Multi-user information sharing method and system based on probabilistic asymmetric encryption protocol

Abstract

The invention discloses a multi-user information sharing method and system based on a probabilistic asymmetric encryption protocol, which introduces a cryptographic security random number and a public quadratic polynomial parameter on the basis of a standard RSA, and generates a ciphertext tuple containing a randomized component through nonlinear mapping, thereby realizing probabilistic encryption, and improving the security of the cryptographic security random number and the public quadratic polynomial parameter. Dictionary attacks and selected plaintext attacks are effectively resisted; in the decryption process, a quadratic congruence equation is constructed, and a plaintext is recovered by using a Tonelli-Shanks algorithm and a Chinese remainder theorem. A forced circulation mechanism of'hop-by-hop decryption-re-encryption 'is adopted to ensure that a data packet of each circulation link has uniqueness and identity binding characteristics, so that accurate tracing of internal data leakage is realized, and meanwhile, the data is ensured not to be tampered through a closed-loop integrity verification mechanism.

Description

Technical Field

[0001] This invention relates to the field of information security technology, specifically to a multi-user information sharing method and system based on a probabilistic asymmetric encryption protocol. Background Technology

[0002] With the rapid development of information technology, data confidentiality, integrity, and non-repudiation have become core security requirements for network communication and data storage. In multi-user circular sharing or collaborative scenarios, access control alone is insufficient to protect data security because it cannot prevent internal leaks by legitimate users. Existing encrypted transmission schemes typically encrypt once and decrypt at multiple points. All users receive the same encrypted text. Once a user with legitimate permissions leaks data, the system cannot distinguish whether the leak originated from user A, user B, or user C. Furthermore, most existing solutions lack integrity verification during the data transfer process. When data flows through multiple nodes, traditional solutions struggle to verify whether the data has been tampered with at any intermediate stage. If the data received by the last node is incorrect, it is difficult to pinpoint which node caused the problem.

[0003] Asymmetric encryption algorithms, especially RSA, are widely used in digital signatures, data encryption, and other fields due to their ease of key management. However, the standard RSA encryption algorithm has inherent flaws, such as: 1. For the same plaintext and encryption key, the resulting ciphertext will always be the same. This characteristic makes the algorithm vulnerable to chosen-plaintext attacks, especially when the plaintext space is limited. Attackers can crack intercepted ciphertext by constructing a "ciphertext-plaintext" dictionary. 2. Attackers can make specific modifications to the ciphertext without decryption, resulting in a predictable mathematical relationship between the decrypted plaintext and the original plaintext. This poses a serious security threat in certain application scenarios.

[0004] To overcome these shortcomings, academia and industry have proposed various enhancement schemes, such as Optimal Asymmetric Encryption Padding (OAEP). However, these encryption schemes heavily rely on complex hash functions and mask generation functions, resulting in high computational overhead and complex implementation. Another example is the Rabin cryptosystem. Although the Rabin system introduces quadratic operations in encryption and its decryption relies on solving the square root modulo, it suffers from vulnerabilities to chosen-plaintext attacks and incompatibility with existing RSA key systems, limiting its widespread application.

[0005] Therefore, there is an urgent need for a new information security sharing method that can fundamentally improve the security of the encryption algorithm itself, adapt to multi-user collaborative environments, prevent data leakage and ensure traceability, and possess adequate robustness. Summary of the Invention

[0006] The present invention aims to at least partially solve one of the technical problems existing in the related art.

[0007] One objective of this invention is to provide a multi-user information sharing method based on a probabilistic asymmetric encryption protocol. This method employs a forced flow mechanism of "hop-by-hop decryption-re-encryption" to ensure that data packets at each flow stage have uniqueness and identity binding characteristics, thereby enabling accurate tracing of internal data leaks. Simultaneously, a closed-loop integrity verification mechanism ensures that the data has not been tampered with.

[0008] Another objective of this invention is to provide a multi-user information sharing system based on a probabilistic asymmetric encryption protocol.

[0009] To achieve the above objectives, the present invention provides a multi-user information sharing method based on a probabilistic asymmetric encryption protocol, comprising the following steps:

[0010] S1. Define a multi-user information sharing framework consisting of a server and N users, where the server is... User-generated For asymmetric key pairs ;

[0011] S2, The server discloses the set of encryption keys to all users. Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set ;

[0012] S3, The server uses the encryption key and For plaintext Perform nested encryption to obtain the initial data packet. And send it to User 1; User 1 uses the decryption key they hold. and For the initial data packet Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Re-execute nested encryption to generate data packets. And forward it to the other users;

[0013] S4. The remaining users cycle through the decryption, encryption, and forwarding steps, with any user... Receive data packets Then, using the decryption key it holds. and right Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Perform nested encryption again to generate a new data packet. and the new data packet Send to user ;

[0014] S5, User 1, acting as the audit node, receives data from the last user. Generate data packets Then, using the decryption key that it had previously held for verification. and For data packets Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext A comparison is performed to verify data integrity.

