A multi-address time-based blockchain covert communication method

Abstract

The present invention discloses a multi-address time-based blockchain covert communication method, including: 1) defining multi-address time-based blockchain covert communication; 2) the transmission process of covert information; 3) transaction interval control in covert communication. This method has the advantages of good anti-detection and good confidentiality, and this method can improve the transmission rate of covert communication.

Description

Technical Field

[0001] The present invention relates to the field of blockchain covert communication technology, and in particular to a covert communication method using multiple addresses to participate in controlling the time interval of blockchain transactions, specifically a multi-address time-based blockchain covert communication method. Background Art

[0002] Covert communication refers to the use of normal communication behavior to transmit secret information. Covert communication can greatly reduce the risk of information being attacked during transmission. Unlike general encrypted communication, covert communication generally uses a public information carrier. The covert information is hidden in the main information and transmitted along with the main information. All users can read or receive the main information, but only the target recipient of the covert communication has a way to decrypt the covert information. Other users cannot detect the ongoing covert communication behavior. However, once the attacker has enough time and computer resources to conduct targeted detection on the communication party with covert behavior, the covert channel can be distinguished and detected.

[0003] Blockchain, especially public blockchain, is known for its decentralization and immutability. The decentralized structure formed by the consensus of most nodes provides an anonymous environment. The transaction content in the block is the transfer process between randomly generated addresses, not the actual account, so the account owner cannot be known through the transaction address. The uniqueness of the hash function is used to connect the generated blocks in series in timestamp order to ensure that the content of the block cannot be tampered with, which has strong security. It is very difficult for a third-party detector to find users with covert communication behavior in a transaction environment with a random address. Therefore, the blockchain platform is an ideal information carrier for realizing covert communication.

[0004] Network covert channels can be divided into storage-type network covert channels and time-type network covert channels. Storage-type network covert channels use the information inside the protocol data unit to transmit covert data, while time-type network covert channels use the time characteristics of the protocol data unit to transmit covert data. Time-type covert communication has better concealment than storage-type covert communication, but the transmission rate is lower than storage-type covert communication.

[0005] Bitcoin and Ethereum are currently the most active and complete public chains, and most of the existing research on blockchain covert communication is based on these two. Most of these studies are based on the idea of ​​hiding the special location of the address or field, which is classified as a storage-type covert method. The time-based blockchain covert method does not rely on special addresses but encodes the interval of transaction timestamps to carry hidden information, which has unique concealment. However, the limited amount of information per unit time in this method limits the transmission rate of covert communication, and there are few related studies. Therefore, it is necessary to propose a method that can improve the transmission rate of time-based blockchain covert communication and can reflect its concealment to a greater extent. Summary of the invention

[0006] The purpose of the present invention is to provide a multi-address time-based blockchain covert communication method to address the deficiencies of the prior art. This method has the advantages of good anti-detection and good confidentiality, and can increase the transmission rate of covert communication.

[0007] The technical solution for achieving the purpose of the present invention is:

[0008] A multi-address time-based blockchain covert communication method, comprising the following steps:

[0009] 1) Define multi-address time-based blockchain covert communication: The sender and receiver of covert communication negotiate in advance to obtain the address pool participating in the covert communication, where special addresses serve as start, end and pause signals, and the remaining addresses serve as carriers of covert information. The sender and receiver unify the encoding and decryption methods of ciphertext. The sender encrypts the ciphertext information to be sent, and the encrypted ciphertext is evenly distributed to all addresses participating in the covert communication as the covert communication task of each address. The sender uses a special address to initiate a transaction pointing to the receiver's address, indicating the start of covert communication. Subsequent transactions are initiated by ordinary addresses in the address pool. The direction of these transactions is not limited to the receiver's address. With the consensus of the blockchain system, these transactions exist in each block. The receiver only needs to traverse the blocks according to the address pool to determine whether these addresses appear, and share the covert communication task to more addresses, which improves the transmission rate of the covert communication system. At the same time, each address has a shorter covert communication time, reducing the specificity of the address; the receiver first obtains the transaction initiation distribution of each address after screening according to the address list, and then sorts it according to the timestamp of transaction initiation until the address that receives the end mark starts decryption. The specific process is as follows:

[0010] 1-1) Preparation before covert communication: Off-chain pre-negotiation content: The address pool for the sender to initiate covert communication includes special addresses, information encoding and encryption rules corresponding to the ciphertext. The negotiation process of exchanging transaction addresses is generally present in the initial stage of blockchain transactions. Therefore, it is reasonable and feasible for both parties to exchange address pool information off-chain.

[0011] 1-2)) Encoding method of ciphertext: In time-based covert communication, multi-base modulation ciphertext requires a longer time interval to correspond to the codeword. The transmission rate of time-based covert communication η=(1+M) / 2log2M, where (1+M) / 2 represents the average block time for transmitting a codeword. η converges to M=4, which is 1.25 blocks to transmit 1 bit. The binary transmission rate is 1.5 blocks to transmit 1 bit. After the extreme point, as the coding base increases, the transaction interval becomes larger and larger, and the transmission rate decreases instead. Therefore, quaternary coding or two-bit binary coding rules can be used to achieve the best effect.

[0012] 1-3) Encryption rules for ciphertext: The ciphertext is encrypted using an asymmetric encryption system based on the public key and private key of the blockchain itself, so that only the recipient with the corresponding key can decrypt the encrypted ciphertext;

[0013] 1-4) Start and end marks of covert communication: the sender uses a special address add s The address sent to the recipient indicates the start and end of the covert communication, and the other addresses correspond to the fragment M of the ciphertext M. i , the special address can be selected from the addresses owned by the sender itself, or generated by the Vanitygen program. The specified address bit is specified with a value and the address is automatically generated. The receiver traverses the blocks where the consensus is completed to see if these addresses participating in the covert communication exist, calculates the timestamp intervals of these addresses appearing in the blocks, and converts the intervals into ciphertext fragments against the ciphertext table. After combining, the complete ciphertext is obtained, so that multiple addresses can participate in the covert communication within one block time, and the covert communication task is shared among more addresses, which improves the transmission rate of the covert communication system. At the same time, each address has a shorter covert communication time, reducing the specificity of the address;

[0014] 1-5) After the receiver receives the transaction from the special address, it starts to traverse all the addresses of the sender that participate in the covert communication in the next block. The transactions of these addresses can point to any address, not just the receiver, so it does not affect the sender's normal transactions. Since the block timestamp does not need to be obtained additionally, the receiver only needs to traverse whether the address in the address pool appears in this block, thus reducing the traversal overhead;

[0015] 1-6) The receiver first obtains the transaction initiation distribution of each address by screening the address list, and then sorts them according to the timestamp of the transaction initiation until the address that receives the end mark starts decryption. The interval between two transactions is represented as hidden information. The short transaction interval Δt1' is set as "0" and the long transaction interval Δt'2 is set as "1" using binary as the modulation method of the ciphertext. The ciphertext fragments corresponding to the transaction intervals of all addresses are combined to obtain the complete encrypted ciphertext. The order of the ciphertext fragments is guaranteed by the order of the address pool. The order of the address pool can be based on the alphabetical order of the address or the rules agreed in advance by both parties. Then, the ciphertext is decrypted according to the encryption rules agreed in advance to obtain the ciphertext;

[0016] 1-7) When a transaction is not packaged into the corresponding block in time due to insufficient transaction fees or congestion of the blockchain system, resulting in the address not being read in the latest block, the sender adds a transaction initiated by a special address in the next block to indicate the suspension and invalidation of this information. The transaction receiver points to the receiver and the delayed packaged address, and the delayed address is suspended from initiating the next communication until the sender and receiver find that the delayed address appears in the subsequent block in the new block, ending the suspension;

