CN113922944A - Quantum homomorphism encryption and decryption method based on multi-value single quantum state - Google Patents

Quantum homomorphism encryption and decryption method based on multi-value single quantum state Download PDF

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CN113922944A
CN113922944A CN202111220956.9A CN202111220956A CN113922944A CN 113922944 A CN113922944 A CN 113922944A CN 202111220956 A CN202111220956 A CN 202111220956A CN 113922944 A CN113922944 A CN 113922944A
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CN113922944B (en
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廖金伟
宋秀丽
董晓茹
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Zhangjiakou Baixin Network Technology Co ltd
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Chongqing University of Post and Telecommunications
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852—Quantum cryptography
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
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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 comprises the steps that an encryption client generates two random keys; sending the encrypted random key to a 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 the evaluation operation according to the calculation requirements of the encryption client, prepares corresponding evaluation operators, executes the evaluation operation on the received ciphertext quantum state, and sends the 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 quantity of information on a single quantum bit and expand the research of quantum states on free space.

Description

Quantum homomorphism encryption and decryption method based on multi-value single quantum state
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 on data on the premise of keeping data privacy, and the safety of the classical algorithm is guaranteed 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 the research of quantum homomorphic encryption algorithms is imperative. Due to the limitations of quantum computer technology and cost, quantum computers cannot be popularized in a short time, so when classical users have quantum computing requirements, complex and huge computing tasks need to be entrusted to the quantum computers for execution.
In the existing research, quantum homomorphic encryption is mainly researched based on two-dimensional and three-dimensional quantum states, and is not beneficial to the expansion of the quantum states in free space. In order to solve the problem, a Chinese patent CN 108847934A in 2018 discloses a multi-dimensional quantum homomorphic encryption method; song et al in 2019 proposed a design method of d-dimensional (t, n) threshold quantum homomorphic encryption algorithm; a multivalued quantum homomorphic encryption scheme was proposed by 2021 et al (Zhang, y., Shang, T. & Liu, j. a multi-valued quantum well total homomorphic encryption scheme 20,101(2021).
Although these quantum homomorphic encryption schemes improve 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, sons et al perfects the phase-based evaluation unitary operator into a phase-and-state-transformation-based evaluation unitary operator. However, in these schemes, only one phase-based or phase and state-transform-based evaluation operator can be performed on a single quantum state. The method can be realized only by means of secret sharing in relatively complete operation based on the phase and evaluation operator, namely the technology needs to complete evaluation operation of a quantum homomorphic encryption method by means of a plurality of servers, and finally, an encryption client can obtain a calculated quantum state after reconstruction.
Disclosure of Invention
Based on the problems 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 a single quantum bit and expand the research of quantum states in the quantum homomorphic encryption method on a free space.
The quantum homomorphic encryption and decryption method based on the multi-value single quantum state mainly comprises five algorithms, namely a random key generation algorithm, an encryption algorithm, an evaluation algorithm, a key updating algorithm and a decryption algorithm. The random key generation algorithm is executed by the 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 to generate a quantum plaintext state, and two encryption keys generated by a random key generation algorithm execute encryption operation on the quantum plaintext state 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 a corresponding evaluation operator according to the evaluation parameters, executes evaluation operation on the quantum ciphertext state, transmits an evaluation result to the decryption client through a quantum security channel, and transmits an evaluation parameter sequence after the public key is encrypted to the decryption client through a classical channel; the decryption client executes a key updating algorithm, performs key updating operation on the 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 the decryption algorithm according to the result of the key updating algorithm to obtain a decryption result, and the decryption result is consistent with the result obtained by directly executing evaluation operation on the plaintext quantum state.
Specifically, the technical problems are solved by the following technical scheme:
a quantum homomorphic encryption and decryption method based on a multi-value single quantum state 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 a random key and sends the encrypted random key to the decryption client;
the encryption client executes a quantum one-time pad 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 security channel;
the server determines parameters of an 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 are 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 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 and reducing the calling of the existing technology to a plurality of quantum servers.
