CN111082933B - Multi-user physical layer safety communication method capable of resisting any plurality of cooperation eavesdroppers - Google Patents

Multi-user physical layer safety communication method capable of resisting any plurality of cooperation eavesdroppers Download PDF

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CN111082933B
CN111082933B CN201911375195.7A CN201911375195A CN111082933B CN 111082933 B CN111082933 B CN 111082933B CN 201911375195 A CN201911375195 A CN 201911375195A CN 111082933 B CN111082933 B CN 111082933B
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legal
key
bit
alice
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CN111082933A (en
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唐杰
许爱东
文红
张宇南
蒋屹新
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University of Electronic Science and Technology of China
Research Institute of Southern Power Grid Co Ltd
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Research Institute of Southern Power Grid Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • 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
    • H04L63/16—Implementing security features at a particular protocol layer
    • 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

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Abstract

The invention provides a multi-user physical layer secure communication method capable of resisting any plurality of cooperative eavesdroppers, and the method can realize multi-user broadcast communication without sharing any secret key by two legal communication parties before communication, so that no matter how many cooperative nodes are used by the eavesdroppers for eavesdropping, the error rate of the receiver secret information can still be ensured to be 0.5, and high-strength physical layer secure transmission is realized. The number of the receiving antennas used by each legal receiver and the number of the required transmitting symbol streams are determined by each legal receiver to the legal transmitter, wherein the number of the antennas and the number of the symbol streams of each legal receiver can be different, the number of the symbol streams, the number of the antennas and the modulation mode of each legal receiver can be flexibly adjusted, and the method has the advantages of low power consumption, low complexity, low interference and the like, can realize the physical layer secure communication of an eavesdropper with any multiple antennas without any additional artificial noise or cooperative interference, and can not increase the additional burden of a network or cause redundant interference to other users.

Description

Multi-user physical layer safety communication method capable of resisting any plurality of cooperation eavesdroppers
Technical Field
The invention relates to the field of information security, in particular to a multi-user physical layer secure communication method capable of resisting any plurality of cooperative eavesdroppers.
Background
With the rapid development of 5G and Internet of things, artificial intelligence and edge computing networks, a large number of novel services and applications are continuously emerging, various confidential and sensitive data and the like in a wireless network are increased in a massive manner, the accompanying information security problem is more and more prominent, and the security is gradually becoming a precondition for various different service applications; compared with the traditional wired network, the broadcasting characteristic and the mobile characteristic of the wireless mobile channel enable the communication of a legal user in the network to be easily intercepted and attacked by an illegal user; in a conventional wireless communication network, cryptography-based encryption technology is generally used at the network layer and upper layers to secure system communication.
However, the existing cryptography security technology is only used for a large amount of services and application scenarios of a future wireless mobile network, especially, massive sensing nodes and edge nodes in an IoT network usually operate under unattended condition with low power consumption, the computing resource and power efficiency are very limited, and the encryption and authentication technology with high computational complexity cannot be supported; the security technology based on the physical channel aims to utilize the randomness and the uniqueness of a wireless communication physical medium, fully utilize the uniqueness and the independent characteristic of a wireless transmission channel, combine the technologies of signal design, modulation, coding and the like, improve the receiving quality of a legal channel, and simultaneously deteriorate and disturb an attacker channel and receiving conditions, so that the mutual information quantity of information intercepted by an eavesdropper and secret information transmitted by both legal parties is 0, and high-strength unconditional security transmission without a secret key is realized.
However, currently, mainstream techniques for physical layer secure transmission, including techniques such as multi-antenna beam forming and precoding, artificial noise, and cooperative interference, cannot directly combat any plurality of cooperable eavesdroppers or cooperative eavesdropping nodes; the cooperative eavesdropping node means that a plurality of eavesdropping nodes are scattered at different positions of a network space for eavesdropping, and eavesdropping information is transmitted to the central node for combination processing; in actual communication, an eavesdropper only needs to increase the number of own cooperative eavesdropping nodes (which can be realized by distributed MIMO or internet of things IoT sensing nodes), and then can utilize signal processing technologies such as maximum ratio combining reception (MRC) or optimal interference cancellation combining to cancel interference and improve the reception quality (signal-to-noise ratio or signal-to-interference-and-noise ratio) of the eavesdropper.
