Semantic effective secure identification communication method based on classical quantum channel

Abstract

A semantically secure identification and communication method based on classical quantum channels comprises the following steps: constructing a classical quantum channel, selecting the input signal distribution and dividing the codeword, constructing an encoder, joint decoding, verification and identification, reliability analysis, and information leakage analysis. This invention divides the communication codeword into a main block and an auxiliary block. The main block uses an output statistical approximation of the transmission codebook, making it impossible for eavesdroppers to distinguish the communication signal from background noise. The auxiliary block uses a hash function for random mapping, preventing eavesdroppers from extracting valid information, thus achieving semantic security. Mapping the identification message to a combination of seed and hash value reduces the probability of confusion between different identification messages, improves identification accuracy, and provides a coding basis for analyzing false alarms, missed alarms, and information leakage. This invention has advantages such as strong confidentiality, strong concealment, high identification accuracy, and the ability to achieve identification communication while satisfying semantically secure requirements. It can be used for classical quantum secure communication.

Description

Technical Field

[0001] This invention belongs to the field of quantum information processing and communication security technology, specifically involving semantically effective confidential identification communication. Background Technology

[0002] The emergence of quantum algorithms such as Shor's algorithm poses a serious threat to the survival of traditional public-key encryption systems based on large integer factorization and discrete logarithm problems. To mitigate the security risks brought by quantum computing, physical layer security technologies utilize the physical properties of the channel itself, such as noise, attenuation, and quantum state superposition, to achieve unconditional security. This has become one of the core research directions for post-quantum communication and future 6G mobile networks.

[0003] Identification communication differs from traditional message transmission models in that the receiver only needs to determine whether the sender has sent a specific message. Research by Ahlswede and Dueck demonstrates that in this model, the number of codewords supported by the system exhibits a remarkable double exponential growth with block length, providing extremely high resource utilization for massive access and ultra-large-scale authentication scenarios. In open communication environments, systems not only face the risk of message content leakage but may also encounter more covert security threats such as the detection of communication behavior and the analysis of transmission characteristics. These risks place higher demands on the reliability and confidentiality of identification communication, requiring the construction of security mechanisms capable of simultaneously resisting content theft and behavioral detection.

[0004] While research on quantum identification channels has made progress under both weak and strong security conditions, proving the universality of double exponential gain in the quantum domain, it still faces two key challenges: First, traditional security standards typically assume that attackers are unaware of the message distribution. However, in complex network environments, powerful attackers often possess prior knowledge about the message source, requiring the system to achieve a level of "semantic secrecy." Second, in special communication or privacy protection scenarios requiring extremely high security, content encryption alone is insufficient; covert communication is also necessary to ensure that the communication itself remains undetected. The academic community has combined these two requirements, proposing a semantically effective security standard. In classical quantum eavesdropping channels, due to the complexity of quantum state non-orthogonality, coherence, and quantum soft-covering properties, how to construct an encoding method that can guarantee semantic secrecy, ensure continuous concealment, and effectively utilize the capacity advantage of identity recognition remains an unresolved bottleneck in the field of quantum information theory. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a semantically effective confidential identification and communication method based on classical quantum channels that has strong confidentiality, strong concealment and high identification accuracy.

[0006] The technical solution adopted to solve the above technical problems is:

[0007] (1) Constructing a classical quantum channel

[0008] Classical quantum channels include legitimate channels Eavesdropping on channels .

[0009] Construct a legitimate channel using the following formula :

[0010]

[0011] in, This represents the classical discrete-state input of the physical layer modulation signal. This represents the quantum density operator corresponding to the legitimate channel receiver.

[0012] Constructing an eavesdropping channel using the following formula :

[0013]

[0014] in, This represents the quantum density operator corresponding to the receiver of the eavesdropping channel.

[0015] (2) Selecting the input signal distribution and dividing the codeword

[0016] Input signal Satisfy physical signal input distribution The security threshold that meets the preset mutual information difference Determine the safety threshold using the following formula. :

[0017]

[0018] in, , This represents the quantum mutual information induced by the legitimate channel on the input signal. This represents the quantum mutual information induced by the eavesdropping channel on the input signal.

[0019] The communication codeword is divided into a main block and an auxiliary block. The main block uses an output statistical approximation transmission codebook, and the transmission rate is... , The auxiliary block uses an effective confidential transmission codebook with a transmission rate of [missing information]. ,

[0020] .

