An anonymous broadcast encryption and multi-party authentication transmission method based on extended chaotic mapping

Abstract

The application discloses an anonymous broadcast encryption and multi-party authentication transmission method based on an extended chaotic mapping and belongs to the technical field of information security. The method comprises the following steps: 1, system initialization: generating a master key and a corresponding public key; 2, key generation: a node calculates a private key by using an extended Chebyshev polynomial in combination with the master key and identity information of the node; 3, signing and encrypting: constructing broadcast information by using an extended chaotic mapping in combination with a Lagrange interpolation polynomial to generate a signature; 4, decrypting the signature: a receiver calculates relevant parameters and verifies the signature, recovers plaintext by using a self key after verification, and terminates decryption if the verification fails; and 5, building a relay transmission network: guaranteeing the anonymity and untraceability of a sender and a receiver. The method has high calculation efficiency and low communication overhead, meets the anonymity, open verifiability, confidentiality and unforgeability, can effectively resist ciphertext disturbance and provides security guarantee for sensitive information transmission.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of information security, and particularly relates to an anonymous broadcast encryption and multi-party authentication transmission method based on an extended chaotic mapping. BACKGROUND

[0002] With the development of digital economy and the popularization of Internet of Things technology, multi-node distributed communication scenarios are increasing. In these scenarios, a large amount of sensitive information (such as user privacy data, transaction credentials, device control instructions, etc.) needs to be broadcasted and transmitted among multiple participants, while the identity anonymity of the sender and the receiver, the confidentiality of the communication content, and the authenticity of the participant's identity need to be strictly protected. Anonymous broadcast encryption technology can securely transmit information to multiple receivers without revealing the identity of the sender, and multi-party authentication technology can ensure that the nodes participating in the communication are legitimate. The combination of the two becomes the core technical support for ensuring the security of multi-node communication. However, with the continuous upgrading of network attack methods, traditional anonymous communication and authentication mechanisms are facing increasingly severe challenges. How to achieve efficient, secure, and scalable anonymous broadcast and multi-party authentication in a complex network environment has become a key problem that needs to be solved in the field of information security.

[0003] Existing anonymous broadcast encryption and multi-party authentication methods have many limitations that are difficult to overcome:

[0004] First, the key management mechanism is complex. Most schemes rely on a centralized key distribution center. Once the center node is attacked, the key system of the entire system will collapse. Some distributed key management schemes have complex key negotiation steps, resulting in significant increase in computational overhead and communication delay, making it difficult to adapt to resource-constrained Internet of Things terminal devices.

[0005] Second, security and efficiency are difficult to balance. Some schemes pursue high anonymity by using complex mathematical operations to construct signature and encryption mechanisms, resulting in long signature and decryption processes that cannot meet the needs of real-time communication scenarios (such as low-latency transmission in Internet of Vehicles). Some lightweight schemes have defects in attack resistance and are vulnerable to forgery attacks, replay attacks, and identity tracking attacks, which cannot guarantee the unforgeability of the signature and the untraceability of the user's identity.

[0006] Third, the system lacks scalability. When new communication nodes are added or removed, existing schemes often need to re-key the entire network or adjust the signature parameters, which is complex and prone to system fluctuations, making it difficult to adapt to large-scale network scenarios with dynamic changes in nodes. In addition, existing methods do not fully utilize the non-linear dynamic characteristics of chaotic mapping, resulting in limited randomness and anti-cracking ability of key generation, further reducing the overall security of the system.

[0007] At present, the solutions to the above problems at home and abroad still have obvious short boards, and a technical system that can simultaneously meet high security, high efficiency and strong scalability has not been formed. SUMMARY

[0008] In view of the problems mentioned in the background art, the present application proposes an anonymous broadcast encryption and multi-party authentication transmission method based on extended chaotic mapping, which optimizes the key generation process by introducing an extended chaotic mapping with stronger nonlinear characteristics, improves the randomness and anti-cracking ability of the key, combines the Lagrange interpolation polynomial to construct an efficient broadcast information processing mechanism, simplifies the signing and decryption process, and reduces the calculation and communication overhead. At the same time, dynamic relay network and parameter updating strategy are adopted to enhance the scalability of the system in the scene of dynamic node change.

