A multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism

Abstract

The application relates to the technical field of information security, in particular to a multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism, which comprises the following steps: generating public and private keys and quantum keys between any two clients; when an encrypted information flow is transferred between any two clients, a sender client performs first-layer encryption on quantum plaintext by using the public keys between the two clients, and then performs second-layer encryption on the quantum plaintext by using the quantum keys to obtain quantum ciphertext; performing homomorphic calculation on the quantum ciphertext according to a pre-defined quantum circuit, and broadcasting the homomorphic calculation result and a quantum decryption key to all the clients except the sender client; all the clients except the sender client perform first-layer decryption on the homomorphic calculation result by using the quantum decryption key, and then perform second-layer decryption on the first quantum ciphertext by using local private keys, and only a target client can decrypt the quantum plaintext. The application can realize safe quantum calculation and data transmission in an untrusted environment.

Description

Technical Field

[0001] This invention relates to the field of information security technology, and more specifically to a multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism. Background Technology

[0002] Homomorphic encryption is a encryption technique that allows specific computational operations to be performed while data remains encrypted. With the development of quantum computing, quantum homomorphic encryption has gained widespread attention as an emerging technology. Quantum homomorphic encryption allows quantum computation to be performed on encrypted quantum data without decryption, thus providing stronger privacy protection.

[0003] However, existing quantum homomorphic encryption schemes have some limitations, particularly in achieving efficient and universal quantum computing and reducing computational overhead. Many schemes rely on highly interactive and computationally intensive processes, leading to low system efficiency. Furthermore, quantum homomorphic encryption faces the phase error problem in T-gate operations, affecting the accuracy of computation.

[0004] Current quantum homomorphic encryption schemes have potential trust issues during computation and transmission. In cases where servers and clients collaborate, private data may be leaked. Furthermore, under the premise of information theory security, quantum homomorphic encryption schemes require a large amount of storage and computing resources. Especially when non-interactive operation and support for general-purpose quantum computing are required, the storage overhead often increases exponentially.

[0005] Ensuring secure quantum computing and data transmission in untrusted environments is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism, which enables secure quantum computing and data transmission in an untrusted environment.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism includes the following steps:

[0009] S1. Assume there are n clients. Any two clients generate a public key and a private key. Each client stores the private key locally and sends the corresponding public key to the other corresponding clients.

[0010] S2. Any two clients transmit their quantum states to a trusted intermediary. The trusted intermediary performs a joint Bell state measurement on these quantum states, returns the successfully measured quantum states to both parties, and generates a quantum key.

[0011] S3. When encrypted information is transferred between any two clients, the sending client uses the public key between the two clients to perform the first layer of encryption on the quantum plaintext to obtain the first quantum ciphertext, and then uses the quantum key to perform the second layer of encryption on the first quantum ciphertext to obtain the second quantum ciphertext.

[0012] S4. Perform homomorphic computation on the second quantum ciphertext according to the predefined quantum circuit, and broadcast the homomorphic computation result to all clients except the sending client;

[0013] S5. Send the quantum decryption key to all clients except the sending client. All clients except the sending client use the quantum decryption key to perform the first layer of decryption on the homomorphic computation result to obtain the first quantum ciphertext. Then, they use their local private key to perform the second layer of decryption on the first quantum ciphertext. Only the target client can decrypt the quantum plaintext.

[0014] Furthermore, S1 includes:

[0015] Suppose there are n clients, and public and private keys are distributed between each pair of clients, with each client generating its own key independently. For public and private keys; for the client and between, , The generated public-private key pair is , , The generated public-private key pair is , ;

[0016] The client verifies its identity with the registration authority, and after successful verification, it authenticates and issues certificates for all public keys it generates through a trusted third-party certificate authority.

[0017] Each client sends its public key certificate to the other corresponding clients.