[0021] The sending system sets the total length of the communication codeword blocks. The length of the codeword block is determined according to formula (1). :

[0022] (1)

[0023]

[0024] in, The length of the main block, The length of the auxiliary block, , , The value can be a finite number of positive integers. This is for rounding up.

[0025] (3) Constructing the encoder

[0026] The sending system introduces an approximate universal hash function. , ; This represents the total set of identification messages supported by the system. 1, 2, , , Indicates the total number of identified messages. The value can be a finite number of positive integers. The set representing the seed sequence of the main block. 1,2, , Indicates the total number of messages in the main block. The value can be a finite number of positive integers. Represents the set of auxiliary block hash values , Indicates the total number of auxiliary block messages. The value can be a finite set of positive integers; from the total set of identified messages Extract identification message , Take a seed from the set of main block seed sequences. Calculate the corresponding hash value h using a hash function:

[0027]

[0028] in, Indicates a given identification message The hash mapping calculation function uses a time-series concatenation method, placing the seed in the system's underlying data sending buffer queue. Corresponding physical signal As a preamble frame, along with the hash value Corresponding physical signal As a subsequent signal frame, the two sequences are concatenated to generate a classic codeword. Build an encoder:

[0029] ;

[0030] The transmission system uses a joint probability distribution Classic coding Send it to a classical quantum channel.

[0031] (4) Joint decoding

[0032] The receiving system receives a legitimate channel. Output quantum state The decoder measures the main block and auxiliary block using positive definite operator values ​​respectively, and performs joint decoding according to the following formula to obtain the seed estimate. and hash estimate :

[0033]

[0034]

[0035] in, This represents the independent variable that yields the maximum value. A function for calculating the trace of the quantum state density matrix; The quantum state density operator represents the corresponding main block of the receiving system. , This represents the quantum state density operator of the auxiliary block at the receiving end. .

[0036] (5) Verification and recognition

[0037] Receive system preset target messages to be identified Call the same approximate general hash function as the sending system. Combined with the extracted seed estimate Calculate the local verification value :

[0038]

[0039] in, Indicates a given target message The hash mapping calculation function receives the local verification value from the system. Compared with hash estimate Verification and judgment. The following decision function is used for judgment:

[0040]

[0041] A value of 1 indicates successful recognition by the receiving system. If the value is 0, the receiving system outputs a rejection signal.

[0042] (6) Reliability analysis

[0043] 1) Determine the underreporting error

[0044] The sending system sends identification messages. Local verification value Compared with hash estimate The unequal conditional probabilities are the false negative error; the upper bound of the false negative error. Seed estimate Error probability and hash estimate The sum of error probabilities; , This indicates the main block fault tolerance threshold. The value is 10 -6 , This represents the fault tolerance threshold of the auxiliary block. The value is 10 -6 underreporting error It meets the error standard.

[0045] 2) Determine the false alarm error

[0046] The sending system sends identification messages. Receiving the system's preset target message is Local verification value Compared with hash estimate Equal conditional probabilities constitute the false alarm error; the upper bound of the false alarm error... For hash collision probability and seed The sum of the estimated error rate, the hash estimated error rate, and the total error rate.

[0047] , This indicates the tolerance of the hash collision system. The value is 10 -9 False alarm

[0048] Difference It meets the error standard.

[0049] (7) Information leakage analysis

[0050] Eavesdropping channels in classical quantum channels Send identification message Output quantum state .

[0051] Determine the total amount of information leakage using the following formula :

[0052]

[0053] =

[0054] in, , , These represent states without information security background; These represent the eavesdropping channels. For length of and The quantum transfer operator tensor product of the input sequence.

[0055] The upper limit of the total information leakage amount is determined by the following formula. :

[0056]

[0057] in, This indicates the upper limit of the average leakage amount of the main block; Indicates the maximum leakage of the auxiliary block;

[0058] , This indicates the threshold for tolerable leakage in the main block. This indicates the threshold for acceptable leakage in the auxiliary block, where the leakage rate meets the error standard.

[0059] In step (2) of the present invention, which involves selecting the input signal distribution and dividing the codewords, the transmitting system sets the length of the total communication codeword block. The length of the codeword block is determined according to formula (1). :

[0060] (1)

[0061]

[0062] in, The length of the main block, The length of the auxiliary block, The value ranges from 930 to 1640. The value ranges from 900 to 1600. The value ranges from 30 to 40.