[0015] A further preferred technical solution of the present invention is that, in step S1, the server is... User-generated For asymmetric key pairs; specifically:

[0016] Based on the standard RSA key generation method, the generated prime number is obtained. Modulus Encryption key index and decryption key index ;

[0017] Select two additional modulo values Coprime integers and As publicly available system parameters;

[0018] Generate key pairs ;

[0019] Repeat the above steps to generate For asymmetric key pairs, we obtain the encryption key set. and decryption key set .

[0020] Preferably, in steps S3 and S4, the user selects plaintext. The specific method for performing nested encryption is as follows:

[0021] Any user For the obtained plaintext First, using the encryption key plaintext Perform inner encryption to obtain inner ciphertext. , is represented as:

[0022] ;

[0023] in, This represents a probabilistic asymmetric encryption algorithm;

[0024] Then the inner ciphertext Serialization yields the inner ciphertext sequence. , is represented as:

[0025] ;

[0026] in, Indicates a serialization operation;

[0027] Finally, the encryption key is used. inner ciphertext sequence Perform outer encryption to obtain outer ciphertext. , is represented as:

[0028] ;

[0029] user Will contain outer ciphertext new data packets Send to user .

[0030] As a preferred option, the probabilistic asymmetric encryption algorithm used in nested encryption is specifically:

[0031] For the text to be encrypted First, generate a cryptographically secure random number. ;

[0032] Then, respectively, the text... and random numbers With encryption key Perform standard RSA encryption to obtain the intermediate ciphertext. and random number ciphertext , respectively represented as:

[0033] ;

[0034] ;

[0035] Then obtain the publicly available system parameters ,Will and Substitute a pre-defined quadratic polynomial Perform non-linear obfuscation to calculate a portion of the final ciphertext. , is represented as:

[0036] ;

[0037] The final generated ciphertext is a ciphertext tuple containing two parts. .

[0038] As a preferred embodiment, the specific method for the user to perform layer-by-layer decryption of the received data packets in steps S3 and S4 is as follows:

[0039] Any user Received data packet from the previous node Then, first use the decryption key it holds. A probabilistic asymmetric decryption algorithm is used to decrypt data packets. Perform outer layer decryption, and then use the decryption key. The inner layer is decrypted using a probabilistic asymmetric decryption algorithm to recover the plaintext. .

[0040] As a preferred method, the probabilistic asymmetric decryption algorithm used during decryption is as follows:

[0041] The user received the ciphertext tuple ;

[0042] Constructing about the unknown quadratic congruence equations ;

[0043] Using the decryption key Prime factors included and The quadratic congruence equation is decomposed into a problem of finding the square root modulus in two prime number fields, i.e., solving the following equations respectively:

[0044] ;

[0045] ;

[0046] use The algorithm solves the modulo square root problem and, in conjunction with the Chinese Remainder Theorem, recovers the original square root. All candidate solutions;

[0047] For all The candidate solutions are decrypted using standard RSA, and the only correct text is selected by verifying the plaintext format. .

[0048] As a preferred option, step S5 specifically involves:

[0049] When the last user Receive and decrypt Obtain plaintext Then, use the encryption key. and For plaintext Encryption is performed to generate the final data packet. and send it back to user 1;

[0050] Distribute a specific set of decryption keys to user 1 on the audit node.

[0051] User 1 received the final data packet. Then, it uses the decryption key from the specific set of decryption keys distributed to the audit node in step S2. and Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext Comparison is performed to verify data integrity;

[0052] User 1 receives and decrypts the original plaintext initially from the server. With verification plaintext Perform a comparison, if If the data is consistent, it proves that the data has not been tampered with during the entire circular sharing lifecycle, and its integrity has been verified; if it is inconsistent, it indicates that the data has been corrupted or maliciously tampered with during transmission.

[0053] Preferably, the initial data packet is obtained at the audit node. When initiating an information sharing process, an alarm mechanism is activated, background monitoring begins, and the process initiation time is recorded.

[0054] If the audit node detects that the difference between the current time and the process initiation time exceeds a preset threshold... If the integrity verification is not yet complete, a mandatory audit instruction is broadcast to all users, and each user reports the timestamp of their last successfully received data packet to the audit node. and forwarded data packet timestamps ;

[0055] Audit nodes analyze the timeline to locate faulty nodes or broken links and issue security alerts.

[0056] As a preferred approach, the alarm mechanism should locate the faulty user node. At that time, the server initiates a temporary bridging mechanism;

[0057] The server uses a temporary key pair generated under the same rules as in step S1 for generating the asymmetric key pair. ;

[0058] The server will temporarily decrypt the key. Distributed to the user of the next node after the faulty node , temporary encryption key and rerouting commands are sent to the user of the node preceding the faulty node. ;

[0059] user Respond to the instruction using the encryption key plaintext Perform inner-layer encryption and use a temporary encryption key. Perform outer encryption to generate bridged data packets. And send directly to the user ;

[0060] user Receive bridged data packets Use temporary decryption key Decrypt the outer layer, then use the decryption key it holds. Decrypt the inner layer to recover the plaintext. And it continues to circulate.