[0018] Furthermore, S2 includes:

[0019] For any two clients and The prepared quantum state and Transmitted to a trusted intermediary;

[0020] Trusted intermediaries for quantum states and Perform joint Bell state measurements, project their states onto one of four possible Bell states, and return the measurement results to both clients via a trusted and certified classical channel;

[0021] Both clients retain the successfully measured quantum state and, according to the agreed encoding rules, map their respective measurement results to bits. ;

[0022] Trusted intermediaries map their measurement results to bits according to the same encoding rules. ;

[0023] Generating quantum keys , ,in, , .

[0024] Furthermore, in S3, the first quantum ciphertext is represented as: ,in, For quantum plaintext, Indicated by quantum public key A quantum encryption operation.

[0025] Furthermore, in S3, the process of using a quantum key to perform a second layer of encryption on the first quantum ciphertext includes:

[0026] A second layer of encryption is applied to the first quantum ciphertext using quantum gate operations. Then apply the X gate if Then the X gate should not be used; if Then apply the Z-gate if Then, without applying the Z gate, the second quantum ciphertext is finally obtained. ,in, Indicates the quantum state operate, Indicates the quantum state operate, This is the first quantum ciphertext;

[0027] Client Design a quantum circuit for the second layer of encryption. And determine that the quantum circuit contains A quantum gate , A series of quantum gate operations are performed on quantum information through a set of quantum gates;

[0028] Client Design a good quantum circuit Afterwards, if Excluding T-doors, then Quantum ciphertext and quantum circuits Send to the computing server, and only send The first quantum cipher will be sent to a trusted intermediary and stored in a quantum circuit. Perform a series of quantum operations;

[0029] when Include When the door is open, the client Share the non-maximally entangled state in advance with the computing server, that is ,in, This indicates the correlation between two qubits; , and The complex coefficients represent the quantum state in the ground state. and The probability amplitude on the quantum state defines the distribution of the quantum state; Indicates the state The probability, Indicates the state The probability of.

[0030] Furthermore, S4 includes:

[0031] The computing server received the second quantum ciphertext. Then, it is evaluated and homomorphically computed according to the predetermined quantum circuit, and the corresponding second quantum ciphertext performs the corresponding operation according to the order of the quantum gates in the quantum circuit;

[0032] When quantum gate At that time, it directly affects the client. The encrypted second quantum ciphertext bit, after calculation, has the following ciphertext form: ,

[0033] Represents the quantum gates passed through in the homomorphic evaluation;

[0034] After the homomorphic computation is completed, the computation server sends the homomorphic computation result to the transmission server. The transmission server then "broadcasts" the homomorphic computation result. Transmitted to clients All other clients besides [the other client].

[0035] Furthermore, S5 includes:

[0036] Trusted intermediaries based on quantum circuits The quantum gate state is updated to obtain the encryption key and the quantum decryption key. And transmit the quantum decryption key through a classical authentication channel. Send to clients All other clients besides;

[0037] Except for the client All other clients use the quantum decryption key sent by the trusted intermediary to perform the first layer of decryption on the homomorphic computation result, recovering the first quantum ciphertext;

[0038] Except for the client All other clients attempted to use their local private key to perform a second-level decryption of the first quantum ciphertext, except for the target client. Obtain the original quantum plaintext .

[0039] Furthermore, if the quantum gate is an X-gate or a Z-gate, then the quantum decryption key... If the quantum gate is an H-gate, then the quantum decryption key... If the quantum gate is a P-gate, then the quantum decryption key... .

[0040] Furthermore, if the quantum gate is a CNOT gate, then the quantum decryption key is updated to... , and This represents the key parameters.

[0041] Furthermore, if the quantum gate is a T-gate, then the quantum decryption key is updated to... , This indicates the result of the client's measurement of the first particle in the quantum state. This indicates the result of the server's measurement of the second particle in the quantum state.