[0017] 2) The transmission process of hidden information: The blockchain system packages transactions in a time period and assigns the same timestamp, while time-based covert communication uses time intervals as a carrier to hide ciphertexts. The length of the intervals corresponds to different codewords. Therefore, the addresses participating in the covert communication will appear in the block with block timestamps at intervals within a period of time. If this rule is used as the judgment condition for detecting whether there are special addresses in the block, a large number of normal samples will be counted as suspicious samples. In addition, because the number of addresses participating in the transmission of ciphertext in this technical solution increases, the time for each address to undertake the covert communication task is greatly shortened, making it more difficult to distinguish from normal samples, so the concealment is better. If the transaction initiation time interval of the detection address, that is, the transaction to be confirmed, is more randomized, the regular covert communication address will become more special and easier to distinguish. The general address transaction behavior of blockchain transactions is used to count and model the general address transaction behavior to optimize the transaction initiation behavior of the covert communication address, and simplify the transaction arrival process of the entire blockchain into a Poisson flow model P with parameter λ. n (t) = (λt) n e -λt / n! , represents the probability of n transactions arriving in time interval t, parameter λ represents the average number of transactions arriving per unit time, the interval between two transactions T must obey exponential distribution, proving that P{T>t+s|T>s}=P{T>t} has Markov property, the interval between transactions is independent of the previous transaction, and the interval distribution function of transactions is exponential distribution 1-e -λt , the transaction initiation behavior in the blockchain is determined by the user, and the address pool is formed by the available addresses of active users. Then, the average number of transactions arriving in the blockchain system per unit time is λ = n T / t B , α·n B Represents the number of transactions initiated by the same address per unit time, then the average number of transactions arriving at the same address is λ α =α·n T / t B , It is concluded that both the transaction interval distribution and the transaction interval distribution of the same address theoretically obey the exponential distribution.

[0018] Among them, n A Indicates the number of addresses participating in covert communication, n B Indicates the number of current valid addresses in the blockchain system, n T Indicates the number of transactions that a block can carry, t A Indicates the time interval between transactions initiated by the same address, t B Indicates the time when the blockchain system completes the block generation, t T represents the transaction interval of the blockchain system, the probability of a single address initiating a transaction per unit time, and the covert communication is carried out in the blockchain transaction system. The transmitted ciphertext is modulated in binary. The short interval contains one block time in an average of 10 minutes, and the long interval contains two block times in an average of 20 minutes. The transmission rate of covert communication is obtained. Assume that the sender has n A The addresses used for covert communication, the probability of the codewords "0" and "1" after s ciphertext modulation is uniformly distributed, that is, the probability of the codewords appearing is equal, and the average time for an address to transmit a codeword is 15 minutes. A The average time for a sender with 1 address to transmit a codeword is 15 / n. A minutes, then the rate is 2n A / 3bit / block, the time to transmit a ciphertext of length m is t=3m / 2n A Block, and t ≥ 2, there are at least two block times to represent two codewords;

[0019] 3) Transaction interval control in covert communication: The probability of the ciphertext codeword appearing corresponds to the probability of the length of the time interval. For uniformly distributed binary ciphertext, the number of transactions contained in the two intervals is the same, and the number of transactions initiated at different times in the long and short intervals will follow the normal distribution N(μ,σ 2 ), adjust the time interval distribution to fit the exponential distribution E(λ), the number of transactions in the long and short intervals is the same, the number of transaction intervals in the long interval obeys the exponential distribution, the transactions in the short interval are concentrated at some time points so that the overall distribution is approximately exponential, and the transactions in the short interval are concentrated at some time points so that the overall distribution is approximately exponential. After completing the covert communication task, the address can enter the next covert communication according to the sender's request, and the sequence of the next covert communication can fill the vacant time point of the previous short interval. The intervals between the two transactions are approximately exponentially distributed. If the statistical sample includes the cumulative number of the two intervals, the long and short intervals are approximately exponentially distributed, and the particularity of the address transaction interval is further reduced.