[0009] Technical scheme: In order to solve the above technical problems, the technical scheme adopted by the present application is as follows:

[0010] An anonymous broadcast encryption and multi-party authentication transmission method based on extended chaotic mapping, comprising the following steps:

[0011] Step 1, system initialization: randomly select different large prime numbers by the private key generation center, calculate the system large integer parameter and the system module parameter, generate the master key and the corresponding public key, and publish the system parameters and keep the master key secret;

[0012] Step 2, key generation: the private key generation center generates large prime numbers for each node, and the node calculates the private key by using the extended Chebyshev polynomial combined with the master key and its own identity information, and calculates the public key and stores it;

[0013] Step 3, signing: the sender randomly selects an integer, calculates the signing parameter and the plaintext encryption parameter by using the extended chaotic mapping, constructs the broadcast information by using the Lagrange interpolation polynomial, generates the signature and forms the final broadcast message containing multiple parameters;

[0014] Step 3.1, the sender randomly selects an integer , calculates the parameters BS and X;

[0015] BS is the signing parameter, which is calculated by the extended Chebyshev polynomial, specifically:

[0016] ,

[0017] X is the plaintext encryption parameter, and the specific calculation formula is:

[0018] ,

[0019] wherein m represents the plaintext to be transmitted, represents the parameter in the public key of the receiver; represents a Chebyshev polynomial operation of degree r; represents a system public key; represents a node parameter;

[0020] Step 3.2, for a set of receivers, calculate the hash value of the receiver ID and the node encryption parameter , get n groups of data, and construct a Lagrange interpolation polynomial based on these data;

[0021] Step 3.3, calculate the weighted sum of the polynomial coefficient and the encryption factor , get the set W;

[0022] Step 3.4, generate a signature, then the sender will combine the signature , the plaintext encryption parameter , the set W, and the sender's signature to form a final broadcast message and send it;

[0023] Step 4, decryption: the receiver calculates the relevant parameters and verifies the signature, and if the verification is passed, the plaintext is recovered using its own key, and if the verification is not passed, the decryption is terminated;

[0024] Step 5, build a relay transmission network: the client obtains active relay node information from the user directory node, randomly selects part of the nodes to form a relay network, and uses identity confusion, stealth address and ring signature mechanism to ensure the anonymity and untraceability of the sender and the receiver.

[0025] As a preferred embodiment, the implementation process of system initialization in step 1 is as follows:

[0026] Step 1.1, the private key generation center randomly selects two different large prime numbers and , according to the selected and , calculate the system large integer parameter , the system module parameter ;

[0027] Step 1.2, select the base master key , calculate the system public key corresponding to the base master key ;

[0028] Step 1.3, the system parameter is public, and the base master key is stored separately by the private key generation center.

[0029] As a preferred embodiment, the implementation steps of key generation in step 2 are as follows:

[0030] Step 2.1: The private key generation center assigns a unique identity ID to each node and randomly generates a large prime number for it. and Then calculate the node parameters;

[0031] Step 2.2: Nodes construct extended Chebyshev polynomials based on their own identity identifiers (IDs).

[0032] Step 2.3: Calculate the node's private key ;

[0033] Step 2.4: Based on the node's private key Compute node public key private key The node's public key is stored locally for confidentiality. Upload it to the private key generation center for filing and public disclosure.

[0034] As a preferred option, the implementation process of step 3.2 is as follows:

[0035] The set of receivers is:

[0036] ,

[0037] in, This represents the nth node of the receiver; n represents the number of receiver nodes.

[0038] The hash value of the i-th node ID of the receiver and node encryption parameters The specific calculation formula is as follows:

[0039] ,

[0040] ,

[0041] Where h() represents the hash function; key represents the shared key; This represents the unique encryption factor for node i. This represents the i-th node of the receiver;

[0042] Obtain n sets of data And based on these data, a Lagrange interpolation polynomial is constructed, specifically:

[0043] ,

[0044] in, Represents the Lagrange interpolation polynomial, represents the polynomial coefficients; n represents the number of nodes at the receiving end; X represents the plaintext encryption parameters calculated in step 3.1; a hash value representing the identity of node i; a hash value representing the identity of node j.