If the total number (density) of the cooperative eavesdropping nodes exceeds a certain proportion of the sum of the antennae of the two legal communication parties, the quality of the received signals of the eavesdropper can exceed the receiving quality of a legal receiver, and finally the safety capacity of communication is enabled to be 0, which means that the physical layer safety transmission method fails; with the rapid development of large-scale IoT, large-scale MIMO and distributed MIMO, it is considered that an eavesdropper with rich resources can deploy a large number of cooperative eavesdropping nodes (sensors, eavesdroppers and the like) in a network space for eavesdropping; considering that in real-world applications, it is impossible for both legitimate communication parties to know how many cooperative eavesdropping nodes are deployed by an eavesdropper and their specific locations, and therefore it is difficult to always use more antennas to combat the eavesdropper.
The current technology cannot resist the situation that the number of cooperative wiretapping nodes (or wiretapping node density) far exceeds the number of antennae of both legal parties; therefore, the method provides a multi-user physical layer secure communication method capable of resisting any plurality of cooperative eavesdropping nodes, and has strong practicability.
Disclosure of Invention
The present invention is directed to solve the above problems, and an object of the present invention is to provide a multi-user physical layer secure communication method capable of countering any number of cooperating eavesdroppers, and a multi-user physical layer secure communication method capable of countering any number of cooperating eavesdroppers, wherein each legitimate receiver determines the number of receiving antennas used by the legitimate receiver and the number of required transmission symbol streams to the legitimate transmitter, the number of antennas and the number of symbol streams of each legitimate receiver may be different, and the number of symbol streams, the number of antennas, and the modulation scheme of each legitimate receiver may be flexibly adjusted.
The method comprises the following steps:
s1: the method comprises the following steps that a legal sender Alice and a plurality of legal receivers Bob carry out communication confirmation;
s2: a legal sender Alice randomly generates keys corresponding to a plurality of Bobs, and modulates a ciphertext bit stream after encrypting confidential bits into a symbol to be sent; mapping key bits corresponding to the N Bobs into key symbols, wherein each key symbol corresponds to a vector for activating different receiving antennas of each Bob;
s3: calculating the precoding of the key symbol corresponding to each Bob activation vector, and broadcasting the encrypted bit modulation symbol by using N Bob precoding matrixes;
s4: a legal receiver Bob independently measures the received signal strength of each activated antenna, estimates an antenna vector, obtains a key symbol and a key bit by inverse mapping, and demodulates the encrypted modulation symbols in sequence to obtain the encrypted bit;
s5: each legal receiver Bob carries out XOR on the key bit observed by the legal receiver Bob and the demodulated ciphertext bit to obtain confidential information;
s6: steps S2 through S5 are repeated.
The step S1 includes:
s11: each Bob determines the number of receiving antennas N required by each Bob to AliceBThe number N of modulation symbol streams transmitted simultaneously with Alice, wherein N is more than or equal to 1 and less than or equal to NB-1 such that:
Figure GDA0003003737400000021
s12: alice sets binary bit source information b as (b)1,b2,...,bN) Dividing into N shares, each share b corresponding to secret bit information sent to each BobiN each contain a bit;
the M isSConstellation signal order for the modulation scheme used by multiple Bob.