[0020] Compared with the prior art, this technical solution has the following characteristics:

[0021] (1) After sending a transaction from a special address, the sender uses multiple addresses to participate in covert communication and initiate transactions. These transactions can point to any address. The receiver obtains the block timestamp intervals of all addresses participating in the covert communication through the consensus broadcast of the blockchain system, converts the intervals into ciphertext fragments according to the ciphertext table, and combines them to obtain the complete ciphertext;

[0022] (2) The time interval between transactions initiated by the same address in Bitcoin is approximately exponentially distributed. Based on this law, a method is provided to adjust the interval between transactions initiated by the address to fit the exponential distribution. The transaction interval corresponding to the ciphertext sequence is added to the normal transaction sequence and compared with the normal sequence. The fitted sequence has a lower KL divergence and better anti-detection performance.

[0023] (3) The transmission rate of the covert communication system using this technical solution increases as the number of addresses participating in the covert communication increases, reducing the specificity of the address from three aspects: first, except for the special address used as a mark, the transaction direction of all other addresses can be any address, so that the address carrying the ciphertext can not disclose the receiving address, reducing the specificity of the receiving address; second, the use of multiple addresses to realize distributed transmission of ciphertext not only improves the transmission rate but also balances the covert communication volume of each address, greatly reduces the duration of address covert communication, and reduces the specificity of the number of times the initiating address appears; third, the initiation time interval of the transaction is optimized to fit the distribution of normal samples, reducing the specificity of the initiation time interval of the sending address.

[0024] This method has the advantages of good anti-detection and good confidentiality, and can improve the transmission rate of covert communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 A schematic diagram of the process of the embodiment method;

[0026] Figure 2 Schematic diagram of the corresponding relationship of addresses in the embodiment;

[0027] Figure 3 This is a schematic diagram of the distribution of Bitcoin transactions with an interval of 0-40 minutes in the embodiment;

[0028] Figure 4 This is a schematic diagram of the transaction interval adjustment process in the embodiment;

[0029] Figure 5 Schematic diagram of approximate exponential distribution of transaction intervals after active adjustment in the embodiment. DETAILED DESCRIPTION

[0030] The content of the present invention is further described below in conjunction with the drawings and embodiments, but the present invention is not limited thereto.

[0031] Example:

[0032] Reference Figure 1 , a multi-address time-based blockchain covert communication method, comprising the following steps:

[0033] 1) Define multi-address time-based blockchain covert communication: The sender and receiver of covert communication negotiate in advance to obtain the address pool participating in the covert communication, where special addresses serve as start, end and pause signals, and the remaining addresses serve as carriers of covert information. The sender and receiver unify the encoding and decryption methods of ciphertext. The sender encrypts the ciphertext information to be sent, and the encrypted ciphertext is evenly distributed to all addresses participating in the covert communication as the covert communication task of each address. The sender uses a special address to initiate a transaction pointing to the receiver's address, indicating the start of covert communication. Subsequent transactions are initiated by ordinary addresses in the address pool. The direction of these transactions is not limited to the receiver's address. With the consensus of the blockchain system, these transactions exist in each block. The receiver only needs to traverse the blocks according to the address pool to determine whether these addresses appear, and share the covert communication task to more addresses, which improves the transmission rate of the covert communication system. At the same time, each address has a shorter covert communication time, reducing the specificity of the address; the receiver first obtains the transaction initiation distribution of each address after screening according to the address list, and then sorts it according to the timestamp of transaction initiation until the address that receives the end mark starts decryption. The specific process is as follows:

[0034] 1-1) Preparation before covert communication: Off-chain pre-negotiation content: The address pool for the sender to initiate covert communication includes special addresses, information encoding and encryption rules corresponding to the ciphertext. The negotiation process of exchanging transaction addresses is generally present in the initial stage of blockchain transactions. Therefore, it is reasonable and feasible for both parties to exchange address pool information off-chain.