[0045] As preferred, the implementation process of step 4 is as follows:

[0046] Step 4.1, the receiver receives the broadcast message, then extracts the parameters in step 3.4, and calls the private key stored by itself and the system large integer parameter , the system public key ;

[0047] Step 4.2, verification of signature: the receiver calculates the signature verification value, if the signature verification value is consistent with the preset signature verification reference value, the signature verification is passed; Otherwise, it is determined that the message is invalid and the decryption process is terminated;

[0048] Step 4.3, after the signature verification is passed, the receiver extracts the corresponding parameters from the set based on its own identity, calculates the random number by the inverse operation of the extended Chebyshev polynomial, and then restores the plaintext m by using the random number and its own public key parameter .

[0049] As preferred, the implementation process of step 5 is as follows:

[0050] Step 5.1, the client sends a relay node query request to the user directory node, and the user directory node returns a list of active relay nodes in the current network, including node identification, communication address and availability score;

[0051] Step 5.2, the client randomly selects k nodes from the active relay node list, and includes the target receiving node, generates a multi-hop relay path from the sender to the receiver through a random path algorithm, and establishes a connection between each node in the path using dynamic port mapping;

[0052] Step 5.3, the sender and the receiver use temporary identity in the relay transmission process, which is composed of random number generated by extended chaotic mapping and time stamp, and is automatically updated after each communication;

[0053] Step 5.4, the sender generates a one-time stealth address by combining the receiver's public key and the random number through a hash function, which is used as the final receiving address in the relay network, and the sender performs ring signature on the header digest of the transmission information, so that the verifier can only confirm that the signature comes from the nodes in the ring, but cannot locate the specific sender;

[0054] Step 5.5, periodically update the relay network topology: the client reselects the relay node and generates a new transmission path, and clears the temporary identity, stealth address and path record of the last round of communication.

[0055] Advantages: Compared with the prior art, the present application has the following advantages:

[0056] (1) The present application introduces an extended chaotic mapping to optimize the key generation process, improving the randomness and anti-cracking ability of the key; combined with the Lagrange interpolation polynomial to simplify the signing and decryption process, the calculation and communication overhead is reduced, solving the problem that the security and efficiency of the existing method are difficult to balance. Through the mechanism of combining identity confusion, stealth address and ring signature, the anonymity and untraceability of the sender and the receiver are enhanced, and the scalability of the system in the node dynamic change scene is improved by using the dynamic relay network strategy, effectively resisting various common attacks, filling the gap of anonymous broadcast encryption and multi-party authentication technology that meets high security, high efficiency and strong scalability at the same time.

[0057] (2) The method proposed in the present application can significantly improve the communication efficiency on the basis of guaranteeing anonymity, public verifiability, confidentiality and unforgeability, effectively resisting common disturbances such as ciphertext attacks and forgery attacks, providing reliable security support for industrial Internet of Things, Internet of Vehicles and other scenes, and has important theoretical research value and broad practical application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0058] Figure 1 is a flowchart of the anonymous broadcast encryption and multi-party authentication transmission method based on the extended chaotic mapping of the present application. DETAILED DESCRIPTION

[0059] The present application will be further illustrated below in conjunction with specific embodiments, which are implemented on the premise of the technical scheme of the present application, and it should be understood that these embodiments are only used to illustrate the present application and not to limit the scope of the present application.

[0060] The anonymous broadcast encryption and multi-party authentication transmission method based on the extended chaotic mapping provided in this embodiment is in the background of multi-agent intelligent collection scene, and through specific parameter setting and process operation, the practical application process of the anonymous broadcast encryption and multi-party authentication transmission method based on the extended chaotic mapping is described in detail.

[0061] This scene contains 1 private key generation center (PKG), 1 sender node (proxy terminal A) and 3 receiver nodes (proxy terminals B, C and D), aiming to realize anonymous broadcast and multi-party identity authentication of the sender to the receiver set, and ensure the secure transmission of sensitive collection data.

[0062] Step 1, system initialization: randomly select different large prime numbers by the private key generation center (PKG), calculate related parameters, generate master key and corresponding public key, disclose system parameters and keep master key secret;

[0063] Step 1.1, the private key generation center randomly selects two different large prime numbers and , according to the selected and , calculate parameters , ;

[0064] Randomly select two 512-bit strong prime numbers and :

[0065]

[0066]

[0067] , The large prime numbers selected in the system initialization stage are the same in bit number and the difference is greater than to avoid trial division cracking.