[0061] Another aspect of the present invention provides a multi-user information sharing system based on a probabilistic asymmetric encryption protocol, comprising:

[0062] A trusted server, configured as follows:

[0063] for User-generated For asymmetric key pairs ;

[0064] Publicly disclose the set of encryption keys to all users Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set ;

[0065] Obtain the encryption key and For plaintext Perform nested encryption to obtain the initial data packet. And send it to user 1;

[0066] User nodes Perform the following operations:

[0067] Receive data packets ;

[0068] Using the decryption key it holds and right Perform layer-by-layer decryption to recover the plaintext. ;

[0069] Obtain the encryption key and For plaintext Perform nested encryption again to generate a new data packet. And send it to the next user node. ;

[0070] User node 1 acts as the audit node when receiving the initial data packet. When the timeout monitoring timer is activated, receive data from the last user node. data packets Then, use the decryption key. and For data packets Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext Comparison is performed to verify data integrity;

[0071] If the monitoring timer times out and data integrity verification is not completed, an alarm mechanism will be triggered.

[0072] In another aspect, the present invention provides a non-transitory computer-readable storage medium having computer instructions stored thereon, the computer instructions causing a computer to execute the above-described multi-user information sharing method based on a probabilistic asymmetric encryption protocol.

[0073] In another aspect, the present invention provides an electronic device, comprising: a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus, and the processor calls logical instructions in the memory to execute the aforementioned multi-user information sharing method based on a probabilistic asymmetric encryption protocol.

[0074] In another aspect, the present invention provides a computer program product, the computer program product comprising a computer program stored on a non-transitory computer-readable storage medium, wherein when the computer program is executed by a processor, the computer executes the above-described multi-user information sharing method based on a probabilistic asymmetric encryption protocol.

[0075] Beneficial effects: The present invention introduces probabilistic asymmetric encryption by introducing random numbers. and quadratic polynomial By performing nonlinear mapping, the ciphertext encrypted with the same plaintext is completely different each time, which fundamentally immunizes against dictionary attacks. At the same time, the complexity of solving the square root modulus is used to improve the anti-analysis capability.

[0076] This invention designs a "decrypt-reencrypt" cyclical flow mechanism. Each node must decrypt the previous data and reencrypt it using the next node's encryption key to generate a completely new data packet. This means that each data packet circulating in the network is unique and bound to a specific user. If data is leaked, by analyzing the data packet format and encryption level, it is possible to accurately trace which user leaked the data. Simultaneously, the closed-loop design allows the initiator to ultimately verify the integrity of the data.

[0077] In ring or chain topologies where multiple users sequentially transmit information, system availability is relatively fragile. Addressing the risks of single points of failure and the lack of fault location and self-healing capabilities, this invention proposes an alarm location and temporary bridging mechanism. By monitoring timeouts of audit nodes and enforcing log auditing, faulty nodes can be accurately located, and it can be determined whether the faulty node is a malicious "data black hole" or a network outage. Simultaneously, the server can dynamically generate a "temporary bridging key," instructing preceding nodes to skip the faulty point and directly encrypt and send the data to subsequent nodes. This achieves system self-healing, ensuring that core business flows remain uninterrupted even when some nodes fail. Attached Figure Description

[0078] Figure 1 This is an overall flowchart of the multi-user information sharing method based on a probabilistic asymmetric encryption protocol of the present invention;

[0079] Figure 2 This is a flowchart of the probabilistic asymmetric encryption algorithm in this invention;

[0080] Figure 3 This is a flowchart of the probabilistic asymmetric decryption algorithm in this invention;

[0081] Figure 4 This is a schematic diagram of data flow during multi-user information sharing in this invention;

[0082] Figure 5 This is a flowchart of the alarm mechanism of the present invention;

[0083] Figure 6 This is a flowchart of the bridging mechanism of the present invention;

[0084] Figure 7 The graph shows the success rate results of information transmission attack simulations using the encryption method of this invention and the standard RSA encryption method. Detailed Implementation

[0085] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, embodiments of this invention, and should not be construed as limiting the invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention. In the description of this invention, it should be understood that the terminology used is for descriptive purposes only and should not be construed as indicating or implying relative importance.

[0086] The following is combined Figures 1-7 This invention describes a multi-user information sharing method and system based on a probabilistic asymmetric encryption protocol.

[0087] Example 1: This example provides a multi-user information sharing method based on a probabilistic asymmetric encryption protocol, which aims to solve the deterministic defects of the standard RSA algorithm and the problems of difficulty in tracing internal leakage and paralysis caused by single point of failure in multi-user collaborative scenarios.