[0063] In step (2) of the present invention, the formula (1) for selecting the input signal distribution and dividing the codeword, the... The optimal value is 1033. The optimal value is 1000. The optimal value is 33.

[0064] In step (3) of the present invention, the total number of identification messages is... Determine by the following formula:

[0065]

[0066] The total number of main block messages Determine by the following formula:

[0067]

[0068] The total number of auxiliary block messages Determine by the following formula:

[0069] .

[0070] In step (3) of the present invention, when constructing the encoder, the joint probability distribution is... The construction method is as follows:

[0071]

[0072]

[0073] in, For the Kronek state indication function, This represents the probability distribution function of the random encoding mapping of the effective secure transmission codebook used by the system's underlying auxiliary blocks.

[0074] This invention, by dividing the communication codeword into main blocks and auxiliary blocks, and combining an approximate universal hash function with a quantum soft overlay mechanism, satisfies the dual requirements of semantic confidentiality and behavioral concealment in classical quantum channels. The main block uses an output statistical approximation of the transmission codebook, making it impossible for eavesdroppers to distinguish the communication signal from background noise. The auxiliary block introduces random mappings through a hash function, preventing eavesdroppers from extracting valid information even with prior knowledge of the message source, thus achieving semantic confidentiality. This invention maps the identification message to a combined encoding form of a seed and a hash value, reducing the probability of confusion between different identification messages, improving the accuracy of the receiving system's identification, and providing a clear coding foundation for analyzing false alarm errors, missed alarm errors, and information leakage. Through joint decoding, hash verification, and the limitation of upper bounds on missed alarm errors, false alarm errors, and total information leakage, this invention enables not only identification communication but also effective semantic confidentiality. The proposed coding structure is concise and efficient, compatible with existing classical quantum communication system architectures, and easy to deploy in classical quantum secure communication devices. Its parameter configuration is flexible, dynamically adjusting the block length and rate according to security requirements, exhibiting good scalability and robustness.

[0075] This invention has the advantages of strong confidentiality, strong concealment, high identification accuracy, and the ability to achieve identification communication while satisfying semantic effective confidentiality. It can be used in classical quantum secure communication. Attached Figure Description

[0076] Figure 1 This is a flowchart of Embodiment 1 of the present invention. Detailed Implementation

[0077] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments, but the present invention is not limited to the following embodiments.

[0078] Example 1

[0079] The semantically effective secure identification communication method based on classical quantum channels in this embodiment consists of the following steps (see...). Figure 1 ):

[0080] (1) Constructing a classical quantum channel

[0081] Classical quantum channels include legitimate channels Eavesdropping on channels .

[0082] Construct a legitimate channel using the following formula :

[0083]

[0084] in, This represents the classical discrete-state input of the physical layer modulation signal. This represents the quantum density operator corresponding to the legitimate channel receiver.

[0085] Constructing an eavesdropping channel using the following formula :

[0086]

[0087] in, This represents the quantum density operator corresponding to the receiver of the eavesdropping channel.

[0088] (2) Selecting the input signal distribution and dividing the codeword

[0089] Input signal Satisfy physical signal input distribution The security threshold that meets the preset mutual information difference Determine the safety threshold using the following formula. :

[0090]

[0091] in, , This represents the quantum mutual information induced by the legitimate channel on the input signal. surface

[0092] This demonstrates the quantum mutual information induced by the eavesdropping channel on the input signal.

[0093] The communication codeword is divided into a main block and an auxiliary block. The main block uses an output statistical approximation transmission codebook, and the transmission rate is... , The auxiliary block uses an effective confidential transmission codebook with a transmission rate of [missing information]. , .

[0094] The sending system sets the total length of the communication codeword blocks. The length of the codeword block is determined according to formula (1). :

[0095] (1)

[0096]

[0097] in, The length of the main block, The length of the auxiliary block, The value ranges from 930 to 1640 in this embodiment. The value is 1033. The value ranges from 900 to 1600 in this embodiment. The value is 1000. The value is between 30 and 40 in this embodiment. The value is 33. This is for rounding up.