The step S2 includes the following steps:
s21: alice randomly generates N MSBit key bit bk＝(bk，1，bk,2,...,bk，N) And use of bkExclusive-or secret information b ═ b1,b2,...,bN) The following were used:
Figure GDA0003003737400000031
s22: alice encrypts the ciphertext bit streambs＝(bs,1,bs,2,...,bs,N) Modulating into a symbol to be transmitted s ═(s)1,..,sN)。
The step S2 further includes the steps of:
s23: alice determines that each key symbol corresponds to a different receive antenna K {0,1,2k-1} and all possible antenna combinations are represented by a vector E;
s24: alice sends the key bit bkMapping to key symbol K ═ (K)1，K2，..,KN)∈K；
S25: different columns E (: K +1) in E are selected as selection references for precoding to transmit different Bobs according to the value of K.
The step S3 includes the following steps:
s31: calculating an alternative pre-coding space W;
s32: dividing the corresponding column of W into corresponding space W (K) according to the number of receiving antennas of each Bobi) Wherein, K isiRespectively correspond to BobiSelecting a space range by a corresponding key symbol;
s33: for each Bob, choose its W (K)i) The number of non-zero columns in corresponding E (K +1) in (1) is W (E);
W(ei)＝W(Ki)E(:,K+1)；
s34: each W (e)i) Combined into W (e) ═ W (e)1),....,W(eN)]；
S35: transmitting symbols s ═(s) using W (e) precoding matrix1,..,sN)。
The step S4 includes the following steps:
s41: each Bob receives the signal
Figure GDA0003003737400000032
The signal plus noise strength of each antenna was then measured directly: alpha is alphai＝|yi|2，i＝1,2,...NB；
S42: selecting one or more of the largest alphaiAccording to eachNumber of communication symbol streams alpha of BobiGet the subscript of each Bob's respective observation ei；
S43: according to eiObtaining an observed key symbol KiAnd a key bit
Figure GDA0003003737400000033
S44: each Bob observed eiIndependently demodulating the encrypted modulation symbol on the antenna serial number corresponding to the medium non-zero element
Figure GDA0003003737400000034
And obtaining demodulated ciphertext bits
Figure GDA0003003737400000035
Further, each legitimate receiver Bob sees its own observed key bits
Figure GDA0003003737400000041
XOR bit
Figure GDA0003003737400000042
Obtaining the confidential bit information transmitted to each Bob by the final Alice broadcast:
Figure GDA0003003737400000043
the invention has the beneficial effects that: the method does not need any secret key shared by both legal communication parties before communication, can realize multi-user broadcast communication under the condition of resisting against any plurality of cooperative eavesdropping nodes, ensures that the error rate of the receiver secret information of the eavesdropping person is still 0.5 no matter how many cooperative nodes the eavesdropping person uses to eavesdrop, and realizes high-strength physical layer safety transmission, and the advantage cannot be achieved by the existing physical layer safety method.
The method has the advantages of low power consumption, low complexity, low interference and the like, can realize the physical layer secure communication of an eavesdropper with any multiple antennas without any additional artificial noise or cooperative interference, and can not increase the additional burden of a network or cause redundant interference to other users.
Drawings
FIG. 1 is a diagram of a communication channel model of the present invention;
FIG. 2 is a flow chart of a method of the present invention;
FIG. 3 is a final error rate performance diagram of Bob and Eve when Eve uses multiple cooperative nodes respectively, wherein Eve uses the optimal ratio to combine and receive the processed signals.
Detailed Description
In order to more clearly understand the technical features, objects, and effects of the present invention, embodiments of the present invention will now be described with reference to the accompanying drawings.
As shown in fig. 1, Alice and Bob1, Bob2 and Bob …, which are both parties of legal communication, surround themselves with a protection area, respectively, R needs to be greater than the uncorrelated distance of the channels, so that an eavesdropper Eve cannot enter the protection area to eavesdrop, that is, the distances between Eve and Alice and Bob1, between Bob2 and … Bob are greater than R, and the channels of Eve and Alice and Bob1, between Bob2 and Bob … Bob are all independent of each other; the length of R is determined by the channel propagation environment and the carrier frequency, and is generally 10cm-100cm under the sufficient scattering environment.