[0088] At the encryption protocol level, this embodiment introduces cryptographically secure random numbers and publicly available quadratic polynomial parameters on top of the standard RSA. Through nonlinear mapping, ciphertext tuples containing randomized components are generated, achieving probabilistic encryption and effectively resisting dictionary attacks and chosen-plaintext attacks. The decryption process utilizes a quadratic congruence equation, the Tonelli-Shanks algorithm, and the Chinese Remainder Theorem (CRT) to recover the plaintext. The multi-user cyclic secure sharing scheme constructed in this embodiment employs a forced flow mechanism of "hop-by-hop decryption-re-encryption" to ensure that data packets at each flow stage possess uniqueness and identity binding characteristics, thereby enabling precise tracing of internal data leaks. Simultaneously, a closed-loop integrity verification mechanism ensures that the data has not been tampered with.

[0089] In addition, this embodiment also designs an alarm mechanism based on timeout monitoring and a dynamic bridging mechanism based on temporary keys, which can automatically build a bypass channel after locating the faulty node, so as to realize the system's fault self-healing and high service availability.

[0090] The overall process of the method in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0091] Step 1: System initialization and key distribution.

[0092] Define a multi-user information sharing framework consisting of a server and N users. The server-side application layer sets security parameters, such as... Bit. The server-side application layer is... User-generated For asymmetric key pairs Each key pair The generation algorithm is as follows:

[0093] Choose two Large prime numbers of bits and .

[0094] Calculate the modulus .

[0095] Calculate Euler's totient function .

[0096] Select encryption key index .

[0097] Calculate the decryption key index .

[0098] Two additional public parameters were selected. and ,make sure and and Mutual elements.

[0099] Define encryption key Decryption key .

[0100] Repeat the above steps to generate For asymmetric key pairs, we obtain the encryption key set. and decryption key set .

[0101] Then the server publishes the encryption key set to all users. Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set .

[0102] Step 2: The server initiates encryption.

[0103] The server obtains the plaintext to be shared. Using encryption keys and For plaintext To perform nested encryption, first use the encryption key. plaintext Perform inner encryption to obtain inner ciphertext. , is represented as:

[0104] ;

[0105] in, This represents a probabilistic asymmetric encryption algorithm;

[0106] Probabilistic asymmetric encryption algorithms, such as Figure 2 As shown, specifically:

[0107] For the text to be encrypted First, generate a cryptographically secure random number. ;

[0108] Then, respectively, the text... and random numbers With encryption key Perform standard RSA encryption to obtain the intermediate ciphertext. and random number ciphertext , respectively represented as:

[0109] ;

[0110] ;

[0111] Then obtain the publicly available system parameters ,Will and Substitute a pre-defined quadratic polynomial Perform non-linear obfuscation to calculate a portion of the final ciphertext. , is represented as:

[0112] ;

[0113] The final generated ciphertext is a ciphertext tuple containing two parts. .

[0114] Then the inner ciphertext Serialization yields the inner ciphertext sequence. , is represented as:

[0115] ;

[0116] in, Indicates a serialization operation;

[0117] Finally, the encryption key is used. inner ciphertext sequence The outer layer encryption is performed using the same probabilistic asymmetric encryption algorithm as the inner layer encryption, resulting in the outer layer ciphertext. , is represented as:

[0118] ;

[0119] The server will contain the outer ciphertext. new data packets Send to user 1.

[0120] Step 3: Information sharing and data transfer among multiple users.

[0121] Data flow process as follows Figure 4 As shown, any user Received data packet from the previous node Then, first use the decryption key it holds. A probabilistic asymmetric decryption algorithm is used to decrypt data packets. Perform outer layer decryption, and then use the decryption key. The inner layer is decrypted using a probabilistic asymmetric decryption algorithm to recover the plaintext. .

[0122] The probabilistic asymmetric decryption algorithm used during decryption, such as... Figure 3 As shown, specifically:

[0123] The user received the ciphertext tuple ;

[0124] Constructing about the unknown quadratic congruence equations ;

[0125] Using the decryption key Prime factors included and The quadratic congruence equation is decomposed into a problem of finding the square root modulus in two prime number fields, i.e., solving the following equations respectively:

[0126] ;

[0127] ;

[0128] use An algorithm for solving the modulo square root problem.

[0129] In this embodiment, the solution under the modulus p is taken as an example to illustrate the solution process.

[0130] (1) Determine whether the algorithm can solve the problem successfully. The prerequisite for the algorithm to solve the problem successfully is... It must be a model The quadratic residue. That is... It must be the square modulo of some number. The result can be obtained by calculating the Legendre symbol. The determination is made using the following calculation process:

[0131] ;

[0132] If the result is 1, then It is a quadratic residue, and the equation has a solution algorithm applicable.

[0133] If the result is -1 (in the modulo) The following is equivalent to ),but It is a quadratic non-residual equation, and the equation has no solution.

[0134] If the result is 0, then Can be Divisible, the solution to the equation is .

[0135] (2) Decompose into an odd number Find the product of a power of 2 and a unique positive integer. and odd numbers , so that:

[0136] ;

[0137] Find a number Make it a model The quadratic non-residual.

[0138] Randomly select a number .

[0139] Calculate its Legendre symbol .