[0042] As can be seen from the above technical solution, compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. Protection against external attacks: This invention ensures the security of quantum key distribution by introducing a trusted intermediary, preventing external eavesdropping or tampering during key generation and distribution. Even if quantum information is intercepted, hackers cannot obtain useful information due to the randomness and no-cloning theorem of quantum keys. During the encryption phase, the measurement-device-independent quantum key distribution (MDI-QKD) protocol and Pauli keys are used to encrypt the data. The Pauli key is the quantum encryption key ek involved in the encryption process. This ensures that the quantum ciphertext is in a completely mixed state, preventing hackers from extracting useful information. Furthermore, during the homomorphic computation phase, the server can only manipulate encrypted data and cannot decrypt or obtain the original data, further ensuring data privacy.

[0044] 2. Protection against internal attacks: This invention effectively prevents internal attacks through independent operation between clients, secure key distribution, and broadcasting mechanisms. Even if an untrusted client attempts to steal data or intercept encrypted information, it cannot obtain the keys or data of other clients. Simultaneously, the server can only operate on encrypted data and cannot access plaintext content, and any illegal activity will be detected by the post-processing steps of the quantum key distribution protocol. Furthermore, the trusted key center Charlie plays a crucial role in key distribution and updates, ensuring the security of keys and quantum circuits and preventing internal leakage.

[0045] 3. The hybrid encryption mechanism of this invention effectively improves the security and privacy protection of quantum homomorphic encryption. Traditional quantum homomorphic encryption schemes often rely on quantum key distribution and quantum encryption / decryption, which may face problems such as low efficiency and high attack risk. The public-key encryption facility introduced in this invention ensures privacy during information transmission while also improving the overall system security.

[0046] 4. This invention utilizes a data broadcasting mechanism, allowing the server to securely transmit encrypted information to all clients without needing to know the target client's identity or the content of the encrypted data. Only the target client can decrypt the information; other clients cannot access the data. This mechanism not only ensures privacy and security during transmission but also further reduces potential security risks by preventing the server from accessing plaintext data, ensuring secure and efficient data transmission even in untrusted environments. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0048] Figure 1 A flowchart of the multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism provided by the present invention;

[0049] Figure 2 A detailed flowchart of the multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism provided by this invention;

[0050] Figure 3 A quantum circuit diagram containing T gates is provided for this invention. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] like Figure 1 As shown, this embodiment of the invention discloses a multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism, comprising the following steps:

[0053] S1. Assume there are n clients. Any two clients generate a public key and a private key. Each client stores the private key locally and sends the corresponding public key to the other corresponding clients.

[0054] S2. Any two clients transmit their quantum states to a trusted intermediary. The trusted intermediary performs a joint Bell state measurement on these quantum states, returns the successfully measured quantum states to both parties, and generates a quantum key.

[0055] S3. When encrypted information is transferred between any two clients, the sending client uses the public key between the two clients to perform the first layer of encryption on the quantum plaintext to obtain the first quantum ciphertext, and then uses the quantum key to perform the second layer of encryption on the first quantum ciphertext to obtain the second quantum ciphertext.

[0056] S4. Perform homomorphic computation on the second quantum ciphertext according to the predefined quantum circuit, and broadcast the homomorphic computation result to all clients except the sending client;

[0057] S5. Send the quantum decryption key to all clients except the sending client. All clients except the sending client use the quantum decryption key to perform the first layer of decryption on the homomorphic computation result to obtain the first quantum ciphertext. Then, they use their local private key to perform the second layer of decryption on the first quantum ciphertext. Only the target client can decrypt the quantum plaintext.

[0058] Below, in conjunction with Figure 2 The above steps will be further explained.

[0059] S1. Generation and distribution of public and private keys.

[0060] Suppose there are n clients, denoted as nn. They distribute public and private keys between each other, and each client generates its own key independently. Public and private keys; client arrive Each person generates their own public and private keys. Table 1 shows the public and private keys generated between each pair of clients to facilitate the subsequent flow of encrypted information.

[0061] Table 1. Each client generates a public-private key pair with the other client.

[0062]

[0063] For the client and between, , The generated public-private key pair is , , The generated public-private key pair is , Each client should strictly keep its private key confidential in order to decrypt encrypted messages sent by that client, and simultaneously keep its corresponding public key secret. It is sent to other corresponding clients and used to encrypt information. The specific process is as follows:

[0064] The client verifies its identity with the Registration Authority (RA), and after successful verification, it authenticates and issues certificates for all public keys it generates through a trusted third-party Certificate Authority (CA).

