CN113922944B - Quantum homomorphic encryption and decryption method based on multi-value single quantum state - Google Patents
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Abstract
The invention relates to the field of quantum communication and quantum cryptography, in particular to a quantum homomorphic encryption and decryption method based on a multi-value single quantum state; the method includes the steps that an encryption client generates two random keys; and sending the encrypted random key to the decryption client; the encryption client encrypts the d-dimensional plaintext quantum state into a d-dimensional ciphertext quantum state through an encryption operator and sends the d-dimensional ciphertext quantum state to the server; the server determines evaluation parameters required by evaluation operation according to the calculation requirement of the encryption client, prepares a corresponding evaluation operator, executes the evaluation operation on the received ciphertext quantum state, and sends an evaluation result and the evaluation parameters to the decryption client; the decryption client generates a new key from the received random key and the evaluation parameter, and negates the encryption key to obtain an updated decryption key; and the decryption client decrypts the evaluation result by using the updated decryption key. The invention can increase the carrying amount of information on single quantum bit and expand the research of quantum state in free space.
Description
Technical Field
The invention relates to the field of quantum communication and quantum cryptography, in particular to a quantum homomorphic encryption and decryption method based on a multi-value single quantum state.
Background
The homomorphic encryption algorithm can operate the data on the premise of keeping the data privacy, and the security of the classical algorithm is ensured by the calculation difficulty of the classical data. With the rapid development of quantum computers, the security of classical homomorphic encryption is gradually threatened, so that research on quantum homomorphic encryption algorithms is imperative. Because of the limitations of quantum computer technology and cost, quantum computers cannot be popularized in a short time, and thus when classical users have quantum computing demands, complex and huge computing tasks need to be delegated to the quantum computers for execution.
In the existing research, quantum homomorphic encryption is mainly based on two-dimensional and three-dimensional quantum states, and is unfavorable for the expansion of the quantum states in free space. To solve this problem, 2018 chinese patent CN 108847934a discloses a multidimensional quantum homomorphic encryption method; song et al in 2019 propose a design method of d-dimensional (t, n) threshold quantum homomorphic encryption algorithm; 2021 et al (Zhang, y., shang, T. & Liu, j.a multi-valued quantum fully homomorphic encryption scheme, quantum Inf Process 20,101 (2021)) propose a multi-valued quantum isohomomorphic encryption scheme.
Although these quantum homomorphic encryption schemes promote the dimensionality of the quantum states, they differ in the choice of evaluation operators. In order to improve the universality and universality of the quantum homomorphic encryption algorithm, song et al perfects the evaluation unitary operator based on the phase into the evaluation unitary operator based on the phase and state transformation. However, in these schemes, only one phase-based or phase-and state-transformation-based evaluation operator can be operated on one single quantum state. In the relatively perfect operation based on the phase and the evaluation operator, the secret sharing thought is still needed to be used, namely the technology needs to complete the evaluation operation of the quantum homomorphic encryption method by a plurality of servers, and finally the encryption client can obtain the calculated quantum state after reconstruction.
Disclosure of Invention
Based on the problems existing in the prior art, the invention provides a quantum homomorphic encryption and decryption method based on a multi-value single quantum state, which can increase the carrying amount of information on single quantum bits and expand the research of the quantum state in free space in the quantum homomorphic encryption method.
The quantum homomorphic encryption and decryption method based on the multi-value single quantum state mainly comprises five algorithms, a random key generation algorithm, an encryption algorithm, an evaluation algorithm, a key update algorithm and a decryption algorithm. The random key generation algorithm is executed by an encryption client, and the encryption client generates two random keys and stores the two random keys in a local classical register; the encryption client executes an encryption algorithm, generates a quantum plaintext state, and executes encryption operation on the quantum plaintext state through two encryption keys generated by a random key generation algorithm to obtain a ciphertext quantum state; the evaluation algorithm is executed by a third-party server, the third-party server generates evaluation parameters according to the calculation requirements of the encryption client, prepares corresponding evaluation operators according to the evaluation parameters, executes evaluation operation on quantum ciphertext states, transmits an evaluation result to the decryption client through a quantum secure channel, and transmits an evaluation parameter sequence encrypted by a public key to the decryption client through a classical channel; the decryption client executes a key updating algorithm, performs key updating operation on classical data received from the encryption client and the server to generate a new key, and performs negation operation on the encryption key to obtain an updated decryption key; and the decryption client executes a decryption algorithm according to the result of the key updating algorithm to obtain a decryption result, wherein the decryption result is consistent with the result obtained by directly executing the evaluation operation on the plaintext quantum state.