[0140] If the result is not equal to -1 (i.e.) If so, then select again. until a condition is found. until.

[0141] (3) Based on the above preparations, initialize the four core variables:

[0142] ;

[0143] ;

[0144] ;

[0145] ;

[0146] (4) The core of the algorithm is to continuously correct it through loops. This brings it closer to the final solution.

[0147] The loop body is as follows:

[0148] Find the smallest Find the smallest integer , making .

[0149] Calculate the correction factor Using the information found in the previous step Calculate the correction factor :

[0150] ;

[0151] Update variables: using Update all four core variables:

[0152] ;

[0153] ;

[0154] ;

[0155] ;

[0156] Return to the beginning of the loop and check again. The value of .

[0157] Loop termination condition: if If the loop ends, the algorithm completes. It is the solution we are looking for.

[0158] When the loop ends, that is When the variable eventually equals 1, The value of is a solution to the equation.

[0159] Based on the property of the modulus of the square root, another solution is... ,Right now:

[0160] ;

[0161] ;

[0162] (5) Using the Chinese Remainder Theorem (CRT), respectively in the model and model By combining the solutions obtained below, we can obtain... In the model All candidate solutions under the given conditions. Specifically, at most two solutions are generated under modulo p and modulo q, denoted as . and Through pairing and combination, for example , At most, four systems of congruence equations can be formed.

[0163] For each system of equations, for example , By applying the Chinese Remainder Theorem, a [property] can be obtained in the model [of the model]. The unique solution is found by iterating through all combinations. All candidate solutions.

[0164] by , For example, the steps are as follows:

[0165] After finding the solutions to these two equations respectively and Then, a system of congruence equations is obtained:

[0166] ;

[0167] in This refers to the intermediate ciphertext that we ultimately want to recover. The Chinese Remainder Theorem's function is to combine these two local solutions ( , ) spliced ​​into a mold (in The unique global solution under ) .

[0168] Solve the system of equations:

[0169] ;

[0170] in and Mutual elements.

[0171] From the first equation It can be seen that, Divide by The remainder is .therefore, It can definitely be written in the following form:

[0172] ;

[0173] in It is some unknown integer.

[0174] The above Substituting the expression into the second equation In, that is:

[0175] ;

[0176] Rearrange the terms in the above equation:

[0177] ;

[0178] In order to separate Multiply both sides of the equation by In the model The multiplicative inverse is obtained by calculating the multiplicative inverse using the extended Euclidean algorithm.

[0179] Let this inverse be denoted as We obtain the following formula:

[0180] ;

[0181] because The equation simplifies to:

[0182] ;

[0183] Therefore, it was calculated that In the model Find the smallest non-negative integer solution and substitute it back into the expression in step 1:

[0184] ;

[0185] This calculation It is in the model The only solution under the modulus, that is, in the modulus The only solution is given.

[0186] Perform standard RSA decryption on all candidate solutions. And by verifying the plaintext format, a unique correct plaintext is selected. .

[0187] In recovering the plain text Afterwards, the user Using encryption keys and For plaintext Perform nested encryption again to generate a new data packet. and the new data packet Send to user The nested encryption method used is the same as the server-side encryption of plaintext in step two. The encryption methods are the same; only the encryption keys are different.

[0188] Step 4: Loop closure and integrity verification.

[0189] When the last user Receive and decrypt Obtain plaintext Then, use the encryption key. and For plaintext Encryption is performed to generate the final data packet. and send it back to user 1;

[0190] Distribute a specific set of decryption keys to user 1 on the audit node.

[0191] User 1 received the final data packet. Then, it uses the decryption key from the specific set of decryption keys distributed to the audit node in step S2. and Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext Comparison is performed to verify data integrity;

[0192] User 1 receives and decrypts the original plaintext initially from the server. With verification plaintext Perform a comparison, if If the data is consistent, it proves that the data has not been tampered with during the entire circular sharing lifecycle, and its integrity has been verified; if it is inconsistent, it indicates that the data has been corrupted or maliciously tampered with during transmission.

[0193] Step 5: Introduce an alarm mechanism (anomaly handling branch).

[0194] like Figure 5 As shown, the initial data packet is obtained at the audit node. When initiating an information sharing process, an alarm mechanism is activated, background monitoring begins, and the process initiation time is recorded.

[0195] If the audit node detects that the difference between the current time and the process initiation time exceeds a preset threshold... If the integrity verification is not yet complete, a mandatory audit instruction is broadcast to all users, and each user reports the timestamp of their last successfully received data packet to the audit node. and forwarded data packet timestamps ;

[0196] Audit nodes analyze the timeline to locate faulty nodes or broken links and issue security alerts.

[0197] Step 6: Introduce a temporary bridging mechanism.