[0065] Each client sends its public key certificate to other corresponding clients so that they can use each other's public keys for encrypted communication.

[0066] Once all clients have exchanged verified public key certificates, each client possesses the public keys of all other clients and has verified their legitimacy through the certificates. Following this step, clients can securely communicate encrypted during the subsequent quantum homomorphic encryption process.

[0067] S2. Generation and distribution of quantum keys.

[0068] In this step, a trusted intermediary, Charlie, is introduced through the MDI-QKD protocol to facilitate the quantum key distribution process. Before explaining this process, it is necessary to understand the meaning of computational basis and Hadamard basis.

[0069] The computational basis is and These are the standard ground states of a qubit, representing binary 0 and 1 respectively, and are represented in the mathematical representation of a qubit as follows: , .

[0070] The Hadamard basis is calculated by H-gates acting on the ground state. and The resulting matrix representation of the H gate is as follows: Specifically, the Hadamard basis consists of the following two states: , .

[0071] The specific steps include:

[0072] S21. For any two clients and The prepared quantum state and Transmitted to a trusted intermediary.

[0073] Client and Prepare one of the following computational bases or Hadamard bases respectively: , , and ,in , . and These represent the client and The prepared quantum state.

[0074] S22, When the client and When these quantum states are transmitted to the trusted intermediary Charlie, they form several pairs of quantum states. , Charlie performs joint Bell state measurements on these quantum states to determine whether the received qubit pair is in a Bell state, which is the maximally entangled state of a two-qubit system. There are typically four basic Bell states, as shown in Table 2:

[0075] Table 2 Bell's State Formula

[0076]

[0077] Next, each symbol and its meaning will be explained in detail:

[0078] , , , As a fundamental quantum state, This indicates a state where both qubits are 0. This indicates a state where the first qubit is 0 and the second is 1. This indicates a state where the first qubit is 1 and the second is 0. This represents a state where both qubits are 1. These fundamental states are product states of the qubits; they do not indicate entanglement, but rather that each qubit is independently in a specific state.

[0079] It is a Bell state (entangled state) in which the states of the two qubits are perfectly entangled. If one qubit is measured to be 0, the other qubit will also be 0; similarly, if one bit is 1, the other will also be 1.

[0080] and The difference is that it changes in phase. If the measurement shows one bit is 0, the other bit will be 0; if one bit is 1, the other bit will be 1.

[0081] This represents the superposition of two qubits in different states (i.e., one is 0 and the other is 1). This state indicates that the two qubits are entangled, but their states are not always the same.

[0082] This also means that the states of the two qubits are entangled, but when the measurement results are the same (one is 0 and the other is 1 or vice versa), there will be a difference in phase.

[0083] Trusted intermediary Charlie, through... , A joint Bell state measurement is performed, aiming to project their states onto one of four possible Bell states. To do this, it performs the following operations:

[0084] 1. Apply CNOT gate: , Entangling terms and operating on only one of the two quantum states maximizes the preservation of the transmitted information.

[0085] 2. Applying the Hadamard gate (H gate): transforms a state into a form suitable for Bell state measurement, specifically transforming the ground state of a quantum state into a superposition state.

[0086] 3. Projection: By measuring the transformed state, Charlie will obtain one of the four Bell states, i.e. .

[0087] 4. Result feedback: Finally, Charlie returns the measurement results to both parties through a trusted and certified classic channel.

[0088] S23. To verify that the quantum channel is secure and reliable, the MDI-QKD protocol requires the two parties sharing the key to set a measurement error threshold. A measurement error refers to a situation where the measurement result returned by the quantum channel does not match the expected result. The error threshold is typically... If the error rate is below the set threshold, it is confirmed that there is no eavesdropper, which proves that the quantum channel is secure between the two clients.