Specifically, the invention solves the technical problems by the following technical scheme:
a quantum homomorphic encryption and decryption method based on multi-value single quantum states mainly comprises the following steps:
the encryption client randomly generates two random keys and stores the random keys locally;
the encryption client executes a public key encryption algorithm, encrypts the random key and sends the encrypted random key to the decryption client;
the encryption client executes a quantum one-time encryption algorithm, encrypts a d-dimensional plaintext quantum state into a d-dimensional ciphertext quantum state by using a locally stored random key through an encryption operator, and sends the d-dimensional ciphertext quantum state to a server through a quantum secure channel;
the server determines parameters of the evaluation operator according to the calculation requirement of the encryption client, and prepares a corresponding evaluation operator; the evaluation parameters are encrypted through a public key encryption algorithm and then sent to a decryption client; the server executes evaluation operation on the received d-dimensional ciphertext quantum state, and sends an evaluation result to the decryption client through a quantum channel;
the decryption client executes a private key decryption algorithm, decrypts the received random key ciphertext and the received evaluation parameter ciphertext, and generates a new key by adopting key updating operation to obtain an updated decryption key;
and the decryption client executes a quantum one-time pad decryption algorithm, and decrypts the evaluation result by using the updated decryption key to obtain a decryption result.
The invention has the beneficial effects that:
1. the invention uses a third party quantum server to realize complex and huge calculation tasks, thereby saving the resource consumption of the encryption client, reducing the call of the existing technology to a plurality of quantum servers, and ensuring the safety of the data because the third party quantum server receives the private data encrypted by the encryption client, so that the third party quantum server cannot obtain any useful information related to the private data.
2. According to the invention, the dimension of the single particle is improved from two dimensions and three dimensions to d dimensions, so that the information carrying capacity of the single particle is greatly improved, a certain contribution is made to the research of a quantum homomorphic encryption method of quantum states in free space, and the safety of the particles in quantum communication is improved.
3. The invention executes the key updating operation, and the decryption client executes the decryption operation after updating the key, so even if an eavesdropper successfully intercepts the information, any hidden and sensitive information can not be obtained because the data can not be correctly decrypted, thereby achieving the aim of further ensuring the data security.
Drawings
FIG. 1 is a flow chart of a quantum homomorphic encryption and decryption method based on a multi-value single quantum state provided by an embodiment of the invention;
fig. 2 is a schematic diagram of a quantum homomorphic encryption and decryption system based on a multi-value single quantum state according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a terminal according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings, in which it is evident that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The present invention will be described below with reference to the accompanying drawings and examples, which illustrate the technical scheme of the present invention in detail. The described embodiments of the module are only used to better illustrate the invention and are not intended to limit the invention. As shown in FIG. 1, the quantum homomorphic encryption and decryption method based on multi-value single quantum states mainly comprises the following steps:
s1, a client randomly generates two random keys and stores the random keys locally;
in the embodiment of the present invention, the step S1 specifically includes:
s11, preparing a random key: the encryption client randomly generates two encryption keys a and b and stores the two encryption keys a and b into a local classical register;
wherein a represents a first random key and b represents a second random key; a corresponds to the key of the encryption operator X, and b corresponds to the key of the encryption operator Z; the two random keys are used as encryption keys for encrypting and decrypting the plaintext quantum state data. In the embodiment of the invention, the public key encryption algorithm is a classical asymmetric encryption algorithm.
S2, the encryption client executes a public key encryption algorithm, encrypts the random key and sends the encrypted random key to the decryption client;
in the embodiment of the invention, the client encrypts the encryption key stored in the classical register in step S11 through the classical public key encryption algorithm and then sends the encrypted encryption key to the decryption client.