[0068] Based on the two prime numbers, the PKG calculates the system parameters, specifically:

[0069]

[0070]

[0071] Among them, is the system large integer parameter, obtained by the product of and , with a length of 1024 bits; is the system module parameter.

[0072] Step 1.2, select base master key , calculate the public key corresponding to the base master key ;

[0073] Then select the base master key , specifically:

[0074]

[0075] Among them, is the base master key held by the PKG, satisfying .

[0076] Calculate the corresponding public key by the extended Euclidean algorithm, specifically:

[0077]

[0078] wherein, is a system public key, and satisfies a modular L inverse relationship, L represents a system modulus parameter calculated in step 1.1. The condition is satisfied.

[0079] Step 1.3, base master key is stored secretly by the PKG, and the system parameter is publicly disclosed.

[0080] Step 2, key generation: the PKG generates a large prime number and other parameters for each node, and the node calculates a private key by using an extended Chebyshev polynomial in combination with a master key and its own identity information, and calculates a public key and stores the same;

[0081] Step 2.1, the private key generation center allocates a unique identity ID for each node, and randomly generates a large prime number and for the node, and then calculates a node parameter;

[0082] is a unique identity of the node, such as the ID of the sender A Agent_A_001, and the IDs of the receivers B, C and D are Agent_B_002, Agent_C_003 and Agent_D_004 respectively.

[0083] wherein, and have the same number of bits as , in step 1.

[0084] Meanwhile, the PKG randomly generates a 512-bit strong prime number , for each node, is a node-specific large prime number (such as B's , ); the calculation formula of the node parameter is:

[0085]

[0086]

[0087] wherein, is a parameter of the node , obtained by the product of and , and is a node modulus parameter.

[0088] Step 2.2, the node constructs an extended Chebyshev polynomial based on its identity ID;

[0089]

[0090] wherein, represents an extended Chebyshev polynomial constructed by the node according to the base master key and the identity ID; represents the base master key; represents a system large integer parameter.

[0091] Step 2.3, calculating the node private key ;

[0092] randomly selecting an integer , the calculation formula of the node private key is:

[0093]

[0094]

[0095] wherein, is the integer randomly selected by the node; represents a node modulus parameter; and are large prime numbers. represents an extended Chebyshev polynomial constructed by the node according to the base master key and its own identity ID in step 2.2.

[0096] Step 2.4, calculating the node public key according to the node private key , so that , the private key is stored secretly by the node locally, and the node public key is uploaded to the private key generation center for record and public disclosure; the calculation formula of the node public key is:

[0097]

[0098] wherein, represents a node modulus parameter. is the node public key, and satisfies the modular inverse relationship.

[0099] For example, the polynomial of the receiver B is , an integer is randomly selected, the private key is calculated, and the public key is obtained according to the private key.The public key is uploaded to the PKG for record disclosure, and the private key is stored secretly by the node locally.

[0100] wherein, represents an extended Chebyshev polynomial of the receiver B, and the nodes in B are calculated according to the base master key and the node identity in B; represents a system large integer parameter; represents a base master key; is an integer converted by the ID of the receiver B through SHA-256 hash value; represents an integer randomly selected by the receiver B; represents a private key of the receiver B; represents a modulus parameter of the receiver B; represents a public key of the receiver B.

[0101] Step 3, sign and encrypt: the sender randomly selects an integer, calculates related parameters by using the extended chaotic mapping, constructs the broadcast information by combining the Lagrange interpolation polynomial, generates a signature, and forms a final broadcast message containing multiple parameters;

[0102] The sign and encryption stage is executed by the sender A, and needs to broadcast the plaintext m=“sensitive collection data: temperature 25℃” to B, C and D (m is the plaintext to be transmitted, which is converted into an integer m=0x123456).

