A method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party

Abstract

The present invention discloses a method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party. First, a user requests a trusted third party to retrieve specific data from user data; the trusted third party prepares a corresponding plaintext superposition state based on the user's search request; then the trusted third party and a cloud server collaborate to homomorphically execute the quantum Grover algorithm on the plaintext superposition state based on the number of Grover iterations; the trusted third party measures the quantum state after the search, and the obtained measurement result is the solution corresponding to the search request; then the trusted third party shares a string of identical keys with the user through quantum key distribution technology, encrypts the measurement result using the shared key, and sends the encrypted measurement result to the user; the user then decrypts the encrypted measurement result using the shared key to obtain the solution corresponding to the proposed search request. This method can effectively improve the efficiency and security of ciphertext retrieval, and achieve fast and secure ciphertext retrieval.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum cryptography, and in particular to a method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party. Background Art

[0002] With the development of cloud computing, more and more users are uploading their personal private data to the cloud for storage. To avoid exposing this private data to cloud servers, users often encrypt it before uploading it. Ciphertext retrieval is a key research area in secure multi-party computation. The core problem of ciphertext retrieval is how to enable cloud servers to quickly and securely retrieve the correct data from encrypted data, based on the user's search question, without the cloud server knowing anything about the data. Ciphertext retrieval, also known as private database query, has broad applications in fields such as medical data query and stock information query.

[0003] The security of classical ciphertext retrieval methods based on homomorphic encryption algorithms relies primarily on the difficulty of solving mathematical problems. However, the emergence of quantum Shor's algorithm, which can factor large numbers in polynomial time, poses a significant threat to the security of classical ciphertext retrieval methods based on homomorphic encryption algorithms. Quantum homomorphic encryption has been extensively researched over the past decade. Its security, guaranteed by the fundamental principles of quantum mechanics, is immune to quantum algorithms. The quantum homomorphic encryption process involves the user encrypting the plaintext and sending it to a cloud server. The cloud server then applies an evaluation algorithm to the ciphertext and returns the result to the user. The user then decrypts the result, which is equivalent to the result obtained by applying the evaluation algorithm directly to the plaintext. Quantum homomorphic encryption protects users' private data from being leaked while ensuring that cloud servers can complete the computing tasks entrusted to them. Therefore, achieving fast and secure ciphertext retrieval and improving its efficiency and security have become urgent challenges. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party. The method uses a trusted third party to mark the ground state of the correct solution corresponding to the search request submitted by the user, so that the cloud server cannot obtain any information about the correct solution, thereby effectively improving the efficiency and security of ciphertext retrieval and realizing fast and secure ciphertext retrieval.

[0005] The purpose of the present invention is achieved through the following technical solutions:

[0006] A method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party, the method comprising:

[0007] Step 1: The user requests a trusted third party to retrieve specific data from the user's data; the specific data is the solution corresponding to the user's search request; wherein the trusted third party is used to mark the ground state of the correct solution in the plaintext superposition state and can perform quantum encryption and quantum decryption operations;

[0008] Step 2: The trusted third party prepares a corresponding plaintext superposition state according to the user's search request and determines the number of Grover iterations to be performed in the quantum Grover algorithm;

[0009] Step 3: The trusted third party and the cloud server then collaborate to homomorphically execute the quantum Grover algorithm on the plaintext superposition state according to the number of Grover iterations to obtain the searched quantum state;

[0010] Step 4: The trusted third party measures the quantum state after the search, and the measurement result obtained is the solution corresponding to the search request proposed by the user;

[0011] Step 5: The trusted third party then shares a string of identical keys with the user through quantum key distribution technology, encrypts the measurement result obtained in step 4 using the shared key, and sends the encrypted measurement result to the user;

[0012] Step 6: The user decrypts the encrypted measurement result according to the shared key, and finally obtains the solution corresponding to the search request.

[0013] It can be seen from the technical solution provided by the above-mentioned present invention that the above-mentioned method uses a trusted third party to mark the base state of the correct solution corresponding to the search request submitted by the user, so that the cloud server cannot obtain any information of the correct solution, thereby effectively improving the efficiency and security of ciphertext retrieval and realizing fast and secure ciphertext retrieval. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0015] Figure 1 A flow chart of a method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0016] The following is a clear and complete description of the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments, and do not constitute a limitation of the present invention. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0017] like Figure 1 FIG2 is a flow chart of a method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party provided by an embodiment of the present invention, wherein the method includes:

[0018] Step 1: The user requests a trusted third party to retrieve specific data from the user's data; the specific data is the solution corresponding to the search request raised by the user;

[0019] In this step, the role of the trusted third party is to mark the ground state of the correct solution in the plaintext superposition state and to perform quantum encryption and quantum decryption operations. Any terminal device with the above functions can serve as a trusted third party;

[0020] Step 2: The trusted third party prepares a corresponding plaintext superposition state according to the user's search request and determines the number of Grover iterations to be performed in the quantum Grover algorithm;