In the embodiment of the invention, the public key encryption algorithm can adopt an asymmetric encryption algorithm commonly used in the field, namely, adopts public key encryption and adopts an algorithm of decrypting by a private key of a decrypting party.
In this embodiment, the transmission encryption key ciphertext and the evaluation parameter ciphertext may be transmitted through a classical channel, which is not particularly limited in the present invention.
S3, the encryption client executes a quantum one-time encryption algorithm, encrypts a d-dimensional plaintext quantum state into a d-dimensional ciphertext quantum state through an encryption operator by using a locally stored random key, and sends the d-dimensional ciphertext quantum state to a server through a quantum channel;
in the embodiment of the present invention, the step S3 mainly includes three processes:
s31, generating a plaintext: encryption client generates d-dimensional quantum plaintext state |sigma>＝t 0 |0>+t 1 |1>+…+t d-1 |d-1>WhereinThe measurement basis of the plaintext quantum state is:
s32, encryption stage: the encryption client uses the encryption key generated in the step S1 to encrypt the plaintext quantum state prepared in the step S31, and the ciphertext quantum state is |ρ>＝X a Z b |σ>Wherein the encryption operators are respectivelyThe final ciphertext quantum state is thus represented as:
wherein ρ is>Representing a d-dimensional ciphertext quantum state; x is X a Representing the encryption operator using the first random key a, i.e. the a-th power of the encryption operator X; z is Z b Representing the encryption operator using the second random key b, i.e. the b power of the encryption operator Z; sigma of I>Represents d-dimensional plaintext quantum state, |sigma, generated by an encryption client>＝t 0 |0>+t 1 |1>+…+t d-1 |d-1>，t x Representing coefficients between different quantum states of the xth d-dimension text quantum state; i x>Represents the state Wen Liangzi of the xth d-dimension,<x| represents |x>Is a conjugate transpose of (2); x ε {0,1, …, d-1}; ω=e 2πi/d 。
S33, transmitting data: the encryption client transmits the ciphertext quantum state to the third party server through the quantum secure channel to execute the next operation.
S4, the server determines a corresponding evaluation operator according to the calculation requirement of the client, performs evaluation operation on the received d-dimensional ciphertext quantum state, and sends an evaluation result to the decryption client through a quantum security channel;
in the embodiment of the invention, a third party quantum server determines an evaluation parameter sequence according to the calculation requirement of an encryption client, and determines each parameter alpha 1 ,β 1 ,α 2 ,β 2 ,...,α n ,β n The method comprises the steps of storing; likewise, it receives the ciphertext quantum state |ρ of the S3 quantum channel>Saving in a quantum register; after the data is received, the third party quantum server generates a corresponding evaluation operator according to the evaluation parameters, and further generates a corresponding result for the ciphertext quantum state |ρ>Performing an evaluation operation to obtain an evaluation result and marking the evaluation result asAfter the evaluation result is obtained, the third party quantum server transmits the evaluation result to the decryption client through the quantum security channel.
In some embodiments, the step S4 may include the following processes:
s41, preparation: after receiving the ciphertext quantum state from the encryption client, the third party server determines an evaluation parameter sequence alpha 1 ,β 1 ,α 2 ,β 2 ,...,α n ,β n The third-party server prepares corresponding evaluation estimators by using the evaluation parameters
Wherein,ω＝e 2πi/d ， α i ∈{0,1,...,d-1},β i ∈{0,1,...,d-1}。
wherein alpha is i ,β i Represents a set of evaluation parameters, alpha i ∈{0,1,...,d-1},β i E {0,1,., d-1}, (1. Ltoreq.i. Ltoreq.n); n represents the number of evaluation operators required for the encryption client to specify the computational task.
It can be understood that the invention adopts n pairs of evaluation parameters, each pair of evaluation parameters corresponds to one evaluation operator, and the whole evaluation operation is to apply n different evaluation operators to a single quantum state, so that the carrying capacity of information on the single bit quantum can be increased, and the study of the quantum state in a free space in the quantum homomorphic encryption method is expanded.