[0198] like Figure 6 As shown, the alarm mechanism locates the faulty user node. At that time, the server initiates a temporary bridging mechanism;

[0199] The server uses a temporary key pair generated under the same rules as in step S1 for generating the asymmetric key pair. ;

[0200] The server will temporarily decrypt the key. Distributed to the user of the next node after the faulty node , temporary encryption key and rerouting commands are sent to the user of the node preceding the faulty node. ;

[0201] user Respond to the instruction using the encryption key plaintext Perform inner-layer encryption and use a temporary encryption key. Perform outer encryption to generate bridged data packets. And send directly to the user ;

[0202] user Receive bridged data packets Use temporary decryption key Decrypt the outer layer, then use the decryption key it holds. Decrypt the inner layer to recover the plaintext. And it continues to circulate.

[0203] The following is a quantitative evaluation of the performance and overhead of the multi-user information sharing method based on the probabilistic asymmetric encryption protocol in this embodiment.

[0204] For quantitative analysis, we first define the cost symbols for the basic operations as shown in Table 1.

[0205] Table 1. Operational Cost Symbol Table

[0206]

[0207] Analyze the theoretical costs of the following encryption methods:

[0208] 1. Encryption process

[0209] Standard RSA: ;

[0210] Calculation cost: ;

[0211] RSA-OAEP calculation cost: ;

[0212] Enhanced encryption protocol: , , ;

[0213] Calculation cost: ;

[0214] 2. Decryption process

[0215] Standard RSA: ;

[0216] Calculation cost: ;

[0217] RSA-OAEP calculation cost: ;

[0218] Enhanced encryption protocol:

[0219] calculate ;

[0220] calculate ;

[0221] calculate ;

[0222] Find the square root of the two modulosities: ;

[0223] Using CRT to combine up to 4 solutions, performing RSA decryption and verification on up to 4 candidate values, the computational cost is:

[0224] ;

[0225] Assuming the security parameter k = 2048 bits, and making the following orders of magnitude assumptions based on typical hardware performance:

[0226] ;

[0227] ;

[0228] ;

[0229] ;

[0230] .

[0231] Taking the final requirement of 2.5 RSA decryptions as an example, the performance and overhead of each scheme are compared in Table 2.

[0232] Table 2 Performance vs. Overhead Comparison

[0233]

[0234] As shown in the table above, although the solution in this embodiment introduces approximately 80% of the decryption process for legitimate users... The additional computational overhead is mainly used to solve the combination of the modulus square root and the CRT, but this is only a sub-second delay, imperceptible to users in most non-high-frequency trading scenarios. However, this negligible legal cost is exchanged for an asymmetric attack cost barrier. For dictionary attacks and chosen-plaintext attacks, which are extremely effective against standard RSA, current technology only requires attackers to... The computational complexity is sufficient to verify the guess by comparing the ciphertext; however, in this embodiment, due to the introduction of the quadratic polynomial nonlinear mapping, an attacker would have to reverse-engineer the solution regarding the quadratic polynomial nonlinear mapping to verify the guess. The quadratic congruence equation. According to computational complexity theory, this operation is equivalent to applying the modulus... By performing factorization, a very high safety cost-performance ratio is achieved.

[0235] To verify the security superiority of the scheme in this embodiment, targeted simulated attack experiments were designed and implemented. The success rate of information transmission attacks using conventional, deterministic RSA encryption methods is as follows: Figure 7 As shown. This demonstrates that the solution in this embodiment can effectively resist known plaintext space attacks.

[0236] Example 2: A multi-user information sharing system based on a probabilistic asymmetric encryption protocol, comprising:

[0237] A trusted server, configured as follows:

[0238] for User-generated For asymmetric key pairs ;

[0239] Publicly disclose the set of encryption keys to all users Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set ;

[0240] Obtain the encryption key and For plaintext Perform nested encryption to obtain the initial data packet. And send it to user 1;

[0241] User nodes Perform the following operations:

[0242] Receive data packets ;

[0243] Using the decryption key it holds and right Perform layer-by-layer decryption to recover the plaintext. ;

[0244] Obtain the encryption key and For plaintext Perform nested encryption again to generate a new data packet. And send it to the next user node. ;

[0245] User node 1 acts as the audit node when receiving the initial data packet. When the timeout monitoring timer is activated, receive data from the last user node. data packets Then, use the decryption key. and For data packets Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext Comparison is performed to verify data integrity;

[0246] If the monitoring timer times out and data integrity verification is not completed, an alarm mechanism will be triggered.

[0247] Example 3: This example provides a non-transitory computer-readable storage medium storing computer instructions that cause a computer to execute a multi-user information sharing method based on a probabilistic asymmetric encryption protocol. The method includes the following steps:

[0248] S1. Define a multi-user information sharing framework consisting of a server and N users, where the server is... User-generated For asymmetric key pairs ;

[0249] S2, The server discloses the set of encryption keys to all users. Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set ;

[0250] S3, The server uses the encryption key and For plaintext Perform nested encryption to obtain the initial data packet. And send it to User 1; User 1 uses the decryption key they hold. and For the initial data packet Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Re-execute nested encryption to generate data packets. And forward it to the other users;

[0251] S4. The remaining users cycle through the decryption, encryption, and forwarding steps, with any user... Receive data packets Then, using the decryption key it holds. and right Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Perform nested encryption again to generate a new data packet. and the new data packet Send to user ;

[0252] S5, User 1, acting as the audit node, receives data from the last user. Generate data packets Then, using the decryption key that it had previously held for verification. and For data packets Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext A comparison is performed to verify data integrity.