[0103] Step 3.1, the sender randomly selects an integer , and calculates parameters BS and X;

[0104] BS is a sign and encryption parameter, which is calculated by an extended Chebyshev polynomial, and specifically is:

[0105]

[0106] X is a plaintext encryption parameter, and the specific calculation formula is:

[0107]

[0108] wherein, is the plaintext to be transmitted, is a parameter in the public key of the receiver; represents a Chebyshev polynomial operation with the number of times r; represents a system public key; represents a parameter of the node , which is calculated by the product of two large prime numbers and .

[0109] In this embodiment, r=1000, which is an integer randomly selected by the sender, satisfies .

[0110] Step 3.2, calculate the hash value of the receiver ID for the receiver set and node encryption parameters , get group data, and construct the Lagrange interpolation polynomial based on these data;

[0111] The receiver set is:

[0112]

[0113] wherein, represents the nth node of the receiver; n represents the number of nodes of the receiver.

[0114] In this embodiment, the ID set of receivers B, C and D is .

[0115] The hash value of the i th node ID of the receiver and node encryption parameters The specific calculation formula is:

[0116]

[0117]

[0118] wherein, h() represents a hash function; key represents a shared key; represents the exclusive encryption factor of node i; represents the i th node of the receiver.

[0119] Get group data (in this embodiment, 3 groups of data are obtained), and construct the Lagrange interpolation polynomial based on these data, specifically:

[0120]

[0121] wherein, is the Lagrange interpolation polynomial, is the polynomial coefficient; n represents the number of nodes of the receiver; X represents the plaintext encryption parameter calculated in step 3.1; represents the identity hash value of node i; represents the identity hash value of node j.

[0122] Step 3.3, calculate the weighted sum of the polynomial coefficient and the encryption factor , get set W;

[0123]

[0124] in, This is the weighted sum of the polynomial coefficients and the encryption factor; n represents the number of receiving nodes; j is an integer from 1 to n. Denotes the coefficients of the Lagrange interpolation polynomial; This represents the unique encryption factor for node i.

[0125] gather ; The set of parameters for the sum of receiver weights. This represents the weighted sum parameter of the nth node; n represents the number of receiver nodes.

[0126] In this embodiment, the set of receivers B, C, and D .

[0127] Step 3.4: Generate a signature Then the sender will Combine them into a broadcast message and send it;

[0128] Calculate the signature using the formula. Specifically:

[0129]

[0130] in, Indicates the sender's signature; Indicated by Chebyshev polynomial operations of degree. This represents the unique encryption factor for node i. This represents a large integer generated during system initialization; BS is the sender's private key; X is the plaintext encryption parameter; and W is the set of parameters for the receiver's weighted sum.

[0131] Step 4, Decryption: The receiver calculates the relevant parameters and verifies the signature. If the verification is successful, the plaintext is recovered using its own key. If the verification fails, the decryption process is terminated.

[0132] The decryption phase is completed by the recipient (taking B as an example). After receiving the broadcast message, B extracts the parameters. and call its own private key and system parameters .

[0133] Step 4.1: The receiver receives the broadcast message and then extracts the information from step 3.4. And call its own stored private key. and publicly available system parameters ;

[0134] Step 4.2, Signature Verification: The receiver calculates the signature verification value. If the signature verification value matches the preset signature verification benchmark value, the signature verification passes; otherwise, the message is deemed invalid and the decryption process is terminated.

[0135] The formula for calculating the signature verification value V is:

[0136]

[0137] in, Indicates using private key Chebyshev chaotic polynomial operations of degree; Indicates the sender's signature; Represents the system's large integer parameters; the signature verification baseline value is... .

[0138] In this embodiment, the correctness of the verification method is determined by derivation, specifically as follows:

[0139] For any identity identifier in the receiver set ( , where n is the number of receiver nodes, and its receiver verification parameters The calculation process can be derived as follows:

[0140]

[0141] in, For the first One receiver parameter, Let i be the identity hash value of node i. For the Lagrange polynomial coefficients, For nodes Its own exclusive encryption factor.

[0142] Therefore, we can conclude that: .

[0143] in, For node parameters, Verify parameters for the recipient. The number of nodes is a prime number, satisfying the system parameter association relationship.