Specifically, in the embodiment of the present invention, the preparation process of the evaluation operator includes giving any two evaluation parameters α and β, where different values of the two evaluation parameters correspond to different evaluation operators, where:
when the first evaluation parameter α=0, the corresponding d-dimensional evaluation operator is represented as a phase transformation-based evaluation operatorn represents the value of the second evaluation parameter, n being any real number;
for example, for example: when the value of beta is equal to 1/2,beta=1/4->When β=1, the corresponding evaluation operator is +.>Similarly, so when β=n, the corresponding evaluation operator is +.>
When the second evaluation parameter β=0, it corresponds toD-dimensional evaluation operator of (2) is an evaluation operator based on state transformation, expressed asm represents the value of the first evaluation parameter, and m is any natural number;
for example, for example: when α=1, the corresponding evaluation operator is:when α=2, the corresponding evaluation operator is: />Similarly, when α=m, the corresponding evaluation operator is: />Where m ε {0,1,..d-1 }.
When α=0, β=0, it is expressed asThe evaluation operator at this time can be analogically to a unit gate I in a two-dimensional quantum state.
When alpha is not equal to 0 and beta is not equal to 0, the corresponding d-dimensional evaluation operator is an operator based on phase and state transformation and expressed asAlpha is {0,1,., d-1}, beta is any real number;
for example, for example: when α=1, β=1, the corresponding evaluation operator is
Wherein, |x>The states of the quanta are represented,<x| represents |x>Is a conjugate transpose of (2); x ε {0,1, …, d-1}; ω=e 2πi/d 。
In the embodiment of the invention, the corresponding quantum gate can be determined according to the calculation requirement of the encryption client, and the corresponding evaluation parameter can be determined according to the quantum gate.
In particular, when the dimension d=2, α=0, β=0 corresponds to G 0,0 Equal to the unit gate I. α=0, β=1 corresponds to G 0,1 Equal to Pauli-Z gate; α=0, β=1/2 corresponds to G 0,1/2 Equal to the phase gate S; α=0, β=1/4 corresponds to G 0,1/4 Equal to pi/8 gate. G corresponding to α=1, β=0 1,0 Equal to Pauli-X gate. α=1, β=1 corresponds to G 1,1 Equal to the Pauli-Y gate.
When the calculation task of the client needs to change the phase value of the d-dimensional quantum state, the value of the first evaluation parameter alpha can be set to 0; accordingly, when the computing task needs to change the state of the d-dimensional quantum state, the value of the second evaluation parameter β may be set to 0. Similarly, when it is desired to change the phase and state of the d-dimensional quantum state simultaneously, the values of both evaluation parameters may be set to be non-0.
S42, evaluation operation: executing corresponding evaluation operation on the ciphertext quantum state received from step S33, and after receiving the ciphertext quantum state transmitted by the encryption client, applying all evaluation operators to obtain an evaluation result:
wherein,representing a result quantum state of directly performing evaluation operation on the ciphertext quantum state sent by the encryption client;
s43, transmitting data: the third party server performs the steps described above to quantum the resultAnd sending the parameters to a decryption client through a quantum secure channel, encrypting the parameters through a public key encryption algorithm, and then sending the parameters to the decryption client through a classical channel.
S5, the decryption client uses the private key to execute decryption operation on the encrypted classical data, decrypts the received random key ciphertext and the received evaluation parameter ciphertext, adopts key updating operation to generate a new key, and executes negation operation on the encryption key, namely the random key ciphertext, so as to obtain an updated decryption key;
in the embodiment of the invention, the key updating algorithm is executed by the decryption client, so that the privacy and the integrity of the data are ensured, and the step S5 mainly comprises the following contents:
s51, receiving data: the decryption client stores the received result quantum state in a quantum register;
wherein the decryption client receives the encryption key pair a, b transmitted by the encryption client and the evaluation parameter sequence alpha transmitted by the server 1 ,β 1 ,α 2 ,β 2 ,...,α n ,β n The encryption key pair and the evaluation parameter sequence herein actually refer to ciphertext data, which needs to be decrypted to obtain corresponding plaintext data.