[0253] Example 4: This example provides an electronic device that may include a processor, a communication interface, a memory, and a communication bus. The processor, communication interface, and memory communicate with each other via the communication bus. The processor can invoke logical instructions from the memory to execute a multi-user information sharing method based on a probabilistic asymmetric encryption protocol. This method includes the following steps:

[0254] S1. Define a multi-user information sharing framework consisting of a server and N users, where the server is... User-generated For asymmetric key pairs ;

[0255] S2, The server discloses the set of encryption keys to all users. Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set ;

[0256] S3, The server uses the encryption key and For plaintext Perform nested encryption to obtain the initial data packet. And send it to User 1; User 1 uses the decryption key they hold. and For the initial data packet Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Re-execute nested encryption to generate data packets. And forward it to the other users;

[0257] S4. The remaining users cycle through the decryption, encryption, and forwarding steps, with any user... Receive data packets Then, using the decryption key it holds. and right Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Perform nested encryption again to generate a new data packet. and the new data packet Send to user ;

[0258] S5, User 1, acting as the audit node, receives data from the last user. Generate data packets Then, using the decryption key that it had previously held for verification. and For data packets Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext A comparison is performed to verify data integrity.

[0259] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0260] Example 5: This example provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute a multi-user information sharing method based on a probabilistic asymmetric encryption protocol. The method includes the following steps:

[0261] S1. Define a multi-user information sharing framework consisting of a server and N users, where the server is... User-generated For asymmetric key pairs ;

[0262] S2, The server discloses the set of encryption keys to all users. Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set ;

[0263] S3, The server uses the encryption key and For plaintext Perform nested encryption to obtain the initial data packet. And send it to User 1; User 1 uses the decryption key they hold. and For the initial data packet Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Re-execute nested encryption to generate data packets. And forward it to the other users;

[0264] S4. The remaining users cycle through the decryption, encryption, and forwarding steps, with any user... Receive data packets Then, using the decryption key it holds. and right Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Perform nested encryption again to generate a new data packet. and the new data packet Send to user ;

[0265] S5, User 1, acting as the audit node, receives data from the last user. Generate data packets Then, using the decryption key that it had previously held for verification. and For data packets Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext A comparison is performed to verify data integrity.

[0266] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0267] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0268] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-user information sharing method based on a probabilistic asymmetric encryption protocol, characterized in that, Includes the following steps: S1. Define a multi-user information sharing framework consisting of a server and N users, where the server is... User-generated For asymmetric key pairs ; S2, The server discloses the set of encryption keys to all users. Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set ; S3, The server uses the encryption key and For plaintext Perform nested encryption to obtain the initial data packet. And send it to User 1; User 1 uses the decryption key they hold. and For the initial data packet Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Re-execute nested encryption to generate data packets. And forward it to the other users; S4. The remaining users cycle through the decryption, encryption, and forwarding steps, with any user... Receive data packets Then, using the decryption key it holds. and right Perform layer-by-layer decryption to recover the plaintext. Then obtain the encryption key. and For plaintext Perform nested encryption again to generate a new data packet. and the new data packet Send to user ; S5, User 1, acting as the audit node, receives data from the last user. Generate data packets Then, using the decryption key that it had previously held for verification. and For data packets Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext A comparison is performed to verify data integrity.

2. The multi-user information sharing method based on a probabilistic asymmetric encryption protocol according to claim 1, characterized in that, The step S1 described above is performed by the server. User-generated For asymmetric key pairs; specifically: Based on the standard RSA key generation method, the generated prime number is obtained. Modulus Encryption key index and decryption key index ; Select two additional modulo values Coprime integers and As publicly available system parameters; Generate key pairs ; Repeat the above steps to generate For asymmetric key pairs, we obtain the encryption key set. and decryption key set .

3. The multi-user information sharing method based on a probabilistic asymmetric encryption protocol according to claim 2, characterized in that, In steps S3 and S4, the user accesses the plaintext. The specific method for performing nested encryption is as follows: Any user For the obtained plaintext First, using the encryption key plaintext Perform inner encryption to obtain inner ciphertext. , is represented as: ； in, This represents a probabilistic asymmetric encryption algorithm; Then the inner ciphertext Serialization yields the inner ciphertext sequence. , is represented as: ； in, Indicates a serialization operation; Finally, the encryption key is used. inner ciphertext sequence Perform outer encryption to obtain outer ciphertext. , is represented as: ； user Will contain outer ciphertext new data packets Send to user .