[0089] Based on the above measurement results Both clients retain the successfully measured quantum state as the preparation basis. Only quantum states prepared using the same preparation basis by both parties are retained. Specifically, the preparation basis refers to a set of ground states used to prepare the quantum state. The choice of preparation basis directly affects the type and security of the quantum state prepared by both communicating parties (client and Charlie). Quantum states are usually represented in the form of ground states. For example, and It is the standard computational basis; and A diagonal basis (also called a phase basis) is the standard set of states used to represent these quantum states. A crucial step in quantum key distribution is that both parties (the client and Charlie) choose the same preparation basis to prepare and measure the quantum states. Only with the same preparation basis can the measurement results be valid and meaningful, ensuring that both parties obtain synchronized results, thereby ensuring the security of the final key. After the step of preserving the quantum states, the client... and This will yield the quantum key for the quantum homomorphic encryption to be performed.

[0090] S24. Both clients, according to the agreed encoding rules, map their respective measurement results to bits. ;for example, and Encoded as the classic bit "0" and Encoded as a classical bit "1", the client then maps its measurement results to these bits to generate a quantum key. If the client measures... or but If the measurement is or but .

[0091] Similarly, the trusted intermediary encodes bits according to the same encoding rules, mapping its own measurement results to bits. In this way, both parties can obtain the same quantum key. , in the form of ,in, .

[0092] S3, the double-layer encryption process, specifically includes:

[0093] S31, The sending client utilizes the target client P j The public key shared by both parties is used to perform the first layer of encryption on the quantum plaintext, resulting in the first quantum ciphertext. Specifically, this includes:

[0094] Assuming that in this invention, the client... and Encrypted information flow between them, i.e., client The quantum information needs to be encrypted and subjected to homomorphic computations before being sent to the target customer. The specific process is as follows:

[0095] First, the client To possess a string of quantum plaintext that needs to be kept confidential and transmitted. , and The coefficients are complex and satisfy the normalization condition: Client use Shared public key Quantum information to be encrypted with quantum key Perform the first layer of encryption.

[0096] It's important to note that classical public-key algorithms (such as RSA) operate on classical data. However, classical public-key algorithms cannot encrypt or decrypt quantum information. In essence, quantum information is fundamentally different from classical information. A quantum bit not only possesses the states of a classical bit (0 or 1) but also exhibits quantum superposition states, as exemplified by the given quantum plaintext. This presents different challenges to quantum information operations compared to classical information. RSA encrypts classical data using a public key and can preserve the ciphertext state for further decryption. However, once quantum information is encrypted, its state changes during measurement, making simple decryption impossible.

[0097] Therefore, the public key used here It will be a series of algorithms for computing quantum information, namely... At the same time, the corresponding private key Similarly, assuming encryption operation Based on quantum public key A quantum encryption operation designed to operate on quantum plaintext. The encrypted quantum state, i.e., the first quantum ciphertext, is obtained as follows: .

[0098] For quantum information, the quantum RSA (QRSA) algorithm should be used. This algorithm is analogous to classical RSA, but the encryption process uses quantum states instead of classical bits. At the same time, the invariance of the quantum state during measurement needs to be guaranteed. Therefore, in the public-key encryption process, the message needs to be encoded in quantum states, rather than directly using classical numbers.

[0099] S32. Use a quantum key to perform a second layer of encryption on the first quantum ciphertext to obtain the second quantum ciphertext, specifically including:

[0100] Client Using the quantum key generated in step S2 To encrypt the first quantum ciphertext The encryption process operates through quantum gates. and If Then apply the X gate if Then the X gate should not be used; if Then apply the Z-gate if Then, without applying the Z gate, the second quantum ciphertext is finally obtained. ,in, Indicates the quantum state operate, Indicates the quantum state operate, and This represents the quantum key value (usually 0 or 1) used in the encryption process. This is the first quantum ciphertext.