S52, decrypting data: the decryption client decrypts the two keys received from the classical channel and the evaluation parameters determined by the calculation requirement using its private key to obtain a, b, a respectively 1 ,β 1 ,α 2 ,β 2 ,...,α n ,β n ；
S53, key updating operation: the decryption client performs a key update algorithm according to the data described in step S42 to obtain an updated key, a ', b', key= -a (β 1 +β 2 +…+β n )+b(α 1 +α 2 +…+α n ) A '= -a, b' = -b, where the symbol "+" represents the modulo d addition.
S6, the decryption client executes a quantum one-time pad decryption algorithm, decrypts the evaluation result by using the updated decryption key, a ', b', and obtains a decryption result, which can be expressed as:
as can be readily seen from the above, the decryption result is directly in the clear textThe result of performing the corresponding evaluation operation on the quantum states is consistent, i.e
It will be appreciated that in embodiments of the present invention, the d-dimensional quantum plaintext state |σ is divided by the generation>＝t 0 |0>+t 1 |1>+…+t d-1 |d-1>Coefficient formula between different quantum states of different plaintext quantum statesThe addition numbers appearing in the present invention are modulo d additions, except for the conventional addition numbers.
The invention introduces a third party quantum server to execute the evaluation operation. The encryption client can delegate complex homomorphic encryption computing tasks to the third party server with the participation of the third party server. After the third-party server determines parameters required by the evaluation operation according to the calculation task of the client, the evaluation operator required by calculation is prepared through the evaluation parameters so as to execute complex evaluation operation, and decryption operation is not required to be executed on the encrypted quantum state in the whole process. After the evaluation operation is finished, the third party server respectively sends the evaluation result and the evaluation parameter to the decryption client, the decryption client executes the decryption operation on the third party server, and the result of the decryption operation is consistent with the result obtained by directly executing the evaluation operation on the quantum plaintext.
Fig. 2 is a schematic structural diagram of a quantum homomorphic encryption and decryption system based on a multi-value single quantum state, and as shown in fig. 2, the quantum homomorphic encryption and decryption system mainly comprises an encryption client, a decryption client and a server; in the encryption client, two actions are mainly completed in the encryption client, namely two random keys are generated, and quantum plaintext is encrypted according to the generated random keys; on the server side, the server side mainly generates an evaluation parameter sequence and executes evaluation operation on the ciphertext quantum state; and in the decryption client, the decryption client mainly executes two actions, namely updating the encryption key to generate a new decryption key, and decrypting the evaluated ciphertext quantum state to finally complete the encryption and decryption process of the data.
In other embodiments of the present invention, the present invention may further provide a terminal, where the quantum homomorphic encryption and decryption method based on multi-valued single quantum state of the present invention may be applied to, but not limited to, a terminal as shown in fig. 3, where the terminal may be, for example, but not limited to, a computer, a server, a tablet computer, a personal digital assistant (english: personal Digital Assistant, abbreviated: PDA), a mobile internet device (english: mobile Internet Device, abbreviated: MID), or a device capable of performing data processing and data storage, which is not limited in any way by the present invention.
As shown in fig. 3, the terminal includes one or more (only one shown in the figure) processors 510 and one or more (only one shown in the figure) memories 530, an operating system 531 and an executable program 532; and input-output interface 540 and internal memory 550; these components communicate with each other via one or more communication buses/signal lines 122.
Specifically, as shown in fig. 3, the terminal includes a processor 510, a memory 530, an internal memory 550, and an input-output interface 540, which are connected by a system bus 520. The memory 530 stores an operating system 531 and an executable program 532, where the executable program 532 is used to implement a quantum homomorphic encryption and decryption method based on multiple-valued single quantum states, which is provided in the embodiment of the invention and is applicable to the invention. The processor 510 is used to provide computing and control capabilities to support the operation of the overall computer device. Internal memory 550 in the computer device provides an environment for the operation of operating system 531 and executable programs 532 in memory 530, and input output interface 540 is used to communicate with the outside world, network or other devices.