[0098] This invention, by dividing the communication codeword into a main block and an auxiliary block, and combining an approximate universal hash function with a quantum soft overlay mechanism, satisfies the dual requirements of semantic confidentiality and behavioral concealment in classical quantum channels. The main block uses an output statistical approximation of the transmission codebook, making it impossible for eavesdroppers to distinguish between communication signals and background noise; the auxiliary block introduces random mappings through a hash function, so even if the eavesdropper has prior knowledge of the message source, they cannot extract valid information from it, thus achieving semantic confidentiality.

[0099] (3) Constructing the encoder

[0100] The sending system introduces an approximate universal hash function. , ; This represents the total set of identification messages supported by the system. 1, 2, , , This indicates the total number of identified messages. Determine by the following formula:

[0101] ,

[0102] The set representing the seed sequence of the main block. 1,2, , This represents the total number of main block messages. Determine by the following formula:

[0103]

[0104] Represents the set of auxiliary block hash values , This represents the total number of auxiliary block messages. Determine by the following formula:

[0105]

[0106] From the total collection of identified messages Extract identification message , Take a seed from the set of main block seed sequences. Calculate the corresponding hash value h using a hash function:

[0107]

[0108] in, Indicates a given identification message The hash mapping calculation function uses a time-series concatenation method, placing the seed in the system's underlying data sending buffer queue. Corresponding physical signal As a preamble frame, along with the hash value Corresponding physical signal As a subsequent signal frame, the two sequences are concatenated to generate a classic codeword. Build an encoder:

[0109]

[0110] The transmission system uses a joint probability distribution Classic coding Send it to a classical quantum channel.

[0111] The joint probability distribution in this embodiment The construction method is as follows:

[0112]

[0113]

[0114] in, For the Kronek state indication function, This represents the probability distribution function of the random encoding mapping of the effective secure transmission codebook used by the system's underlying auxiliary blocks.

[0115] Because this invention maps identification messages into a combined encoding form of seeds and hash values, it reduces the probability of confusion between different identification messages, improves the accuracy of identification by the receiving system, and provides a clear encoding basis for the analysis of false alarm errors, missed alarm errors, and information leakage.

[0116] (4) Joint decoding

[0117] The receiving system receives a legitimate channel. Output quantum state The decoder measures the main block and auxiliary block using positive definite operator values ​​respectively, and performs joint decoding according to the following formula to obtain the seed estimate. and hash estimate :

[0118]

[0119]

[0120] in, This represents the independent variable that yields the maximum value. A function for calculating the trace of the quantum state density matrix; The quantum state density operator represents the corresponding main block of the receiving system. , This represents the quantum state density operator of the auxiliary block at the receiving end. .

[0121] (5) Verification and recognition

[0122] Receive system preset target messages to be identified Call the same approximate general hash function as the sending system. Combined with the extracted seed estimate Calculate the local verification value :

[0123]

[0124] in, Indicates a given target message The hash mapping calculation function receives the local verification value from the system. Compared with hash estimate Verification and judgment are performed according to the following decision function.

[0125]

[0126] A value of 1 indicates successful recognition by the receiving system. If the value is 0, the receiving system outputs a rejection signal.

[0127] (6) Reliability analysis

[0128] 1) Determine the underreporting error

[0129] The sending system sends identification messages. Local verification value Compared with hash estimate The unequal conditional probabilities are the false negative error; the upper bound of the false negative error. Seed estimate Error probability and hash estimate The sum of error probabilities; , This indicates the main block fault tolerance threshold. The value is 10 -6 , This represents the fault tolerance threshold of the auxiliary block. The value is 10 -6 underreporting error It meets the error standard.

[0130] 2) Determine the false alarm error

[0131] The sending system sends identification messages. Receiving the system's preset target message is Local verification value Compared with hash estimate Equal conditional probabilities constitute the false alarm error; the upper bound of the false alarm error... For hash collision probability and seed The sum of the estimated error rate, the hash estimated error rate, and the total error rate.

[0132] , This indicates the tolerance of the hash collision system. The value is 10 -9 False alarm

[0133] Difference It meets the error standard.

[0134] (7) Information leakage analysis

[0135] Eavesdropping channels in classical quantum channels Send identification message Output quantum state .

[0136] Determine the total amount of information leakage using the following formula :

[0137]

[0138] =

[0139] in, , , These represent states without information security background; These represent the eavesdropping channels. For length of and The quantum transfer operator tensor product of the input sequence.

