realized;
in another embodiment, after the first source node obtains the second plaintext b, the first plaintext a is deleted; when the second source node obtains the first plaintext a and deletes the second plaintext b, it can be understood that the second plaintext b is obtained at the first source node, and then the first plaintext a is deleted, although the first plaintext a still remains in the first source node for a period of time, the data amount of the first plaintext a is small, and the storage resource is not occupied basically, and this is also true for the second plaintext b still remains in the second source node for a period of time, which is not described herein again. And it is understood that: the plaintext represents the truly useful information that is sent out by the source node.
When the operation instruction is a change instruction, recording the sequence of the change instruction as p, and recording the sequence of the new key content as n;
the relay node will change signal betachaRespectively to the first source node and the second source node, wherein,
Figure GDA0003349126200000081
the first source node and the second source node utilize an old key text qm and a change signal beta, respectivelychaObtaining an intermediate quantity beta by a fifth formulamidThe fifth formula is
Figure GDA0003349126200000082
From said intermediate quantity betamidHas obtained the sequence p of the change instruction and applies the intermediate quantity betamidThe second half part n and q of the middle p are spliced into qn in sequence, and then the new first transmission information beta is respectively transmittedA*And new second transmission information betaB*And sending the information to the relay node, wherein,
Figure GDA0003349126200000083
and
Figure GDA0003349126200000084
pn represents an information sequence formed by splicing p and n in series.
At this point, the old key content m is immediately removed from use and deleted. And when the first source node and the second source node send the plaintext again, encrypting the plaintext by utilizing the qn key.
Wherein, the length of the sequence p of the change instruction is the same as the length of the sequence q of the normal instruction, and the length of the sequence m of the key content is the same as the length of the sequence n of the new key content, so as to ensure the information sequence alignment of pn and qm and avoid errors.
The lengths of the first plaintext and the second plaintext are respectively integral multiples of the length of the key text F, so that the first plaintext and the second plaintext can be completely covered by the key text.
Wherein a plurality of the superimposition information βcomIs an integral multiple of the length of pn, qm and/or qn, further ensuring the information sequence alignment of pn, qm and/or qn and avoiding errors.
The relay node updates the change instruction randomly or at a preset frequency, wherein the preset frequency can be 1 update time in 1 minute, 1 update time in 5 minutes and the like, and the confidentiality of plaintext transmission between different source nodes is further ensured.
The mapping rules for PNC are shown in table 1 below: if any other communication related technologies such as modulation, channel coding, etc. are added to the present application, there always exists a mapping scheme corresponding to the technology that can be implemented
Figure GDA0003349126200000091
To (3) is performed.
Table 1:
βA βB βAB βR
0 0 0 0
1 0 1 1
0 1 1 1
1 1 2 0
the application discloses a physical layer network coding encryption transceiving system based on relay control, wherein a relay node and each source node encrypt a sent plaintext in an aliasing mode, the relay node and each source node encrypt the sent plaintext in the aliasing mode, and specifically, the relay node and each source node encrypt any data to be sent: first transmission information betaASecond transmission information betaBThe superposition sending information and the like are all operation results, any first plaintext a and any second plaintext b which originally participate in the operation cannot be deduced only from the operation results, and in the data transmission process, the information received by a malicious third party is the operation result, namely aliasing information which has no recovery value, so that each source node completes the secret transmission of the plaintext; compared with the common TWRC scene brought by PNC, the method has the advantages that the throughput can be doubled, any data sent at any moment is realized by simple XOR operation defined by plaintext and key text and carried out in G (2), the calculation amount is small, real-time communication is not influenced, and the transmission efficiency is guaranteed. And because no other factors are involved except for adding codes and no limitation is made to other parts involved in communication, the relay control-based physical layer network coding encryption transceiving system can be theoretically connected with any other partCommunication technologies cooperate to implement more complex communication systems.