[0035] 1-2)) Encoding method of ciphertext: In time-based covert communication, multi-base modulation ciphertext requires a longer time interval to correspond to the codeword. The transmission rate of time-based covert communication η=(1+M) / 2log2M, where (1+M) / 2 represents the average block time for transmitting a codeword. η converges to M=4, which is 1.25 blocks to transmit 1 bit. The binary transmission rate is 1.5 blocks to transmit 1 bit. After the extreme point, as the coding base increases, the transaction interval becomes larger and larger, and the transmission rate decreases instead. Therefore, quaternary coding or two-bit binary coding rules can be used to achieve the best effect.

[0036] 1-3) Encryption rules for ciphertext: The ciphertext is encrypted using an asymmetric encryption system based on the public key and private key of the blockchain itself, so that only the recipient with the corresponding key can decrypt the encrypted ciphertext;

[0037] 1-4) Start and end marks of covert communication: the sender uses a special address add sThe address sent to the recipient indicates the start and end of covert communication, such as Figure 2 As shown, other addresses correspond to fragment M of ciphertext M i , the special address can be selected from the addresses owned by the sender itself, or generated by the Vanitygen program. The specified address bit is specified with a value and the address is automatically generated. The receiver traverses the blocks where the consensus is completed to see if these addresses participating in the covert communication exist, calculates the timestamp intervals of these addresses appearing in the blocks, and converts the intervals into ciphertext fragments against the ciphertext table. After combining, the complete ciphertext is obtained, so that multiple addresses can participate in the covert communication within one block time, and the covert communication task is shared among more addresses, which improves the transmission rate of the covert communication system. At the same time, each address has a shorter covert communication time, reducing the specificity of the address;

[0038] 1-5) After the receiver receives the transaction from the special address, it starts to traverse all the addresses of the sender that participate in the covert communication in the next block. The transactions of these addresses can point to any address, not just the receiver, so it does not affect the sender's normal transactions. Since the block timestamp does not need to be obtained additionally, the receiver only needs to traverse whether the address in the address pool appears in this block, thus reducing the traversal overhead;

[0039] 1-6) The receiver first obtains the transaction initiation distribution of each address by screening the address list, and then sorts them according to the timestamp of the transaction initiation until the address that receives the end mark starts decryption. The interval between two transactions is represented as hidden information. The short transaction interval Δt1' is set as "0" and the long transaction interval Δt'2 is set as "1" using binary as the modulation method of the ciphertext. The ciphertext fragments corresponding to the transaction intervals of all addresses are combined to obtain the complete encrypted ciphertext. The order of the ciphertext fragments is guaranteed by the order of the address pool. The order of the address pool can be based on the alphabetical order of the address or the rules agreed in advance by both parties. Then, the ciphertext is decrypted according to the encryption rules agreed in advance to obtain the ciphertext;

[0040] 1-7) When a transaction is not packaged into the corresponding block in time due to insufficient transaction fees or congestion of the blockchain system, resulting in the address not being read in the latest block, the sender adds a transaction initiated by a special address in the next block to indicate the suspension and invalidation of this information. The transaction receiver points to the receiver and the delayed packaged address, and the delayed address is suspended from initiating the next communication until the sender and receiver find that the delayed address appears in the subsequent block in the new block, ending the suspension;