[0140] The upper limit of the total information leakage amount is determined by the following formula. :

[0141]

[0142] in, This indicates the upper limit of the average leakage amount of the main block. This indicates the maximum leakage of the auxiliary block.

[0143] , This indicates the threshold for tolerable leakage in the main block. This indicates the threshold for acceptable leakage in the auxiliary block, where the leakage rate meets the error standard.

[0144] This invention enables the method to not only identify communication but also satisfy semantically effective confidentiality by combining decoding, hash verification, and limiting the upper bounds of missed detection error, false detection error, and total information leakage.

[0145] Complete a semantically effective secure identification and communication method based on classical quantum channels.

[0146] Example 2

[0147] The semantically effective secure identification communication method based on classical quantum channels in this embodiment consists of the following steps:

[0148] (1) Constructing a classical quantum channel

[0149] The steps are the same as in Example 1.

[0150] (2) Selecting the input signal distribution and dividing the codeword

[0151] The sending system sets the total length of the communication codeword blocks. The length of the codeword block is determined according to formula (1). :

[0152] The expression of equation (1) is the same as that in Example 1.

[0153] In equation (1), The length of the main block, The length of the auxiliary block, The value ranges from 930 to 1640 in this embodiment. The value is 930. The value ranges from 900 to 1600 in this embodiment. The value is 900. The value is between 30 and 40 in this embodiment. The value is 30. The other parameters and variables in equation (1) and their ranges are the same as in Example 1.

[0154] The other steps in this procedure are the same as in Example 1.

[0155] The other steps are the same as in Example 1, thus completing the semantically effective confidential identification and communication method based on classical quantum channels.

[0156] Example 3

[0157] The semantically effective secure identification communication method based on classical quantum channels in this embodiment consists of the following steps:

[0158] (1) Constructing a classical quantum channel

[0159] The steps are the same as in Example 1.

[0160] (2) Selecting the input signal distribution and dividing the codeword

[0161] The sending system sets the total length of the communication codeword blocks. The length of the codeword block is determined according to formula (1). :

[0162] The expression of equation (1) is the same as that in Example 1.

[0163] In equation (1), The length of the main block, The length of the auxiliary block, The value ranges from 930 to 1640 in this embodiment. The value is 1640. The value ranges from 900 to 1600 in this embodiment. The value is 1600. The value is between 30 and 40 in this embodiment. The value is 40. The other parameters and variables in equation (1) and their ranges are the same as in Example 1.

[0164] The other steps in this procedure are the same as in Example 1.

[0165] The other steps are the same as in Example 1, thus completing the semantically effective confidential identification and communication method based on classical quantum channels.