Two parties of the legal communication, namely Alice and Bob1, Bob2 and … Bobn, need to be provided with more than 2 antennas; considering the downlink, then the sum of the number of antennas for all Bob is no greater than the sum of Alice's transmit antennas (and vice versa); the following embodiments are all described by taking downlink as an example, and for easy understanding, N is usedAAnd NBRespectively representing the number of antennas of Alice and each Bob; the different number of antennas used by each Bob is within the scope of this patent.
In this embodiment, each Bob determines the number of receiving antennas used by the Bob and the number of required transmission symbol streams to Alice, where the number of antennas and the number of symbol streams of each Bob may be different, and the number of symbol streams, the number of antennas, and the modulation mode of each Bob may be flexibly adjusted according to the requirements of the method framework of the present invention; for ease of understanding, in the present embodiment, each Bob employs received 1-stream symbols, and 2 antennas NBFor example, 2 and BPSK modulation are used as an example to illustrate the skill in the artIt will be understood by those skilled in the art that the scope of the invention as claimed is not limited thereby.
The multi-user physical layer secure communication method capable of resisting any plurality of cooperative eavesdroppers as shown in fig. 2 comprises the following steps:
s1: the method comprises the following steps that a legal sender Alice and a plurality of legal receivers Bob carry out communication confirmation;
s2: the legal sender Alice modulates the encrypted bit stream into a symbol to be sent; mapping key bits corresponding to the N Bobs into key symbols, wherein each key symbol corresponds to a vector for activating different receiving antennas of each Bob;
s3: calculating the precoding of the key symbol corresponding to each Bob activation vector, and broadcasting the encrypted bit modulation symbol by using N Bob precoding matrixes;
s4: a legal receiver Bob independently measures the received signal strength of each activated antenna, estimates an antenna vector, performs inverse mapping to obtain a key symbol and a key bit, and demodulates the encrypted modulation symbols in sequence to obtain a ciphertext bit;
s5: each legal receiver Bob obtains confidential information by carrying out XOR on the key bit observed by each legal receiver Bob;
s6: steps S2 through S5 are repeated.
In the step S1:
each Bob selects the required number N of receive antennasBThe number N of modulation symbol streams transmitted simultaneously with Alice, wherein N is more than or equal to 1 and less than or equal to NB1, such that
Figure GDA0003003737400000051
According to different modulation modes, the number of symbol streams and the number of receiving antennas, the steps are determined by a legal party in advance before communication is started;
alice sets binary bit source information b as (b)1,b2,...,bN) Dividing into N shares, each share b corresponding to secret bit information sent to each Bobi,i＝1,2,...,N，MS＝log2M comprisesBit, MSThe constellation signal order of the modulation scheme used by Bob; here, for example, BPSK modulation scheme, MS1, M adopted by the systemSCorresponding to the number of receive antennas of each Bob and the number of modulation symbol streams sent to it by Alice.
The step S2 includes the following steps:
s21: alice randomly generates N MSBit key bit bk＝(bk，1，bk,2,...,bk，N) And use of bkExclusive-or secret information b ═ b1,b2,...,bN) The following were used:
Figure GDA0003003737400000052
s22: alice encrypts the bit stream bs＝(bs,1,bs,2,...,bs,N) Modulating into a symbol to be transmitted s ═(s)1,..,sN) Ready for simultaneous broadcast to N Bob.
S23: alice establishes a key symbol and activates a different receiving antenna K {0,1, 2.. once.n.for each Bob, corresponding to each key symbolk-1} and all possible antenna combinations are represented by a vector E; for example, N in the present embodimentB2, N is 1, then K is 2, and all possible antenna combinations E are represented as:
Figure GDA0003003737400000061
where the first column vector E of E11 in Bob indicates the first antenna of Bob is activated, 0 indicates the second antenna of Bob is not activated, and so on;
s24: alice sends the key bit bkMapping to key symbol K ═ (K)1，K2，..,KN)∈K；
S25: different columns E (: K +1) in E are selected as selection references for precoding to transmit different Bobs according to the value of K.