[0041] 2) The transmission process of hidden information: The blockchain system packages transactions in a time period and assigns the same timestamp, while time-based covert communication uses time intervals as a carrier to hide ciphertexts. The length of the intervals corresponds to different codewords. Therefore, the addresses participating in covert communication will appear in the block with block timestamps at intervals within a period of time. If this rule is used as the judgment condition for detecting whether there are special addresses in the block, a large number of normal samples will be counted as suspicious samples. Because the number of addresses participating in the transmission of ciphertext in this example increases, the time for each address to undertake the covert communication task is greatly shortened, making it more difficult to distinguish from normal samples, so the concealment is better. If the transaction initiation time interval of the detection address, that is, the transaction to be confirmed, is more randomized, the regular covert communication address will become more special and easier to distinguish. In this example, the general address transaction behavior of blockchain transactions is used to count and model the general address transaction behavior, so as to optimize the transaction initiation behavior of the covert communication address, and simplify the transaction arrival process of the entire blockchain into a Poisson flow model P with parameter λ. n (t) = (λt) n e -λt / n! , represents the probability of n transactions arriving in time interval t, parameter λ represents the average number of transactions arriving per unit time, the interval between two transactions T must obey exponential distribution, proving that P{T>t+s|T>s}=P{T>t} has Markov property, the interval between transactions is independent of the previous transaction, and the interval distribution function of transactions is exponential distribution 1-e -λt , the transaction initiation behavior in the blockchain is determined by the user, and the address pool is formed by the available addresses of active users. Then, the average number of transactions arriving in the blockchain system per unit time is λ = n T / t B , α·n B Represents the number of transactions initiated by the same address per unit time, then the average number of transactions arriving at the same address is λ α =α·n T / t B , It is concluded that both the transaction interval distribution and the transaction interval distribution of the same address theoretically obey the exponential distribution.

[0042] Among them, n A Indicates the number of addresses participating in covert communication, n B Indicates the number of current valid addresses in the blockchain system, n T Indicates the number of transactions that a block can carry, t A Indicates the time interval between transactions initiated by the same address, t B Indicates the time when the blockchain system completes the block generation, t T It represents the transaction interval of the blockchain system, and the probability of a single address initiating a transaction per unit time is α, such as Figure 3 As shown in Figure 1, in order to obtain the real transaction interval distribution, this example collects one week of transaction initiation time data from the blockchain, and analyzes the transaction initiation interval of the address to obtain the general rule of the transaction initiation interval: the rule of the number of transaction initiation intervals at the same address is similar to the probability density function curve of the exponential distribution, as shown in Figure 1. Figure 4 As shown, covert communication is carried out in the blockchain transaction system. The transmitted ciphertext is modulated in binary. The short interval contains one block time in an average of 10 minutes, and the long interval contains two block times in an average of 20 minutes. The transmission rate of covert communication is obtained. Assume that the sender has n A The addresses used for covert communication, the probability of the codewords "0" and "1" after s ciphertext modulation is uniformly distributed, that is, the probability of the codewords appearing is equal, and the average time for an address to transmit a codeword is 15 minutes. A The average time for a sender with 1 address to transmit a codeword is 15 / n. A minutes, then the rate is 2n A / 3bit / block, the time to transmit a ciphertext of length m is t=3m / 2n A Block, and t ≥ 2, there are at least two block times to represent two codewords;

[0043] 3) Transaction interval control in covert communication: Figure 5 As shown in the figure, the probability of the ciphertext codeword appearing corresponds to the probability of the length of the time interval. For uniformly distributed binary ciphertext, the two intervals contain the same number of transactions, and the number of transactions initiated at different times in the long and short intervals will follow the normal distribution N(μ,σ 2 ), adjust the time interval distribution to fit the exponential distribution E(λ), the number of transactions in the long and short intervals is the same, the number of transaction intervals in the long interval obeys the exponential distribution, the transactions in the short interval are concentrated at some time points so that the overall distribution is approximately exponential, and the transactions in the short interval are concentrated at some time points so that the overall distribution is approximately exponential. After completing the covert communication task, the address can enter the next covert communication according to the sender's request, and the sequence of the next covert communication can fill the vacant time point of the previous short interval. The intervals between the two transactions are approximately exponentially distributed. If the statistical sample includes the cumulative number of the two intervals, the long and short intervals are approximately exponentially distributed, and the particularity of the address transaction interval is further reduced.