[0101] The X gate and Z gate here refer to... The corresponding quantum gate in the text, and the T gate mentioned later, is the quantum gate required in the homomorphic evaluation step. Homomorphic evaluation, after being encrypted with the S31 public key, ensures the security of subsequent information computation and transmission. (Client...) Design a quantum circuit for the second layer of encryption. And determine that the quantum circuit contains A quantum gate , A series of quantum gate operations are performed on quantum information through a set of quantum gates. These operations include common Clifford gates such as X, Z, H, and CNOT, as well as non-Clifford gates. The circuit design usually depends on the specific encryption requirements and encryption key of the quantum information, and it also affects the subsequent quantum decryption process.

[0102] Client Design a good quantum circuit Afterwards, if Excluding T-doors, then Quantum ciphertext and quantum circuits Send to the computing server, and only send The first quantum cipher will be sent to a trusted intermediary and stored in a quantum circuit. Perform a series of quantum operations;

[0103] when Include To address the phase error problem in T-gate operations during homomorphic evaluation, the client... The non-maximally entangled state needs to be shared with the computing server in advance, that is , and represent It is in a non-maximally entangled state. This indicates the correlation between two qubits. In this non-maximally entangled state, when a measurement is performed on one qubit, it will affect the state of the other qubit, but its degree of entanglement is not as strong as that of the maximally entangled state. , and The complex coefficients represent the quantum state in the ground state. and The probability amplitude on the quantum state defines the distribution of the quantum state; Indicates the state The probability, Indicates the state The probability, which means and The sum of all 1s equals 1, ensuring the validity of the quantum state and conforming to the basic principles of quantum mechanics.

[0104] S4. Quantum homomorphic computation, specifically including:

[0105] During the encryption phase, the client The information to be sent is actually not limited to a single quantum message. It can send multiple messages, so the computing server receives the second quantum ciphertext. Then, it is evaluated and homomorphically computed according to the predetermined quantum circuit, which specifically involves performing the corresponding operations on the corresponding second quantum cipher in the order of the quantum gates in the quantum circuit.

[0106] To analyze this scheme intuitively and accurately, we only need to analyze some typical Clifford gates in the homomorphic evaluation phase, such as... This eliminates the need to introduce excessive quantum gates, so when quantum gates... At that time, it directly affects the client. The encrypted second quantum ciphertext bit, after calculation, has the following ciphertext form:

[0107] , Represents the quantum gate passed through in the homomorphic evaluation; and because The circuit is composed of Clifford gates, and according to the MDI-QKD protocol, Charlie can directly update the decryption key during the subsequent decryption process.

[0108] After the homomorphic computation is completed, the computation server sends the homomorphic computation result to the transmission server. The transmission server then "broadcasts" the homomorphic computation result. Transmitted to clients This applies to all clients other than those already connected to the target client. The aim is to ensure that the server accurately conveys confidential data to the target client without their knowledge of the information. This also further enhances the reliability and security of information flow within the solution. Of course, after the data is "broadcast," the target customers... You also need to determine for yourself whether the information belongs to you; the specific process will be described in S5.

[0109] S5, key update and decryption, specifically includes:

[0110] S51, Trusted intermediary based on quantum circuit The quantum gate state is updated to obtain the encryption key and the quantum decryption key. And transmit the quantum decryption key through a classical authentication channel. Send to clients All other clients besides [the other client].

[0111] According to the encryption key If the quantum gate is an X-gate or a Z-gate, then the quantum decryption key... Assuming the quantum information after homomorphic evaluation is Then the subsequent decryption calculation process is... If the quantum gate is an H-gate, then the quantum decryption key... The decryption calculation process is as follows: The decryption calculation process is as follows: If the quantum gate is a P-gate, then the quantum decryption key... Next, Table 3 will explain how to use the encryption key. and quantum circuits To obtain the decryption key.

[0112] Table 3 Key Update Rules (X, Z, H, P Gates)

[0113]

[0114] If the quantum gate is a CNOT gate, since CNOT is a two-qubit gate, and both its control qubit and target qubit require encryption keys, then the corresponding encryption key is:

[0115] Then the quantum decryption key is updated to , and This indicates the key parameters, from which we can determine whether they are introduced. and It depends on how the quantum circuit is constructed.