As shown in fig. 2, a physical layer network coding encryption transceiving method based on relay control according to an embodiment of the present invention includes the following steps:
s1, randomly selecting two of the source nodes, and respectively recording the two as a first source node and a second source node; respectively storing the same key text F in a relay node, the first source node and the second source node;
s2, generating a first sending message β from the first plaintext a to be sent by the first source node and the key F by exclusive-or operationA，
Figure GDA0003349126200000101
Generating second sending information beta by using the second plaintext b to be sent by the second source node and the key F through the XOR operationB，
Figure GDA0003349126200000102
And respectively transmitting the first transmission information beta through the first source node and the second source nodeAAnd the second transmission information betaBSending the information to the relay node;
the first plaintext a, the second plaintext b, the first transmission information, and the second transmission information belong to a galois field G (2), and an exclusive or operation is defined in the galois field G (2) as:
Figure GDA0003349126200000103
the XOR operation satisfies the commutative, associative, and distributive laws in the Galois field G (2), and
Figure GDA00033491262000001012
and
Figure GDA0003349126200000104
s3, the total data information received by the relay node is betaABAnd converting the total data information betaABMapping physical layer network coding (PNC) to obtain a mapping signal betaRWherein, in the step (A),
Figure GDA0003349126200000105
Figure GDA0003349126200000106
the relay node maps the mapping signal betaRObtaining the superposition information beta by a first formulacomThe first formula is:
Figure GDA0003349126200000107
the relay node then couples the superposition information betacomAfter the XOR operation is carried out, the superposed sending information is obtained
Figure GDA0003349126200000108
The relay node sends the superposition sending information
Figure GDA0003349126200000109
Respectively sending the data to the first source node and the second source node;
s4, the first source node and the second source node send information to the superposition by a second formula using the respective key texts F
Figure GDA00033491262000001010
Respectively obtaining the superposition information beta after processingcomThe second formula is:
Figure GDA00033491262000001011
s5, the first source node uses the first plaintext a to overlap the information beta through a third formulacomThe second plaintext b is obtained after the processing, and the second sourceThe node uses the second plaintext b to add the information beta through a fourth formulacomProcessing to obtain the first plaintext a; the third formula is:
Figure GDA0003349126200000111
the fourth formula is:
Figure GDA0003349126200000112
the application discloses a physical layer network coding encryption transceiving method based on relay control, wherein a relay node and each source node encrypt a sent plaintext in an aliasing mode, the relay node and each source node encrypt the sent plaintext in the aliasing mode, and specifically, the relay node and each source node encrypt any data to be sent: first transmission information betaASecond transmission information betaBThe superposition sending information and the like are all operation results, any first plaintext a and any second plaintext b which originally participate in the operation cannot be deduced only from the operation results, and in the data transmission process, the information received by a malicious third party is the operation result, namely aliasing information which has no recovery value, so that each source node completes the secret transmission of the plaintext; compared with the common TWRC scene brought by PNC, the method has the advantages that the throughput can be doubled, any data sent at any moment is realized by simple XOR operation defined by plaintext and key text and carried out in G (2), the calculation amount is small, real-time communication is not influenced, and the transmission efficiency is guaranteed. And because no other factors are involved except for adding codes and no limitation is made to other parts involved in communication, the relay control-based physical layer network coding encryption transceiving system can be matched with any other communication technology in theory.
Preferably, in the above technical solution, the method further comprises: defining an information sequence formed by splicing the first sequence C and the second sequence D in sequence from front to back as a CD;
the key F comprises an operation instruction and key content, when the operation instruction is a common instruction, a sequence of the common instruction is marked as q, a sequence of the key content is marked as m, the key F is generated to be qm according to q and m, and qm represents an information sequence formed by splicing q and m in sequence.
Preferably, in the above technical solution, the method further comprises: when the operation instruction is a change instruction, recording the sequence of the change instruction as p, and recording the sequence of the new key content as n;
the relay node will change signal betachaRespectively to the first source node and the second source node, wherein,
Figure GDA0003349126200000113
the first source node and the second source node utilize an old key text qm and a change signal beta, respectivelychaObtaining an intermediate quantity beta by a fifth formulamidThe fifth formula is:
Figure GDA0003349126200000114
from said intermediate quantity betamidHas obtained the sequence p of the change instruction and applies the intermediate quantity betamidThe second half part n and q of the middle p are spliced into qn in sequence, and then the new first transmission information beta is respectively transmittedA*And new second transmission information betaB*Sending the information to the relay node;
wherein the content of the first and second substances,
Figure GDA0003349126200000121
and
Figure GDA0003349126200000122
pn represents an information sequence formed by splicing p and n in series.