[0144] In signature verification, based on the semigroup property of extended Chebyshev polynomials, it can be derived that:

[0145]

[0146] in, To extend the Chebyshev polynomial, For the system public key, Sign for the sender, For system large integer parameters, For the receiver to verify the parameters, The hash value of the sender ID. The equation is valid, which indicates that the signature is valid, the sender's identity is legal, and the message has not been tampered with. Indicates the signature generated by the sender , the number of applications is Chebyshev polynomial operation. Indicates the hash value of the sender's identity , the number of applications is Chebyshev polynomial operation.

[0147] The plaintext recovery link, the receiver calculates through the private key:

[0148]

[0149] Where, is the plaintext, X is the plaintext encryption parameter, D is the intermediate parameter calculated by the receiver, is the node prime number, is the modular inverse of .

[0150]

[0151] Where, is the receiver's private key, r is the sender's random number, which can accurately restore the original plaintext, and verifies the consistency of the encryption and decryption process. Indicates the Chebyshev polynomial operation with times; is the system public key; Indicates the Chebyshev polynomial operation on the system public key with random number r times; is the node prime number.

[0152] Step 4.3, after the signature verification is passed, the receiver extracts the corresponding parameters from the set based on its own identity , calculates through the extended Chebyshev polynomial inverse operation, and then restores the plaintext m using and its own public key parameter .

[0153] The calculation formula of the random number calculated by the receiver is:

[0154]

[0155] Where, Indicates the Chebyshev polynomial operation on the system public key with random number r times, Indicates the The number of times Chebyshev polynomial inverse operation; The parameters of the node .

[0156] In this embodiment, after the signature verification passes, B extracts based on its own identity from , calculates by extending the Chebyshev polynomial inverse operation, and finally restores the plaintext m using and its own public key parameter .

[0157] Step 5, build relay transmission network: the client obtains active relay node information from the user directory node, randomly selects part of the nodes (including the target node) to form a relay network, and uses identity confusion, stealth address and ring signature mechanism to ensure the anonymity and untraceability of the sender and the receiver.

[0158] Step 5.1, the client sends a relay node query request to the user directory node, and the user directory node returns a list of active relay nodes in the current network with normal status, including node identification, communication address and availability score;

[0159] Step 5.2, the client randomly selects k nodes (k≥3) from the active relay node list, and includes the target receiving node, generates a multi-hop relay path from the sender to the receiver through a random path algorithm, and establishes a connection between each node in the path using dynamic port mapping;

[0160] The construction of the relay transmission network aims to ensure anonymity and untraceability. The client (sender A) first sends a query request to the user directory node to obtain a list containing 20 active relay nodes (availability score ≥ 90%), and then randomly selects 5 nodes (including target nodes B, C, and D), generates a 3-hop transmission path (A→relay node 1→relay node 2→B / C / D) through a random path algorithm, and establishes a connection between each node in the path through dynamic port (5000-6000 random port) mapping.

[0161] Step 5.3, the sender and the receiver use temporary identity (TID) in the relay transmission process, TID is composed of random number generated by extended chaotic mapping and timestamp, and is automatically updated after each round of communication, temporary identity has no direct relationship with real identity;

[0162] Step 5.4. For each transmission task, the sender combines the receiver's public key and the random number through a hash function to generate a one-time stealth address as the final receiving address in the relay network, which is only valid within the validity period of this transmission; at the same time, the sender performs ring signature on the header digest of the transmission information, and the signature participants include all selected relay nodes, and the verifier can only confirm that the signature comes from the nodes in the ring, but cannot locate the specific sender.

[0163] Step 5.5. Regularly update the relay network topology: every time a preset time window (such as 30 minutes) is passed, the client reselects the relay nodes and generates a new transmission path, and at the same time, the temporary identity, stealth address and path record of the previous round of communication are cleared to ensure that the historical transmission behavior is not traceable.

[0164] In this embodiment, to balance security and efficiency, the parameters need to follow certain criteria: the large prime number and the node prime number are both strong prime numbers with the same number of bits (512 bits), ensuring that is a 1024-bit large integer; contains a large prime factor, and (the greatest common divisor) value is as small as possible; avoid (that is, needs to be large enough to prevent trial division cracking. The public key parameter needs to be a large integer no less than ; selecting is prohibited to avoid periodic special values of the extended Chebyshev polynomial; ensure that is not a square residue modulo to prevent attackers from cracking the private key through discrete logarithm transformation. The proportion of active nodes is 5% (not more than 50), and the path update time window is set to 30 minutes.