2. The invention improves the dimensionality of the single particle from two-dimensional and three-dimensional to d-dimensional, thereby greatly improving the information carrying capacity of the single particle, making certain contribution to the research of quantum homomorphic encryption method of quantum state in free space, and simultaneously improving the safety of the particle in quantum communication.
3. The invention executes the key updating operation, and the decryption client executes the decryption operation after updating the key, so that even if an eavesdropper successfully intercepts the information, no private and sensitive information can be obtained because the data cannot be correctly decrypted, thereby achieving the aim of further ensuring the data security.
Drawings
Fig. 1 is a flowchart of a quantum homomorphic encryption and decryption method based on a multiple-valued single quantum state according to an embodiment of the present invention;
fig. 2 is a schematic structural diagram of a quantum homomorphic encryption and decryption system based on a multiple-valued single quantum state according to an embodiment of the present invention;
fig. 3 is a diagram of a terminal structure according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention will be described in detail with reference to the accompanying drawings and examples, and technical solutions of the invention will be discussed in detail. The embodiments described in this block are only for better illustration of the invention and are not intended to limit the invention. As shown in fig. 1, the invention provides a quantum homomorphic encryption and decryption method based on a multi-value single quantum state, which mainly comprises the following steps:
s1, the client randomly generates two random keys and stores the random keys locally;
in this 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 in a local classical register;
wherein a represents a first random key, b represents a second random key; a corresponds to the key of the encryption operator X, 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 classic asymmetric encryption algorithm.
S2, the encryption client executes a public key encryption algorithm, encrypts a random key and sends the encrypted random key to the decryption client;
in the embodiment of the present invention, the client sends the encryption key stored in the classical register in step S11 to the decryption client after encrypting it by the classical public key encryption algorithm.
In the embodiment of the present invention, the public key encryption algorithm may adopt an asymmetric encryption algorithm commonly used in the art, that is, an algorithm of adopting public key encryption and adopting a private key of a decryption party to decrypt.
In this embodiment, the encryption key ciphertext and the evaluation parameter ciphertext may be transmitted through a classical channel, which is not specifically limited in the present invention.
S3, the encryption client executes a quantum one-time pad 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, plaintext generation: generation of d-dimensional quantum plaintext state [ sigma ] by encryption client>＝t0|0>+t1|1>+…+td-1|d-1>Wherein
Figure BDA0003312588980000051
The measurement bases of the plaintext quantum state are as follows:
Figure BDA0003312588980000052
s32, encryption stage: the encryption client uses the encryption key generated in step S1 to perform encryption operation on the plaintext quantum state prepared in step S31 to obtain the ciphertext quantum state | ρ |>＝XaZb|σ>Wherein the cryptographic operators are respectively
Figure BDA0003312588980000053
The final ciphertext quantum state is thus represented as:
Figure BDA0003312588980000054
wherein, | ρ>Representing d-dimensional ciphertext quantum states; xaRepresents the encryption operator using the first random key a, i.e. the encryption operator X raised to the power a; zbRepresents the encryption operator using the second random key b, i.e. the encryption operator Z raised to the power b; i sigma>Represents d-dimensional plaintext quantum state, | σ, generated by encryption client>＝t0|0>+t1|1>+…+td-1|d-1>，txRepresenting coefficients among different quantum states of the x d-dimension plaintext quantum state; | x>Representing the xth d-dimensional plaintext quantum state,<x | represents | x>The conjugate transpose of (1); x ∈ {0,1, …, d-1 }; e ═ e2πi/d。
S33, transfer data: and the encryption client transmits the ciphertext quantum state to the third-party server through the quantum security channel to execute the next operation.