Preferably, in the above technical solution, the method further comprises: the length of the sequence p of the change instruction is the same as the length of the sequence q of the ordinary instruction; the length of the sequence m of key content is the same as the length of the sequence n of new key content.
Preferably, in the above technical solution, the method further comprises: the lengths of the first plaintext and the second plaintext are respectively integral multiples of the length of the key text F.
Preferably, in the above technical solution, the method further comprises: further comprising: a plurality of the superimposed information betacomIs an integer multiple of the length of pn, qm and/or qn.
Preferably, in the above technical solution, the method further comprises: the first source node obtains the second plaintext b and deletes the first plaintext a; and deleting the second plaintext b after the second source node obtains the first plaintext a.
Preferably, in the above technical solution, the method further comprises: and the relay node updates the change instruction randomly or at a preset frequency.
For the above steps of the relay control-based physical layer network coding encryption transceiving method according to the present invention, reference may be made to the above embodiments of a relay control-based physical layer network coding encryption transceiving system, which are not described herein again.
In the present invention, the terms "first", "second" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present invention, "a plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above are not necessarily intended to refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, various embodiments or examples and features of different embodiments or examples described in this specification can be combined and combined by one skilled in the art without contradiction.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.

Claims (9)

1. A physical layer network coding encryption transceiving system based on relay control is characterized in that two of a plurality of source nodes are selected randomly and are respectively marked as a first source node and a second source node;
the relay node, the first source node and the second source node all store the same key F;
generating first sending information beta by using an XOR operation between a first plaintext a to be sent by the first source node and the key FA(ii) a Generating second sending information beta by using the second plaintext b to be sent by the second source node and the key F through the XOR operationBWherein, in the step (A),
Figure FDA0003349126190000011
the first source node and the second source node respectively transmit the first transmission information betaAAnd the second transmission information betaBSending the information to the relay node;
the first plaintext a, the second plaintext b, the first transmission information βAAnd the second transmission information betaBBelongs to a galois field G (2) where the galois field G (2) defines the xor operation as:
Figure FDA0003349126190000012
the XOR operation satisfies the commutative, associative, and distributive laws in the Galois field G (2), and
Figure FDA0003349126190000013
and
Figure FDA0003349126190000014
the total data information received by the relay node is betaABThe total data information betaABMapping physical layer network coding (PNC) to obtain a mapping signal betaRWherein, in the step (A),
Figure FDA0003349126190000015
Figure FDA0003349126190000016
the relay node maps the mapping signal betaRObtaining the superposition information beta by a first formulacomThe first formula is:
Figure FDA0003349126190000017
the relay node then couples the superposition information betacomAfter the XOR operation is carried out, the superposed sending information is obtained
Figure FDA0003349126190000018
Figure FDA0003349126190000019
The relay node sends the superposition sending information
Figure FDA00033491261900000110
Respectively sending the data to the first source node and the second source node;
the first source node and the second source node use the respective key text F to send information to the superposition through a second formula
Figure FDA0003349126190000021
Respectively obtaining the superposition information beta after processingcomThe second formula is:
Figure FDA0003349126190000022
the first source node uses the first plaintext a to superimpose the information beta by a third formulacomProcessing the first plaintext b to obtain a second plaintext b, and using the second plaintext b by the second source node to obtain the superposition information beta through a fourth formulacomAnd obtaining the first plaintext a after processing, wherein the third formula is as follows:
Figure FDA0003349126190000023
the fourth formula is:
Figure FDA0003349126190000024
2. the relay control-based physical layer network coding encryption transceiving system according to claim 1, further comprising: the key F comprises an operation instruction and key content, when the operation instruction is a common instruction, a sequence of the common instruction is marked as q, a sequence of the key content is marked as m, the key F is generated to be qm according to q and m, and qm represents an information sequence formed by splicing q and m in sequence.