Claims

1. A semantically efficient secure identification and communication method based on classical quantum channels, characterized in that... It consists of the following steps: (1) Constructing a classical quantum channel Classical quantum channels include legitimate channels Eavesdropping on channels ; Construct a legitimate channel using the following formula : in, This represents the classical discrete-state input of the physical layer modulation signal. This represents the quantum density operator corresponding to the legitimate channel receiver. Constructing an eavesdropping channel using the following formula : in, This represents the quantum density operator corresponding to the receiver of the eavesdropping channel. (2) Selecting the input signal distribution and dividing the codeword Input signal Satisfy physical signal input distribution The security threshold that meets the preset mutual information difference Determine the safety threshold using the following formula. : in, , This represents the quantum mutual information induced by the legitimate channel on the input signal. This represents the quantum mutual information induced by the eavesdropping channel on the input signal; The communication codeword is divided into a main block and an auxiliary block. The main block uses an output statistical approximation transmission codebook, and the transmission rate is... , The auxiliary block uses an effective confidential transmission codebook with a transmission rate of [missing information]. , ; The sending system sets the total length of the communication codeword blocks. The length of the codeword block is determined according to formula (1). : （1） in, The length of the main block, The length of the auxiliary block, , , The value can be a finite number of positive integers. To round up; (3) Constructing the encoder The sending system introduces an approximate universal hash function. , ; This represents the total set of identification messages supported by the system. 1, 2, , , Indicates the total number of identified messages. The value can be a finite number of positive integers. The set representing the seed sequence of the main block. 1,2, , Indicates the total number of messages in the main block. The value can be a finite number of positive integers. Represents the set of auxiliary block hash values , Indicates the total number of auxiliary block messages. The value can be a finite set of positive integers; from the total set of identified messages Extract identification message , Take a seed from the set of main block seed sequences. Calculate the corresponding hash value h using a hash function: in, Indicates a given identification message The hash mapping calculation function uses a time-series concatenation method, placing the seed in the system's underlying data sending buffer queue. Corresponding physical signal As a preamble frame, along with the hash value Corresponding physical signal As a subsequent signal frame, the two sequences are concatenated to generate a classic codeword. Build an encoder: ； The transmission system uses a joint probability distribution Classic coding Send to a classical quantum channel; (4) Joint decoding The receiving system receives a legitimate channel. Output quantum state The decoder measures the main block and auxiliary block using positive definite operator values ​​respectively, and performs joint decoding according to the following formula to obtain the seed estimate. and hash estimate : in, This represents the independent variable that yields the maximum value. A function for calculating the trace of the quantum state density matrix; The quantum state density operator represents the corresponding main block of the receiving system. , Indicates the corresponding auxiliary receiver. Quantum state density operator of the auxiliary block ; (5) Verification and recognition Receive system preset target messages to be identified Call the same approximate general hash function as the sending system. Combined with the extracted seed estimate Calculate the local verification value : in, Indicates a given target message The hash mapping calculation function receives the local verification value from the system. Compared with hash estimate The verification and judgment are performed according to the following decision function: A value of 1 indicates successful recognition by the receiving system. A value of 0 indicates that the receiving system outputs a rejection signal. (6) Reliability analysis 1) Determine the underreporting error The sending system sends identification messages. Local verification value Compared with hash estimate The unequal conditional probabilities are the false negative error; the upper bound of the false negative error. Seed estimate Error probability and hash estimate The sum of error probabilities; , This indicates the main block fault tolerance threshold. The value is 10 -6 , This represents the fault tolerance threshold of the auxiliary block. The value is 10 -6 underreporting error Meets error standards; 2) Determine the false alarm error The sending system sends identification messages. Receiving the system's preset target message is Local verification value Compared with hash estimate Equal conditional probabilities constitute the false alarm error; the upper bound of the false alarm error... For hash collision probability and seed The sum of the estimated error rate, the hash estimated error rate, and the total error rate; , This indicates the tolerance of the hash collision system. The value is 10 -9 False alarm error Meets error standards; (7) Information leakage analysis Eavesdropping channels in classical quantum channels Send identification message Output quantum state , Determine the total amount of information leakage using the following formula : = in, , , These represent states without information security background; These represent the eavesdropping channels. For length of and The quantum transfer operator tensor product of the input sequence; The upper limit of the total information leakage amount is determined by the following formula. : in, This indicates the upper limit of the average leakage amount of the main block. Indicates the maximum leakage of the auxiliary block; , This indicates the threshold for tolerable leakage in the main block. This indicates the threshold for acceptable leakage in the auxiliary block, where the leakage rate meets the error standard.

2. The semantically efficient secure identification and communication method based on classical quantum channels according to claim 1, characterized in that... In step (2), when selecting the input signal distribution and dividing the codewords, the transmitting system sets the total length of the communication codeword block. The length of the codeword block is determined according to formula (1). : （1） in, The length of the main block, The length of the auxiliary block, The value ranges from 930 to 1640. The value ranges from 900 to 1600. The value ranges from 30 to 40.

3. The semantically efficient secure identification and communication method based on classical quantum channels according to claim 1 or 2, characterized in that: In step (2), the input signal distribution and codeword division formula (1) are selected. The value is 1033. The value is 1000. The value is 33.

4. The semantically efficient secure identification and communication method based on classical quantum channels according to claim 1, characterized in that... In step (3) of constructing the encoder, the total number of identification messages... Determine using the following formula: The total number of main block messages Determine using the following formula: The total number of auxiliary block messages Determine using the following formula: 。 5. The semantically effective confidential identification and communication method based on classical quantum channels according to claim 1, characterized in that... In step (3) of constructing the encoder, the joint probability distribution The construction method is as follows: in, For the Kronek state indication function, This represents the probability distribution function of the random encoding mapping of the effective secure transmission codebook used by the system's underlying auxiliary blocks.

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