[0165] The specific experimental content in this application is as follows:

[0166] The symmetric encryption algorithms Blowfish, AES-256, 3DES and the asymmetric encryption algorithms RSA-3072, ECC-256, Elgamal-512, as well as the RSA-based anonymous broadcast (RSA-Anon) and the ECC-based anonymous broadcast (ECC-Anon) are selected. Comparison is made from three aspects of encryption and decryption efficiency, key generation speed and resource consumption.

[0167] Encryption and decryption efficiency: broadcast encryption time (sender) and decryption time (receiver average) under different plaintext sizes.

[0168] Key generation efficiency: node private key generation time, signature key generation time, and system master key generation time.

[0169] Resource consumption: peak memory occupation in encryption and decryption process, unit data (1MB) encryption and decryption power consumption.

[0170] Table 1: Encryption and decryption efficiency comparison (unit: ms)

[0171]

[0172] According to the experimental results in Table 1, it can be analyzed that the method of the present application is slower than the unicast Blowfish and AES because it needs to process the logic of anonymous broadcast and authentication, but the encryption efficiency and decryption efficiency are both superior to the traditional method compared with the traditional anonymous scheme.

[0173] Table 2: Key generation efficiency comparison (unit: ms)

[0174]

[0175] From the data in Table 2, it can be seen that the key generation efficiency of the method of the present application is significantly superior to the traditional scheme, because the iteration operation of the extended Chebyshev polynomial does not need large prime number decomposition or elliptic curve point operation, so that the key generation time is greatly reduced.

[0176] Table 3: Resource consumption comparison (unit: KB)

[0177]

[0178] From Table 3, it can be seen that the resource consumption of the method of the present application maintains the optimal index performance in the experiments of different plaintext sizes.

[0179] In summary, the experiments prove that the method is superior to other comparison methods in encryption and decryption efficiency, key generation speed and resource consumption. Through specific parameter setting, flow verification and performance comparison, the feasibility, security and high efficiency of the anonymous broadcast encryption and multi-party authentication transmission method based on the extended chaotic mapping are fully proved, which can effectively meet the core needs of sensitive information transmission scenarios.

[0180] The above only describes the preferred embodiments of the present application, and it should be pointed out that for ordinary skilled persons in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should be considered as the protection scope of the present application.

Claims

1. A method for anonymous broadcast encryption and multi-party authentication transmission based on extended chaotic mapping, characterized in that, Includes the following steps: Step 1, System Initialization: The private key generation center randomly selects different large prime numbers, calculates the system's large integer parameters and system modulo parameters, generates the master key and corresponding public key, publishes the system parameters, and keeps the master key secret; Step 2, Key Generation: The private key generation center generates large prime numbers for each node. The node uses the extended Chebyshev polynomial, combined with the master key and its own identity information, to calculate the private key, and at the same time calculates and stores the public key. Step 3, Sign-crypt: The sender randomly selects an integer, uses the extended chaotic mapping to calculate the sign-crypt parameters and plaintext encryption parameters, combines the Lagrange interpolation polynomial to construct the broadcast information, generates a signature, and forms the final broadcast message containing multiple parameters; Step 3.1: The sender randomly selects an integer. Calculate the parameters BS and X; BS is the signature parameter, calculated using the extended Chebyshev polynomial, specifically: ， X is the plaintext encryption parameter, and the specific calculation formula is as follows: ， Where m represents the plaintext to be transmitted. This represents the parameters in the recipient's public key; This represents a Chebyshev polynomial operation of degree r; Represents the system public key; Represents a node Parameters; Step 3.2: For the set of receivers, calculate the hash value of the receiver ID. and node encryption parameters ,get A set of data, and construct a Lagrange interpolation polynomial based on this data; Step 3.3: Calculate the weighted sum of the polynomial coefficients and the encryption factor. We obtain set W; Step 3.4: Generate a signature, and then the sender will send the signature parameters. Plaintext encryption parameters Set W, sender signature Combine the components to form the final broadcast message and send it; Step 4, Decryption: The receiver calculates the relevant parameters and verifies the signature. If the verification is successful, the plaintext is recovered using its own key. If the verification fails, the decryption process is terminated. Step 5: Construct a relay network: The client obtains information on active relay nodes from the user directory node, randomly selects some nodes to form a relay network, and ensures the anonymity and untraceability of the sender and receiver through identity obfuscation, stealth address and ring signature mechanisms.