3. The system according to claim 2, wherein when the operation command is a change command, the sequence of the change command is denoted by p, and the sequence of the new key content is denoted by n;
the relay node will change signal betachaRespectively to the first source node and the second source node, wherein,
Figure FDA0003349126190000025
the first source node and the second source node utilize an old key text qm and a change signal beta, respectivelychaObtaining an intermediate quantity beta by a fifth formulamidThe fifth formula is:
Figure FDA0003349126190000026
from said intermediate quantity betamidHas obtained the sequence p of the change instruction and applies the intermediate quantity betamidThe second half part n and q of the middle p are spliced into qn in sequence, and then the new first sending information is respectively sent
Figure FDA0003349126190000027
And new second transmission information
Figure FDA0003349126190000028
Sending the information to the relay node;
wherein the content of the first and second substances,
Figure FDA0003349126190000029
and
Figure FDA00033491261900000210
pn represents an information sequence formed by splicing p and n in series.
4. The relay control-based physical layer network coding encryption transceiving system according to claim 3, further comprising:
the length of the sequence p of the change instruction is the same as the length of the sequence q of the ordinary instruction;
the length of the sequence m of key content is the same as the length of the sequence n of new key content.
5. The system according to claim 4, wherein the lengths of the first plaintext and the second plaintext are respectively integer multiples of the length of the key frame F.
6. The relay control-based physical layer network coding encryption transceiving system according to claim 5, further comprising: a plurality of the superimposed information betacomIs an integer multiple of the length of pn, qm and/or qn.
7. The relay control-based physical layer network coding encryption transceiving system according to any one of claims 3 to 6, further comprising: the first source node obtains the second plaintext b and deletes the first plaintext a; and deleting the second plaintext b after the second source node obtains the first plaintext a.
8. The relay control-based physical layer network coding encryption transceiving system according to claim 7, further comprising: and the relay node updates the change instruction randomly or at a preset frequency.
9. A physical layer network coding encryption transceiving method based on relay control is characterized by comprising the following steps:
s1, randomly selecting two of the source nodes, and respectively recording the two as a first source node and a second source node; respectively storing the same key text F in a relay node, the first source node and the second source node;
s2, generating a first sending message β from the first plaintext a to be sent by the first source node and the key F by exclusive-or operationA，
Figure FDA0003349126190000031
Generating second sending information beta by using the second plaintext b to be sent by the second source node and the key F through the XOR operationB，
Figure FDA0003349126190000032
And respectively transmitting the first transmission information beta through the first source node and the second source nodeAAnd the second transmission information betaBSending the information to the relay node;
the first plaintext a, the second plaintext b, the first transmission information, and the second transmission information belong to a galois field G (2), and an exclusive or operation is defined in the galois field G (2) as:
Figure FDA0003349126190000041
the XOR operation satisfies the commutative, associative, and distributive laws in the Galois field G (2), and
Figure FDA0003349126190000042
and
Figure FDA0003349126190000043
s3, the total data information received by the relay node is betaABAnd converting the total data information betaABMapping physical layer network coding (PNC) to obtain a mapping signal betaRWherein, in the step (A),
Figure FDA0003349126190000044
Figure FDA0003349126190000045
the relay node maps the mapping signal betaRObtaining the superposition information beta by a first formulacom：
The first formula is:
Figure FDA0003349126190000046
the relay node then couples the superposition information betacomAfter the XOR operation is carried out, a superposed sending message is obtainedInformation processing device
Figure FDA0003349126190000047
Figure FDA0003349126190000048
The relay node sends the superposition sending information
Figure FDA0003349126190000049
Respectively sending the data to the first source node and the second source node;
s4, the first source node and the second source node send information to the superposition by a second formula using the respective key texts F
Figure FDA00033491261900000410
Respectively obtaining the superposition information beta after processingcomThe second formula is:
Figure FDA00033491261900000411
s5, the first source node uses the first plaintext a to overlap the information beta through a third formulacomProcessing the first plaintext b to obtain a second plaintext b, and using the second plaintext b by the second source node to obtain the superposition information beta through a fourth formulacomThe first plaintext a is obtained after the processing, and the third formula is as follows:
Figure FDA00033491261900000412
the fourth formula is:
Figure FDA00033491261900000413
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