S4, the server determines a corresponding evaluation operator according to the calculation requirements of the client, performs evaluation operation on the received d-dimensional ciphertext quantum state, and sends the evaluation result to the decryption client through a quantum security channel;
in the embodiment of the invention, the third-party quantum server determines the evaluation parameter sequence according to the calculation requirement of the encryption client, and determines each parameter alpha1,β1,α2,β2,...,αn,βnStoring the obtained product; similarly, it is received into the ciphertext quantum state | ρ of the S3 quantum channel>Saving the data into a quantum register; and after the data is received, the third-party quantum server generates a corresponding evaluation operator according to the evaluation parameters so as to further perform ciphertext quantum state | rho>Performing evaluation operation to obtain evaluation result and marking as
Figure BDA0003312588980000067
And after 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 stage: the third party server receives the cipher text amount from the encryption clientAfter the sub-state, an evaluation parameter sequence alpha is determined1,β1,α2,β2,...,αn,βnThe evaluation parameters of the third-party server prepare corresponding evaluation sub
Figure BDA0003312588980000061
Wherein the content of the first and second substances,
Figure BDA0003312588980000062
ω＝e2πi/d， αi∈{0,1,...,d-1},βi∈{0,1,...,d-1}。
wherein alpha isi,βiRepresenting a set of evaluation parameters, αi∈{0,1,...,d-1},βiE is e {0, 1., d-1}, (1 ≦ i ≦ n); n represents the number of evaluation operators required by the cryptographic client to specify the computing task.
It can be understood that n pairs of evaluation parameters are adopted, each pair of evaluation parameters corresponds to one evaluation operator, and the whole evaluation operation is realized by applying n different evaluation operators to a single quantum state in such a way, so that the carrying quantity of information on a single-bit quantum can be increased, and the research of the quantum state in the quantum homomorphic encryption method on the free space is expanded.
Specifically, in the embodiment of the present invention, the preparation process of the evaluation operator includes providing any two evaluation parameters α and β, and different values of the two evaluation parameters correspond to different evaluation operators, where:
when the first evaluation parameter α is 0, the corresponding d-dimensional evaluation operator is represented as a phase transformation-based evaluation operator
Figure BDA0003312588980000063
n represents the value of the second evaluation parameter, and n represents any real number;
for example, for example: when the beta value is 1/2, the beta value,
Figure BDA0003312588980000064
when the beta value is 1/4, the beta value,
Figure BDA0003312588980000065
when β is 1, the corresponding evaluation operator is
Figure BDA0003312588980000066
By analogy, when β is equal to n, the corresponding evaluation operator is
Figure BDA0003312588980000071
When the second evaluation parameter β is 0, the corresponding d-dimensional evaluation operator is a state-transformation-based evaluation operator, denoted as
Figure BDA0003312588980000072
m represents the value of the first evaluation parameter, and m is any natural number;
for example, for example: when α is 1, the corresponding evaluation operator is:
Figure BDA0003312588980000073
when α is 2, the corresponding evaluation operator is:
Figure BDA0003312588980000074
by analogy, when α ═ m, the corresponding evaluation operator is:
Figure BDA0003312588980000075
where m is an element of {0,1,. d-1 }.
When α is 0 and β is 0, it is represented as
Figure BDA0003312588980000076
The evaluation operator at this time can be analogized to a unit gate I in a two-dimensional quantum state.
When α ≠ 0, β ≠ 0, the corresponding d-dimensional evaluation operator is an operator based on phase and state transformations, expressed as
Figure BDA0003312588980000077
Alpha belongs to {0,1,. multidot.d-1 }, and beta is any real number;
for example, an exampleFor example: when α is 1 and β is 1, the corresponding evaluation operator is
Figure BDA0003312588980000078
Wherein, | x>The quantum state is represented by a quantum state,<x | represents | x>The conjugate transpose of (1); x ∈ {0,1, …, d-1 }; e ═ e2πi/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 is 2, α is 0 and β is 0, corresponding to G0,0Equal to the unit gate I. G corresponding to α ═ 0 and β ═ 10,1Equal to Pauli-Z gate; g corresponding to α -0 and β -1/20,1/2Equal to phase gate S; g corresponding to α -0 and β -1/40,1/4Equal to a pi/8 gate. G corresponding to α ═ 1 and β ═ 01,0Equal to the Pauli-X gate. G corresponding to 1, or 11,1Equal to the Pauli-Y gate.
When the computation task of the client needs to change the phase value of the d-dimensional quantum state, the value of the first evaluation parameter α may be set to 0; correspondingly, when the computational task requires a change of 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 both the phase and the state of a d-dimensional quantum state, the values of both evaluation parameters may be set to be other than 0.