2. The anonymous broadcast encryption and multi-party authentication transmission method based on extended chaotic mapping according to claim 1, characterized in that, The system initialization process in step 1 is as follows: Step 1.1: The private key generation center randomly selects two different large prime numbers. and According to the selected and Calculate the large integer parameters of the system System module parameters ; Step 1.2: Select the base master key Calculate the master key Corresponding system public key ; Step 1.3: Set system parameters Public, master key It is stored securely and separately by the private key generation center.

3. The anonymous broadcast encryption and multi-party authentication transmission method based on extended chaotic mapping according to claim 1, characterized in that, The key generation process in step 2 is as follows: Step 2.1: The private key generation center assigns a unique identity ID to each node and randomly generates a large prime number for it. and Then calculate the node parameters; Step 2.2: Nodes construct extended Chebyshev polynomials based on their own identity identifiers (IDs). Step 2.3: Calculate the node's private key ; Step 2.4: Based on the node's private key Compute node public key private key The node's public key is stored locally for confidentiality. Upload it to the private key generation center for filing and public disclosure.

4. The anonymous broadcast encryption and multi-party authentication transmission method based on extended chaotic mapping according to claim 1, characterized in that, The implementation process of step 3.2 is as follows: The set of receivers is: ， in, This represents the nth node of the receiver; n represents the number of receiver nodes. The hash value of the i-th node ID of the receiver and node encryption parameters The specific calculation formula is as follows: ， ， Where h() represents the hash function; key represents the shared key; This represents the unique encryption factor for node i. This represents the i-th node of the receiver; Obtain n sets of data And based on these data, a Lagrange interpolation polynomial is constructed, specifically: ， in, Represents the Lagrange interpolation polynomial, represents the polynomial coefficients; n represents the number of nodes at the receiving end; X represents the plaintext encryption parameters calculated in step 3.1; This represents the identity hash value of node i; This represents the identity hash value of node j.

5. The anonymous broadcast encryption and multi-party authentication transmission method based on extended chaotic mapping according to claim 1, characterized in that, The process of decryption in step 4 is as follows: Step 4.1: The receiver receives the broadcast message, then extracts the parameters from step 3.4, and retrieves its own stored private key. and system large integer parameters System public key ; Step 4.2, Signature Verification: The receiver calculates the signature verification value. If the signature verification value matches the preset signature verification benchmark value, the signature verification passes; otherwise, the message is deemed invalid and the decryption process is terminated. Step 4.3: After successful signature verification, the recipient, based on its own identity, retrieves data from the set. Extract the weighted sum of polynomial coefficients and encryption factor. Random numbers are calculated by inverse operation of extended Chebyshev polynomials. Then use random numbers and its own public key parameters , restore plaintext m.

6. The anonymous broadcast encryption and multi-party authentication transmission method based on extended chaotic mapping according to claim 1, characterized in that, The implementation process for constructing the relay transmission network in step 5 is as follows: Step 5.1: The client sends a relay node query request to the user directory node. The user directory node returns a list of active relay nodes in the current network that are in normal condition, including node identifier, communication address and availability score. Step 5.2: The client randomly selects k nodes from the list of active relay nodes and includes the target receiving node in them. A multi-hop relay path from the sender to the receiver is generated through a random path algorithm. The connection between each node in the path is established using dynamic port mapping. Step 5.3: The sender and receiver use temporary identifiers during relay transmission. The temporary identifiers are composed of a random number generated by the extended chaotic map and a timestamp, and are automatically updated after each round of communication. Step 5.4: The sender generates a one-time stealth address by combining the receiver's public key and a random number with a hash function. This one-time stealth address serves as the final receiving address in the relay network. At the same time, the sender performs a ring signature on the header digest of the transmitted information, so that the verifier can only confirm that the signature comes from a node within the ring and cannot locate the specific sender. Step 5.5: Periodically update the relay network topology: The client reselects a relay node and generates a new transmission path, while clearing the temporary identity, stealth address, and path record of the previous round of communication.

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