It will be appreciated by those skilled in the art that the structure shown in fig. 3 is merely a block diagram of a portion of the structure associated with the present application and does not constitute a limitation of the terminal to which the present application is applied, and in particular, the terminal may include more or less components than those shown in the drawings, or may combine some components, or have a different arrangement of components.
The processor 510 may be a central processing unit (central processing unit, CPU), a network processor (network processor, NP) or a combination of CPU and NP.
The processor 510 may further include a hardware chip. The hardware chip may be an application-specific integrated circuit (ASIC), a programmable logic device (programmable logic device, PLD), or a combination thereof. The PLD may be a complex programmable logic device (complex programmable logic device, CPLD), a field-programmable gate array (field-programmable gate array, FPGA), general-purpose array logic (generic array logic, GAL), or any combination thereof.
The memory 530 may also include volatile memory (RAM), such as random-access memory (RAM); the memory may also include a nonvolatile memory (non-volatile memory), such as a flash memory (flash memory), a hard disk (HDD) or a Solid State Drive (SSD); the memory may also comprise a combination of the above-mentioned types of memory.
Optionally, the memory is further used to store program instructions. The processor may call the program instructions stored in the memory to implement the methods according to the first and second embodiments of the present invention.
The bus may be a peripheral component interconnect standard (peripheral component interconnect, PCI) bus or an extended industry standard architecture (extended industry standard architecture, EISA) bus, among others. The bus may be classified as an address bus, a data bus, a control bus, etc. For ease of illustration, only one thick line is shown in fig. 3, but not only one bus or one type of bus.
It will be appreciated that the terminal structure shown in fig. 3 is merely illustrative, and that the terminal may also include more or fewer components than shown in fig. 3, or have a different configuration than shown in fig. 3, and that the components shown in fig. 3 may be implemented in hardware, software, or a combination thereof.
On the basis of the above embodiment, each module in this embodiment specifically includes:
a memory 530 for storing code data of an executable program 532;
a processor 510 for invoking the executable program 532 in the memory 530, the steps performed comprising:
the encryption client randomly generates two random keys and stores the random keys locally;
the encryption client executes a public key encryption algorithm, encrypts the random key and sends the encrypted random key to the decryption client;
the encryption client executes a quantum one-time encryption algorithm, encrypts a d-dimensional plaintext quantum state into a d-dimensional ciphertext quantum state by using a locally stored random key through an encryption operator, and sends the d-dimensional ciphertext quantum state to a server through a quantum secure channel;
the server determines parameters of the evaluation operator according to the calculation requirement of the encryption client, and prepares a corresponding evaluation operator; the evaluation parameters are encrypted through a public key encryption algorithm and then sent to a decryption client; the server executes evaluation operation on the received d-dimensional ciphertext quantum state, and sends an evaluation result to the decryption client through a quantum channel;
the decryption client executes a private key decryption algorithm, decrypts the received random key ciphertext and the received evaluation parameter ciphertext, and generates a new key by adopting key updating operation to obtain an updated decryption key;
and the decryption client executes a quantum one-time pad decryption algorithm, and decrypts the evaluation result by using the updated decryption key to obtain a decryption result.