[0044] In this example, the time interval distribution is adjusted to fit the exponential distribution E(λ). The transaction time interval in the short interval is mapped to 5-14 minutes, with an average of 10 minutes. The transaction time interval in the long interval is mapped to 15-24 minutes, with an average of 20 minutes. The number of occurrences of different time intervals fits the exponential distribution. If all time points are assigned corresponding transaction quantities, the transaction quantity in the short interval will far exceed that in the long interval. Therefore, in the short interval, the transaction quantity is concentrated on a part of the time points.

Claims

1. A multi-address time-based blockchain covert communication method, characterized in that: The steps include: 1) Define multi-address time-based blockchain covert communication: The sender and receiver of covert communication negotiate in advance to obtain the address pool participating in the covert communication, where special addresses serve as start, end and pause signals, and the remaining addresses serve as carriers of covert information. The sender and receiver unify the encoding and decryption methods of ciphertext. The sender encrypts the ciphertext information to be sent, and the encrypted ciphertext is evenly distributed to all addresses participating in the covert communication. As the covert communication task of each address, the sender uses a special address to initiate a transaction pointing to the receiver's address, indicating the start of covert communication. Subsequent transactions are initiated by ordinary addresses in the address pool. The direction of these transactions is not limited to the receiver's address. With the consensus of the blockchain system, these transactions exist in each block. The receiver only needs to traverse the blocks according to the address pool to determine whether these addresses appear. The receiver first obtains the transaction initiation distribution of each address after screening according to the address list, and then sorts them according to the timestamp of transaction initiation until the address that receives the end mark starts decryption. The specific process is: 1-1) Preparation before covert communication begins: negotiate in advance off-chain to determine the address pool for the sender to initiate covert communication, including special addresses, information encoding corresponding to the ciphertext, and encryption rules; 1-2)) Encoding method of ciphertext: In time-based covert communication, multi-base modulation is used. Ciphertext requires a time interval to correspond to the codeword. The transmission rate of time-based covert communication is η = (1+M) / 2log2M, where (1+M) / 2 represents the average block time for transmitting a codeword. η converges to M = 4, which means 1.25 blocks are used to transmit 1 bit. The binary transmission rate is 1.5 blocks to transmit 1 bit. 1-3) Encryption rules for ciphertext: The ciphertext is encrypted using an asymmetric encryption system based on the public key and private key of the blockchain itself, so that only the recipient with the corresponding key can decrypt the encrypted ciphertext; 1-4) Start and end marks of covert communication: the sender uses a special address add s The address sent to the recipient indicates the start and end of the covert communication, and the other addresses correspond to the fragment M of the ciphertext M. i , the special address is selected from the addresses owned by the sender itself, or generated using the Vanitygen program, which specifies values ​​for the specified address bits and automatically generates addresses; 1-5) When the receiver receives the transaction from the special address, it starts to traverse all the addresses of the sender participating in the covert communication in the next block. The transactions of these addresses point to any address, not just the receiver. The block timestamp does not need to be obtained additionally. The receiver only needs to traverse whether the address in the address pool appears in this block; 1-6) The receiver first obtains the transaction initiation distribution of each address by screening the address list, and then sorts them according to the timestamp of the transaction initiation until the address that receives the end mark starts decryption. The interval between two transactions is represented as hidden information. The short transaction interval Δt1' is set as "0" and the long transaction interval Δt'2 is set as "1" using binary as the modulation method of the ciphertext. The ciphertext fragments corresponding to the transaction intervals of all addresses are combined to obtain the complete encrypted ciphertext. The order of the ciphertext fragments is guaranteed by the order of the address pool. The order of the address pool can be based on the alphabetical order of the address or the rules agreed in advance by both parties. Then, the ciphertext is decrypted according to the encryption rules agreed in advance to obtain the ciphertext; 1-7) When a transaction is not packaged into the corresponding block in time due to insufficient transaction fees or