The step S3 includes the following steps:
s31: computing an alternative precoding space W:each Bob sends a pilot frequency sequence to Alice in turn, and the Alice estimates an uplink equivalent channel HBAAnd transposes to obtain the downlink channel
Figure GDA0003003737400000062
Wherein HAB＝[HAB,1；HAB,2]Corresponding to the channel from Alice to each Bob, Alice obtains a candidate precoding space W according to the following processing:
Figure GDA0003003737400000063
Figure GDA0003003737400000064
s32: according to the number of receiving antennas of each Bob, Alice divides the corresponding column of W into corresponding space W (K)i) Wherein, K isiRespectively correspond to BobiSelecting a space range by a corresponding key symbol; for example, when N is 2, the division W is as follows, where K1 and K2 correspond to key symbol selection space ranges corresponding to Bob1 and Bob2, respectively. The rest is analogized in turn:
Figure GDA0003003737400000065
s33: alice selects its W (K) for each Bobi) The number of non-zero columns in corresponding E (K +1) in (1) is W (E);
W(ei)＝W(Ki)E(:,K+1)；
s34: alice sends each W (e)i) Combined into W (e) ═ W (e)1),....,W(eN)]；
S35: alice transmits a symbol s ═(s) using a W (e) precoding matrix1,..,sN) (ii) a In this example, if N is 2, the transmission signal can be expressed as:
Figure GDA0003003737400000066
the step S4 includes the following steps:
s41: each Bob receives its own signal
Figure GDA0003003737400000071
The signal plus noise strength SPN of each antenna is then measured directly as follows: alpha is alphai＝|yi|2，i＝1,2,...NB；
S42: each Bob selects the largest one (or more) of alphaiThe subscript is the position corresponding to the non-zero element in e, and the column is, when N is 1,
Figure GDA0003003737400000072
Figure GDA0003003737400000073
each Bob thus gets a respective observed ei；
S43: according to eiObtaining an observed key symbol KiAnd a key bit
Figure GDA0003003737400000074
S44: each Bob observed eiIndependent demodulation symbol on antenna serial number corresponding to medium non-zero element
Figure GDA0003003737400000075
And obtain demodulated ciphertext bits
Figure GDA0003003737400000076
I.e. independently demodulating the encrypted modulation symbols
Figure GDA0003003737400000077
And obtaining the encrypted bits
Figure GDA0003003737400000078
Step S5: each legitimate receiver Bob uses the observation key bits
Figure GDA0003003737400000079
Exclusive OR (XOR)
Figure GDA00030037374000000710
Obtaining the confidential bit information that is finally transmitted by Alice to each Bob
Figure GDA00030037374000000711
Repeating steps S2 to S5, and securely transmitting the confidential information between the two parties of the legal communication; bob and Eve final bit error rate performance are shown in FIG. 3, where Eve uses 4,8,100 cooperative nodes, respectively.
The foregoing shows and describes the general principles and broad features of the present invention and advantages thereof. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims.