[0021] In this step, the trusted third party prepares the corresponding plaintext superposition state according to the user's search request in the following specific steps:

[0022] If the user data is 2 n Then the trusted third party sets n quantum bits with all values ​​of |0> and applies n H gates to these n quantum bits |0> to obtain the corresponding plaintext superposition state. Right now:

[0023]

[0024] in, represents a single quantum bit, represents a double quantum bit, |00…0> represents the direct product of n quantum bits, and the value of n is a natural number, that is, a non-negative integer; the H gate is the Hadamard gate, and its matrix expression is It acts on a single quantum bit and The processes are as follows:

[0025]

[0026]

[0027] |x0> represents the plaintext superposition state The ground state of the correct solution in ;

[0028] And determine the number of Grover iterations performed in the quantum Grover algorithm as Is the rounding symbol, that is, regardless of the rounding rules, as long as there is a decimal after it, the integer in front will be increased by 1, for example

[0029] Step 3: The trusted third party and the cloud server then collaborate to homomorphically execute the quantum Grover algorithm on the plaintext superposition state according to the number of Grover iterations to obtain the searched quantum state;

[0030] In this step, the marking solution operation of the first round of Grover iteration is first performed, specifically, the trusted third party uses the quantum oracle to mark the correct solution base state in the plaintext superposition state; for example, in the first round of Grover iteration, the trusted third party uses the quantum oracle to mark the correct solution base state in the plaintext superposition state. Mark the correct ground state of the solution |x0> and obtain the marked plaintext superposition state Right now:

[0031]

[0032] Since the quantum unitary operation used by the quantum oracle to identify and mark the solution is completed in a black box, neither the trusted third party nor the cloud server can obtain information about the solution from the quantum oracle;

[0033] The trusted third party uses the quantum one-time pad technology to encrypt the marked plaintext superposition state based on the randomly generated encryption key and sends the encrypted plaintext superposition state to the cloud server; for example, the trusted third party uses the randomly generated 2n-bit encryption key The superposition state of the marked plaintext Encrypt and get Right now:

[0034]

[0035] Among them, X and Z belong to quantum Pauli gates, and their matrix expressions are and They act on a single qubit and The processes are as follows:

[0036]

[0037]

[0038]

[0039]

[0040] and It is an encryption key and is taken from integers 0 and 1. and The superscript 1 represents the first round of Grover iteration, and the subscript i represents the quantum gate and Acting on n quantum bits The trusted third party will encrypt the marked plaintext superposition state Send it to the cloud server to perform other quantum unitary operations of this round of Grover iteration, so that the cloud server cannot obtain any information about the solution from the encrypted marked superposition state;

[0041] The cloud server then performs Hadamard transformation, conditional phase shift transformation and Hadamard transformation on the encrypted plaintext superposition state, and returns the encrypted first round Grover iterative quantum state to the trusted third party; wherein the Hadamard transformation is The conditional phase shift is transformed into

[0042] These quantum unitary operations do not require the consumption of auxiliary qubits during the homomorphic evaluation process of quantum homomorphic encryption, making the rules for the trusted third party to update the decryption key simple and efficient.

[0043] The trusted third party obtains the decryption key according to the key update rule, and uses the decryption key to decrypt the encrypted quantum state of the first round of Grover iteration to obtain the quantum state after the first round of Grover iteration; for example, according to the key update rule, the decryption key obtained by the trusted third party is updated to in, and It is the decryption key, which is obtained according to the key update rule of quantum homomorphic encryption and is either 0 or 1; and The superscript 1 represents the first round of Grover iteration, and the subscript i represents the decryption operation (i.e., the quantum gate and ) acts on n quantum bits The first round of Grover iterative quantum state encrypted by the trusted third party Decrypt and get the quantum state after the first round of Grover iteration

[0044] The trusted third party and the cloud server then continue to execute the remaining rounds of Grover iterations to complete the entire quantum Grover algorithm process and obtain the searched quantum state.

[0045] Step 4: The trusted third party measures the quantum state after the search, and the measurement result obtained is the solution corresponding to the search request proposed by the user;

[0046] Step 5: The trusted third party then shares a string of identical keys with the user through quantum key distribution technology, encrypts the measurement result obtained in step 4 using the shared key, and sends the encrypted measurement result to the user;

[0047] In this step, the trusted third party shares a 2n-bit key (e1e2…e n ,f1f2…f n ), where e i and f i It is an encryption key and is taken from integers 0 and 1; e i and f i The subscript i indicates that the encryption operation is performed on the i-th quantum bit of n quantum bits. Due to the unconditional security of quantum key distribution technology, the cloud server or eavesdropper cannot obtain the information of these keys.

[0048] And use the shared key (e1e2…e n ,f1f2…f n ) Encrypt the measurement result obtained in step 4 and send the encrypted measurement result to the user, further ensuring that the cloud server cannot obtain the solution information corresponding to the search request proposed by the user.