congestion of the blockchain system, resulting in the address not being read in the latest block, the sender adds a transaction initiated by a special address in the next block to indicate the suspension and invalidation of this information. The transaction receiver points to the receiver and the delayed packaged address, and the delayed address is suspended from initiating the next communication until the sender and receiver find that the delayed address appears in the subsequent block in the new block, ending the suspension; 2) The transmission process of hidden information: The blockchain system packages transactions in a time period and assigns the same timestamp, while time-based covert communication uses time intervals as a carrier to hide ciphertext. The length of the interval corresponds to different codewords. The addresses participating in the covert communication will appear in the block at intervals of block timestamps within a period of time. The general address transaction behavior is statistically analyzed and modeled, and the transaction arrival process of the entire blockchain is simplified to a Poisson flow model P with a parameter of λ. n (t) = (λt) n e -λt / n! , represents the probability of n transactions arriving in time interval t, parameter λ represents the average number of transactions arriving per unit time, the interval between two transactions T must obey exponential distribution, proving that P{T>t+s|T>s}=P{T>t} has Markov property, the interval between transactions is independent of the previous transaction, and the interval distribution function of transactions is exponential distribution 1-e -λt , the transaction initiation behavior in the blockchain is determined by the user, and the address pool is formed by the available addresses of active users. Then, the average number of transactions arriving in the blockchain system per unit time is λ = n T / t B , α·n B Represents the number of transactions initiated by the same address per unit time, then the average number of transactions arriving at the same address is λ α =α·n T / t B , It is concluded that both the transaction interval distribution and the transaction interval distribution of the same address are theoretically subject to exponential distribution, where n A Indicates the number of addresses participating in covert communication, n B Indicates the number of current valid addresses in the blockchain system, n T Indicates the number of transactions that a block can carry, t A Indicates the time interval between transactions initiated by the same address, t B Indicates the time when the blockchain system completes the block generation, t T represents the transaction interval of the blockchain system, the probability of a single address initiating a transaction per unit time, and the covert communication is carried out in the blockchain transaction system. The transmitted ciphertext is modulated in binary. The short interval contains one block time in an average of 10 minutes, and the long interval contains two block times in an average of 20 minutes. The transmission rate of covert communication is obtained. Assume that the sender has n A The addresses used for covert communication, the probability of the codewords "0" and "1" after s ciphertext modulation is uniformly distributed, that is, the probability of the codewords appearing is equal, and the average time for an address to transmit a codeword is 15 minutes. A The average time for a sender with 1 address to transmit a codeword is 15 / n. A minutes, then the rate is 2n A / 3bit / block, the time to transmit a ciphertext of length m is t=3m / 2n A Block, and t ≥ 2, there are at least two block times to represent two codewords; 3) Transaction interval control in covert communication: The probability of the ciphertext codeword appearing corresponds to the probability of the length of the time interval. For uniformly distributed binary ciphertext, the number of transactions contained in the two intervals is the same, and the number of transactions initiated at different times in the long and short intervals will follow the normal distribution N(μ,σ 2 ), adjust the time interval distribution to fit the exponential distribution E(λ), the number of transactions in the long and short intervals is the same, the number of transaction intervals in the long interval obeys the exponential distribution, the transactions in the short interval are concentrated at some time points so that the overall distribution is approximately exponential, and the transactions in the short interval are concentrated at some time points so that the overall distribution is approximately exponential. After completing the covert communication task, the address enters the next covert communication according to the sender's request, and the sequence of the next covert communication fills the time point of the previous short interval. The intervals between the two transactions are approximately exponentially distributed. If the statistical sample contains the cumulative number of the two intervals, the long and short intervals are approximately exponentially distributed.

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