Claims (5)

1. A multi-user physical layer secure communication method capable of resisting against any plurality of cooperative eavesdroppers is characterized in that each legal receiver determines the number of receiving antennas used by the legal receiver and the number of required transmitted symbol streams to the legal transmitter, wherein the number of the antennas and the number of the symbol streams of each legal receiver can be different, and the number of the symbol streams, the number of the antennas and the modulation mode of each legal receiver can be flexibly adjusted; the method comprises the following steps:
s1: the method comprises the following steps that a legal sender Alice and a plurality of legal receivers Bob carry out communication confirmation;
s2: a legal sender Alice randomly generates keys corresponding to a plurality of Bobs, and modulates a ciphertext bit stream after encrypting confidential bits into a symbol to be sent; mapping key bits corresponding to the N Bobs into key symbols, wherein each key symbol corresponds to a vector for activating different receiving antennas of each Bob;
s3: calculating the precoding of the key symbol corresponding to each Bob activation vector, and broadcasting the encrypted modulation symbol by using N Bob precoding matrixes;
s4: a legal receiver Bob independently measures the received signal strength of each activated antenna, estimates an antenna vector, obtains a key symbol and a key bit by inverse mapping, and demodulates the encrypted modulation symbols in sequence to obtain the encrypted bit;
s5: each legal receiver Bob XOR-demodulates the key bit observed by the legal receiver Bob to obtain the confidential bit information;
s6: repeating steps S2 through S5;
the step S2 includes the following steps:
s21: alice randomly generates N MSBit key bit bk＝(bk，1，bk,2,...,bk，N) And use of bkExclusive-or secret information b ═ b1,b2,...,bN) The following were used:
Figure FDA0003003737390000011
s22: alice encrypts the ciphertext bit stream bs＝(bs,1,bs,2,...,bs,N) Modulating into a symbol to be transmitted s ═(s)1,..,sN)；
S23: alice determines that each key symbol corresponds to a different receive antenna K {0,1,2k-1} and all possible antenna combinations are represented by a vector E;
s24: alice sends the key bit bkMapping to key symbol K ═ (K)1，K2，..,KN)∈K；
S25: different columns E (: K +1) in E are selected as selection references for precoding to transmit different Bobs according to the value of K.
2. The method for multi-user physical layer secure communication against any number of cooperating eavesdroppers of claim 1, wherein the step S1 comprises:
s11: each Bob determines the number of receiving antennas N required by each Bob to AliceBThe number N of modulation symbol streams transmitted simultaneously with Alice, wherein N is more than or equal to 1 and less than or equal to NB-1 such that:
Figure FDA0003003737390000012
MS＝log2(NK)；
s12: alice sets binary bit source information b as (b)1,b2,...,bN) Dividing into N shares, each share b corresponding to secret bit information sent to each BobiN each contain a bit;
the M isSConstellation signal order for the modulation scheme used by multiple Bob.
3. The method of multi-user physical layer secure communication against any number of cooperating eavesdroppers of claim 1, wherein the step S3 comprises the steps of:
s31: calculating an alternative pre-coding space W;
s32: dividing the corresponding column of W into corresponding space W (K) according to the number of receiving antennas of each Bobi) Wherein, K isiRespectively correspond to BobiSelecting a space range by a corresponding key symbol;
s33: for each Bob, choose its W (K)i) The number of non-zero columns in the corresponding E ═ E (: K +1) in (a) is w (E);
W(ei)＝W(Ki)E(:,K+1)；
s34: each W (e)i) Combined into W (e) ═ W (e)1),....,W(eN)]；
S35: transmitting symbols s ═(s) using W (e) precoding matrix1,..,sN)。
4. The method of multi-user physical layer secure communication against any number of cooperating eavesdroppers of claim 1, wherein the step S4 comprises the steps of:
s41: each Bob receives the signal
Figure FDA0003003737390000021
The signal plus noise strength of each antenna was then measured directly: alpha is alphai＝|yi|2，i＝1,2,...NB；
S42: selecting one or more of the largest alphaiGet the e of each Bob's individual observation according to its indexi；
S43: according to eiObtaining an observed key symbol KiAnd a key bit
Figure FDA0003003737390000022
S44: each Bob observed eiIndependently demodulating the encrypted modulation symbols on the antenna serial numbers corresponding to the N nonzero elements
Figure FDA0003003737390000023
And obtain the ciphertext bit
Figure FDA0003003737390000024
5. The multi-user physical layer secure communication method against any number of cooperating eavesdroppers of claim 1, wherein each legitimate receiver Bob observes its own bits of the key
Figure FDA0003003737390000025
XOR the encrypted bits
Figure FDA0003003737390000026
Obtaining the confidential bit information which is finally transmitted to each Bob by Alice broadcasting:
Figure FDA0003003737390000027
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