[0049] Step 6: The user decrypts the encrypted measurement result according to the shared key, and finally obtains the solution corresponding to the search request.

[0050] It should be noted that the contents not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

[0051] In summary, the method described in the embodiment of the present invention is based on the high efficiency of the quantum Grover algorithm. In each round of Grover iteration, the operation of marking the solution is completed by a trusted third-party quantum oracle, and operations such as Hadamard transform and conditional phase shift transform are completed by the cloud server, thereby improving the efficiency of ciphertext retrieval.

[0052] Based on the high security of quantum homomorphic encryption, a trusted third party encrypts the marked quantum state and then sends it to the cloud server to perform other quantum unitary operations in the Grover iteration. This prevents the cloud server from obtaining any information about the corresponding data from the encrypted marked quantum state and the quantum unitary operations it performs, thus improving the security of ciphertext retrieval.

[0053] Based on the unconditional security of quantum key distribution technology, a trusted third party encrypts the measurement results with a shared key and sends the encrypted measurement results to the user, ensuring that the measurement results will not be leaked to the cloud server or external eavesdroppers during transmission.

[0054] In addition, those skilled in the art will understand that all or part of the steps in the above-mentioned embodiment method can be implemented by instructing the relevant hardware through a program, and the corresponding program can be stored in a computer-readable storage medium. The above-mentioned storage medium can be a read-only memory, a disk or an optical disk, etc.

[0055] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by any person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims. The information disclosed in the background technology section of this article is only intended to deepen the understanding of the overall background technology of the present invention, and should not be regarded as an admission or any form of implication that the information constitutes prior art already known to those skilled in the art.

Claims

1. A method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party, characterized in that: The method comprises: Step 1: The user requests a trusted third party to retrieve specific data from the user's data; the specific data is the solution corresponding to the user's search request; wherein the trusted third party is used to mark the ground state of the correct solution in the plaintext superposition state and can perform quantum encryption and quantum decryption operations; Step 2: The trusted third party prepares a corresponding plaintext superposition state according to the user's search request and determines the number of Grover iterations to be performed in the quantum Grover algorithm; Step 3: The trusted third party and the cloud server cooperate to homomorphically execute the quantum Grover algorithm on the plaintext superposition state according to the number of Grover iterations to obtain the searched quantum state; Step 4: The trusted third party measures the quantum state after the search, and the measurement result obtained is the solution corresponding to the search request proposed by the user; Step 5: The trusted third party shares a common key with the user through quantum key distribution technology, encrypts the measurement result obtained in step 4 using the shared key, and sends the encrypted measurement result to the user; Step 6: The user decrypts the encrypted measurement result according to the shared key, and finally obtains the solution corresponding to the search request.

2. The method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party according to claim 1, characterized in that: In step 2, the trusted third party prepares the corresponding plaintext superposition state according to the user's search request in the following specific steps: If the user data is 2 n Then the trusted third party sets n quantum bits with all values ​​of |0> and applies n H gates to these n quantum bits |0> to obtain the corresponding plaintext superposition state. Right now: in, represents a single quantum bit, represents a double quantum bit, |00…0> represents the direct product of n quantum bits, and the value of n is a natural number; the H gate is the Hadamard gate, and its matrix expression is It acts on a single quantum bit and The processes are as follows: |x0> represents the plaintext superposition state The ground state of the correct solution in ; And determine the number of Grover iterations performed in the quantum Grover algorithm as Is the ceiling symbol.

3. The method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party according to claim 1, characterized in that: The process of step 3 is: First, the first round of Grover iteration mark solution operation is performed, specifically, a trusted third party uses a quantum oracle to mark the ground state of the correct solution in the plaintext superposition state; The trusted third party encrypts the marked plaintext superposition state using the quantum one-time pad technology based on the randomly generated encryption key and sends the encrypted plaintext superposition state to the cloud server; The cloud server then homomorphically performs Hadamard transformation, conditional phase shift transformation, and Hadamard transformation on the encrypted plaintext superposition state, and returns the obtained encrypted first-round Grover iterative quantum state to the trusted third party; The trusted third party obtains a decryption key according to the key update rule, and uses the decryption key to decrypt the encrypted quantum state of the first round of Grover iteration to obtain the quantum state after the first round of Grover iteration; The trusted third party and the cloud server then continue to execute the remaining rounds of Grover iterations to complete the entire quantum Grover algorithm process and obtain the searched quantum state.

4. The method for quantum homomorphic encryption ciphertext retrieval based on a trusted third party according to claim 1, characterized in that: In step 5, the trusted third party shares a 2n-bit key (e1e2…e n ,f1f2…f n ), where e i and f i It is an encryption key and is taken from integers 0 and 1; e i and f i The subscript i in indicates that the encryption operation acts on the i-th qubit of n qubits; And use the shared key (e1e2…e n ,f1f2…f n ) Encrypt the measurement result obtained in step 4, and send the encrypted measurement result to the user.

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