4. The multi-user information sharing method based on a probabilistic asymmetric encryption protocol according to claim 3, characterized in that, The probabilistic asymmetric encryption algorithm used in nested encryption is as follows: For the text to be encrypted First, generate a cryptographically secure random number. ; Then, respectively, the text... and random numbers With encryption key Perform standard RSA encryption to obtain the intermediate ciphertext. and random number ciphertext , respectively represented as: ； ； Then obtain the publicly available system parameters ,Will and Substitute a pre-defined quadratic polynomial Perform non-linear obfuscation to calculate a portion of the final ciphertext. , is represented as: ； The final generated ciphertext is a ciphertext tuple containing two parts. .

5. The multi-user information sharing method based on a probabilistic asymmetric encryption protocol according to claim 4, characterized in that, The specific method for the user to perform layer-by-layer decryption of the received data packets in steps S3 and S4 is as follows: Any user Received data packet from the previous node Then, first use the decryption key it holds. A probabilistic asymmetric decryption algorithm is used to decrypt data packets. Perform outer layer decryption, and then use the decryption key. The inner layer is decrypted using a probabilistic asymmetric decryption algorithm to recover the plaintext. .

6. The multi-user information sharing method based on a probabilistic asymmetric encryption protocol according to claim 5, characterized in that, The probabilistic asymmetric decryption algorithm used during decryption is as follows: The user received the ciphertext tuple ; Constructing about the unknown quadratic congruence equations ; Using the decryption key Prime factors included and The quadratic congruence equation is decomposed into a problem of finding the square root modulus in two prime number fields, i.e., solving the following equations respectively: ； ； use The algorithm solves the modulo square root problem and, in conjunction with the Chinese Remainder Theorem, recovers the original square root. All candidate solutions; For all The candidate solutions are decrypted using standard RSA, and the only correct text is selected by verifying the plaintext format. .

7. The multi-user information sharing method based on a probabilistic asymmetric encryption protocol according to claim 1, characterized in that, Step S5 is as follows: When the last user Receive and decrypt Obtain plaintext Then, use the encryption key. and For plaintext Encryption is performed to generate the final data packet. and send it back to user 1; Distribute a specific set of decryption keys to user 1 on the audit node. User 1 received the final data packet. Then, it uses the decryption key from the specific set of decryption keys distributed to the audit node in step S2. and Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext Comparison is performed to verify data integrity; User 1 receives and decrypts the original plaintext initially from the server. With verification plaintext Perform a comparison, if If the data is consistent, it proves that the data has not been tampered with during the entire circular sharing lifecycle, and its integrity has been verified; if it is inconsistent, it indicates that the data has been corrupted or maliciously tampered with during transmission.

8. The multi-user information sharing method based on a probabilistic asymmetric encryption protocol according to claim 1, characterized in that, Obtain the initial data packet at the audit node. When initiating an information sharing process, an alarm mechanism is activated, background monitoring begins, and the process initiation time is recorded. If the audit node detects that the difference between the current time and the process initiation time exceeds a preset threshold... If the integrity verification is not yet complete, a mandatory audit instruction is broadcast to all users, and each user reports the timestamp of their last successfully received data packet to the audit node. and forwarded data packet timestamps ; Audit nodes analyze the timeline to locate faulty nodes or broken links and issue security alerts.

9. The multi-user information sharing method based on a probabilistic asymmetric encryption protocol according to claim 8, characterized in that, The alarm mechanism locates the user at the fault node. At that time, the server initiates a temporary bridging mechanism; The server uses a temporary key pair generated under the same rules as in step S1 for generating the asymmetric key pair. ; The server will temporarily decrypt the key. Distributed to the user of the next node after the faulty node , temporary encryption key and rerouting commands are sent to the user of the node preceding the faulty node. ; user Respond to the instruction using the encryption key plaintext Perform inner-layer encryption and use a temporary encryption key. Perform outer encryption to generate bridged data packets. And send directly to the user ; user Receive bridged data packets Use temporary decryption key Decrypt the outer layer, then use the decryption key it holds. Decrypt the inner layer to recover the plaintext. And it continues to circulate.

10. A multi-user information sharing system based on a probabilistic asymmetric encryption protocol, characterized in that, include: A trusted server, configured as follows: for User-generated For asymmetric key pairs ; Publicly disclose the set of encryption keys to all users Distribute a specific set of decryption keys to user 1, who is defined as an audit node. to other users Distribute decryption key set ; Obtain the encryption key and For plaintext Perform nested encryption to obtain the initial data packet. And send it to user 1; User nodes Perform the following operations: Receive data packets ; Using the decryption key it holds and right Perform layer-by-layer decryption to recover the plaintext. ; Obtain the encryption key and For plaintext Perform nested encryption again to generate a new data packet. And send it to the next user node. ; User node 1 acts as the audit node when receiving the initial data packet. When the timeout monitoring timer is activated, receive data from the last user node. data packets Then, use the decryption key. and For data packets Decrypt to obtain the verification plaintext. And will verify plaintext With the original plaintext Comparison is performed to verify data integrity; If the monitoring timer times out and data integrity verification is not completed, an alarm mechanism will be triggered.

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