[0116] If the quantum gate is a T-gate, then the T-gate does not possess the property of commuting with the Pauli group, i.e. When applied to encrypted quantum states, the result will be... , Representing a phase error, the client operates on the first particle in the non-maximally entangled state, i.e. ,in It is the encryption key obtained by the client in S1. The value of this expression represents Acting on On the first particle, the unit operation I acts on The second particle is then measured. In this case, the rule for updating the encryption key requires the results of both measurements after the T-gate evaluation. Figure 3 As can be seen, the first particle in the quantum state is processed through quantum gate operations and is ultimately measured by the client; the result of this measurement is... This corresponds to the state of the qubit measured by the client. The second particle in the quantum state is processed by the server; after performing a series of operations including CNOT and Hadamard gates, it is finally measured by the server. The result of this measurement is... This corresponds to the state of the qubit measured by the server. As you can see... Figure 3 The results are as follows: and Then the quantum decryption key is updated to The key update rules are shown in Table 4:

[0117] Table 4 Key Update Rules (CNOT, T-gate)

[0118]

[0119] Update decryption key Afterwards, except for the client All other clients, except for those using the quantum decryption key sent by the trusted intermediary, perform the first layer of decryption on the homomorphic computation result, at which point they all obtain the quantum plaintext. The quantum information encrypted with a public key is called the first quantum ciphertext. .

[0120] S52, private key decryption (second-level decryption), specifically includes:

[0121] Besides the client All clients other than those mentioned above obtained quantum information after following the above steps. However, a final decryption process is still required to obtain the quantum plaintext. ,and The ultimate goal is to transmit this data to the target customer. ,so Only public keys can be used corresponding private key The decrypted, while other clients, such as These unrelated clients' private keys It is impossible to Decryption was successfully completed. Therefore, in this stage, except for... After other customers attempted to decrypt the information, only the target customer was able to access it. Ultimately, the original quantum plaintext will be obtained. Other customers could not obtain it. Thus, Successfully completed the quantum information The system ensures accurate transmission and guarantees that the transmission server and other clients are completely unaware of the quantum plaintext of the encrypted information and the identity of its target client.

[0122] This invention enables data exchange between clients and ensures absolute security during data transmission. It allows any number of clients to request homomorphic quantum computations in parallel on an untrusted transmission server, while guaranteeing the precise flow of private data. In short, this invention achieves secure homomorphic evaluation of multi-party quantum encrypted data and ensures key security through a trusted public-key infrastructure and a quantum key distribution center.

[0123] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0124] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism, characterized in that, Includes the following steps: S1. Assume there are n clients. Any two clients generate a public key and a private key. Each client stores its private key locally and sends the corresponding public key to the other clients. Any two clients use the QRSA algorithm to generate a public key and a private key. During the public key encryption process, the message needs to be encoded in quantum states. S2. Any two clients transmit their quantum states to a trusted intermediary. The trusted intermediary performs a joint Bell state measurement on these quantum states, returns the successfully measured quantum states to both parties, and generates a quantum key. S3. When encrypted information is transferred between any two clients, the sending client uses the public key between the two clients to perform the first layer of encryption on the quantum plaintext to obtain the first quantum ciphertext, and then uses the quantum key to perform the second layer of encryption on the first quantum ciphertext to obtain the second quantum ciphertext. S4. Perform homomorphic computation on the second quantum ciphertext according to the predefined quantum circuit, and broadcast the homomorphic computation result to all clients except the sending client; S5. Send the quantum decryption key to all clients except the sending client. All clients except the sending client use the quantum decryption key to perform the first layer of decryption on the homomorphic computation result to obtain the first quantum ciphertext. Then, they use their local private key to perform the second layer of decryption on the first quantum ciphertext. Only the target client can decrypt the quantum plaintext.

2. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 1, characterized in that, S1 includes: Suppose there are n clients, and public and private keys are distributed between each pair of clients, with each client generating its own key independently. For public and private keys; for the client and between, , The generated public-private key pair is , , The generated public-private key pair is , ; The client verifies its identity with the registration authority, and after successful verification, it authenticates and issues certificates for all public keys it generates through a trusted third-party certificate authority. Each client sends its public key certificate to the other corresponding clients.

3. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 1, characterized in that, S2 include: For any two clients and The prepared quantum state and Transmitted to a trusted intermediary; Trusted intermediaries for quantum states and Perform joint Bell state measurements, project their states onto one of four possible Bell states, and return the measurement results to both clients via a trusted and certified classical channel; Both clients retain the successfully measured quantum state and, according to the agreed encoding rules, map their respective measurement results to bits. ; Trusted intermediaries map their measurement results to bits according to the same encoding rules. ; Generating quantum keys , ,in, , .

4. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 1, characterized in that, In S3, the first quantum ciphertext is represented as: ,in, For quantum plaintext, Indicated by quantum public key A quantum encryption operation.

5. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 3, characterized in that, In S3, the process of using a quantum key to perform a second layer of encryption on the first quantum ciphertext includes: A second layer of encryption is applied to the first quantum ciphertext using quantum gate operations. Then apply the X gate if Then the X gate should not be used; if Then apply the Z-gate if Then, without applying the Z gate, the second quantum ciphertext is finally obtained. ,in, Indicates the quantum state operate, Indicates the quantum state operate, This is the first quantum ciphertext; Client Design a quantum circuit for the second layer of encryption. And determine that the quantum circuit contains A quantum gate , A series of quantum gate operations are performed on quantum information through a set of quantum gates; Client Design a good quantum circuit Afterwards, if Excluding T-doors, then Quantum ciphertext and quantum circuits Send to the computing server, and only send The first quantum cipher will be sent to a trusted intermediary and stored in a quantum circuit. Perform a series of quantum operations; when Include When the door is open, the client Share the non-maximally entangled state in advance with the computing server, that is ,in, This indicates the correlation between two qubits; , and The complex coefficients represent the quantum state in the ground state. and The probability amplitude on the quantum state defines the distribution of the quantum state; Indicates the state The probability, Indicates the state The probability of.

6. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 1, characterized in that, S4 include: The computing server received the second quantum ciphertext. Then, it is evaluated and homomorphically computed according to the predetermined quantum circuit, and the corresponding second quantum ciphertext performs the corresponding operation according to the order of the quantum gates in the quantum circuit; When quantum gate At that time, it directly affects the client. The encrypted second quantum ciphertext bit, after calculation, has the following ciphertext form: , Represents the quantum gate passed through in the homomorphic evaluation; After the homomorphic computation is completed, the computation server sends the homomorphic computation result to the transmission server, which then "broadcasts" the result. Transmitted to clients All other clients besides [the other client].

7. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 1, characterized in that, S5 include: Trusted intermediaries based on quantum circuits The quantum gate state is updated to obtain the encryption key and the quantum decryption key. And transmit the quantum decryption key through a classical authentication channel. Send to clients All other clients besides; Except for the client All other clients use the quantum decryption key sent by the trusted intermediary to perform the first layer of decryption on the homomorphic computation result, recovering the first quantum ciphertext; Except for the client All other clients attempted to use their local private key to perform a second-level decryption of the first quantum ciphertext, except for the target client. Obtain the original quantum plaintext .

8. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 7, characterized in that, If the quantum gate is an X-gate or a Z-gate, then the quantum decryption key... If the quantum gate is an H-gate, then the quantum decryption key... If the quantum gate is a P-gate, then the quantum decryption key... .

9. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 7, characterized in that, If the quantum gate is a CNOT gate, then the quantum decryption key is updated to... , and This represents the key parameter.

10. The multi-party quantum homomorphic encryption method based on a hybrid encryption mechanism according to claim 7, characterized in that, If the quantum gate is a T-gate, then the quantum decryption key is updated to... , This indicates the result of the client's measurement of the first particle in the quantum state. This indicates the result of the server's measurement of the second particle in the quantum state.

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