In the present invention, unless explicitly specified and limited otherwise, the terms "mounted," "configured," "connected," "secured," "rotated," and the like are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; either directly or indirectly through intermediaries, or in communication with each other or in interaction with each other, unless explicitly defined otherwise, the meaning of the terms described above in this application will be understood by those of ordinary skill in the art in view of the specific circumstances.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (3)
1. The quantum homomorphic encryption and decryption method based on the multi-value single quantum state is characterized by comprising the following steps of:
the encryption client randomly generates two random keys and stores the random keys locally;
the encryption client executes a public key encryption algorithm, encrypts the random key and sends the encrypted random key to the decryption client;
the encryption client executes a quantum one-time-encryption algorithm, encrypts a d-dimensional plaintext quantum state into a d-dimensional ciphertext quantum state by using a locally stored random key through an encryption operator, and sends the d-dimensional ciphertext quantum state to a server through a quantum channel, and the method specifically comprises the following steps:
s31, generating a plaintext: encryption client generates d-dimensional quantum plaintext state |sigma>＝t 0 |0>+t 1 |1>+…+t d-1 |d-1>WhereinThe measurement basis of the plaintext quantum state is:
s32, encryption stage: the encryption client uses the random key to encrypt the plaintext quantum state prepared in the step S31, and the ciphertext quantum state is |ρ>＝X a Z b |σ>Wherein the encryption operators are respectivelyThe final ciphertext quantum state is represented as:
wherein ρ is>Representing a d-dimensional ciphertext quantum state; x is X a Representing the encryption operator using the first random key a, i.e. the a-th power of the encryption operator X; z is Z b Representing the encryption operator using the second random key b, i.e. the b power of the encryption operator Z; sigma of I>Represents d-dimensional plaintext quantum state, |sigma, generated by an encryption client>＝t 0 |0>+t 1 |1>+…+t d-1 |d-1>，t x Representing coefficients between different quantum states of the xth d-dimension text quantum state; i x>Represents the state Wen Liangzi of the xth d-dimension,<x| represents |x>Is a conjugate transpose of (2); x ε {0,1, …, d-1}; ω=e 2πi/d ；
S33, transmitting data: the encryption client transmits the ciphertext quantum state to a third party server through a quantum secure channel so as to execute the next operation;
the server determines parameters of the evaluation operator according to the calculation requirement of the encryption client, and prepares a corresponding evaluation operator; the evaluation parameters are encrypted through a public key encryption algorithm and then sent to a decryption client; the server executes evaluation operation on the received d-dimensional ciphertext quantum state, and sends an evaluation result to the decryption client through a quantum security channel;
the evaluation estimator is expressed as:
wherein,representing the evaluation parameter alpha i ,β i Corresponding evaluation operator, alpha i ∈{0,1,…,d-1},β i E {0,1, …, d-1}, (1. Ltoreq.i.ltoreq.n); n represents the number of evaluation operators required by the encryption client to specify the computing task; i x>Represents the state Wen Liangzi of the xth d-dimension,<x| represents |x>Is a conjugate transpose of (2); x ε {0,1, …, d-1};
the decryption client executes a private key decryption algorithm, decrypts the received random key ciphertext and the received evaluation parameter ciphertext, and generates a new key by adopting key updating operation to obtain an updated decryption key;
the decryption client executes a quantum one-time pad decryption algorithm, and decrypts the evaluation result by using the updated decryption key to obtain a decryption result;
the decryption client executes a quantum one-time pad decryption algorithm, decrypts the evaluation result by using the updated decryption key, a ', b', and obtains a decryption result, which is expressed as:
performing an evaluation operation on the received d-dimensional ciphertext quantum state is represented as:
wherein,representing the resulting quantum state of the evaluation operation directly on the ciphertext quantum state sent by the encryption client.
2. The quantum homomorphic encryption and decryption method based on multi-value single quantum states as claimed in claim 1, wherein the preparation process of the evaluation operator comprises the steps of giving any two evaluation parameters alpha and beta, wherein different values of the two evaluation parameters correspond to different evaluation operators, and wherein:
when the first isWhen an evaluation parameter alpha=0, the corresponding d-dimensional evaluation operator is an evaluation operator based on phase transformation and expressed asn represents the value of the second evaluation parameter, n is any real number;
when the second evaluation parameter β=0, the corresponding d-dimensional evaluation operator is a state-transformation-based evaluation operator, expressed asm represents the value of the first evaluation parameter, m is any natural number,
when α=0, β=0, the corresponding d-dimensional evaluation operator is the unit gate I in the two-dimensional quantum state, expressed as
When α is not equal to 0 and β is not equal to 0, the corresponding d-dimensional evaluation operator is an operator based on phase and state transformation, expressed asAlpha epsilon {0,1,., d-1}, beta is any real number.
3. The method for encrypting and decrypting quantum homomorphic data based on multi-value single quantum state according to claim 1, wherein the steps of decrypting the received random key ciphertext and the evaluation parameter ciphertext and generating a new key by using a key update operation are as follows:
key＝-a(β 1 +β 2 +…+β n )+b(α 1 +α 2 +…+α n )
where key represents the newly generated key and the symbol "+" represents the modulo d addition.
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