S42, evaluation operation: executing corresponding evaluation operation on the ciphertext quantum state received from the step S33, and applying all evaluation operators after receiving the ciphertext quantum state transmitted by the encryption client to obtain an evaluation result:
Figure BDA0003312588980000081
wherein the content of the first and second substances,
Figure BDA0003312588980000082
representing the node directly performing evaluation operation on the quantum state of the ciphertext sent by the encryption clientQuantum state of the fruit;
s43, transfer data: the third party server executes the quantum state of the result after the steps are completed
Figure BDA0003312588980000083
And sending the evaluation parameters to a decryption client through a quantum secure channel, and transmitting the evaluation parameters to the decryption client through a classical channel after the evaluation parameters are encrypted by a public key encryption algorithm.
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 evaluation parameter ciphertext, generates a new key by adopting key updating operation, and executes negation operation on the encryption key, namely the random key ciphertext to obtain an updated decryption key;
in the embodiment of the present invention, the key update algorithm is executed by the decryption client, so as to ensure privacy and integrity of data, and the step S5 mainly includes the following steps:
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 server1,β1,α2,β2,...,αn,βnThe encryption key pair and the evaluation parameter sequence herein refer to ciphertext data, and need 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 parameter determined by the calculation requirement by using the private key thereof to obtain a, b and alpha respectively1,β1,α2,β2,...,αn,βn；
S53, key update operation: the decryption client executes the key updating algorithm according to the data in step S42 to obtain the updated key, a ', b', key ═ a (β)1+β2+…+βn)+b(α1+α2+…+αn)，a'＝-a，b' ═ b, where the symbol "+" represents the modulo d addition operation.
S6, the decryption client executes the quantum one-time pad decryption algorithm, and decrypts the evaluation result by using the updated decryption key, a ', b', to obtain a decryption result, which may be represented as:
Figure BDA0003312588980000091
as is apparent from the above, the above-described decryption result is consistent with the result of performing the corresponding evaluation operation directly on the plaintext quantum state, i.e.
Figure BDA0003312588980000092
It is understood that, in the embodiment of the present invention, the generated d-dimensional quantum plaintext state | σ is divided>＝t0|0>+t1|1>+…+td-1|d-1>And coefficient formula between different quantum states of each plaintext quantum state
Figure RE-GDA0003341721770000093
The plus signs in the invention are all modulo-d plus signs, except for the common plus signs.
The invention introduces a third party quantum server to execute the evaluation operation. Under the participation of the third-party server, the encryption client can delegate the complex homomorphic encryption calculation task to the third-party server. After determining the parameters required by the evaluation operation according to the calculation task of the client, the third-party server prepares the evaluation operator required by calculation through the evaluation parameters and then executes the complex evaluation operation, and the decryption operation of the encrypted quantum state is not required in the whole process. After the evaluation operation is completed, the third-party server respectively sends the evaluation result and the evaluation parameters to the decryption client, the decryption client executes decryption operation on the decryption client, and the decryption operation result is consistent with the result obtained by directly executing the evaluation operation on the quantum plaintext state.
Fig. 2 is a schematic structural diagram of a quantum homomorphic encryption and decryption system based on a multiple-valued single quantum state according to an embodiment of the present invention, and as shown in fig. 2, the quantum homomorphic encryption and decryption system of the present invention mainly includes an encryption client, a decryption client, and a server; in the encryption client, the encryption client mainly completes two actions, namely generating two random keys and encrypting the quantum plaintext state according to the generated random keys; at the server end, the server end mainly generates an evaluation parameter sequence and executes evaluation operation on the ciphertext quantum state; at the decryption client, the decryption client mainly executes two actions, namely, updating the encryption key to generate a new decryption key on one hand, and needing to decrypt the evaluated ciphertext quantum state on the other hand to finally complete the data encryption and decryption process.
In other embodiments of the present invention, the present invention may also provide a terminal, and the quantum homomorphic encryption and decryption method based on the multiple-valued single quantum state of the present invention may be applied to, but is 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 (PDA), a Mobile Internet Device (MID), and other devices capable of performing data processing and data storage, and the present invention is not limited in this respect.
As shown in fig. 3, the terminal includes one or more processors 510 (only one shown) and one or more memories 530 (only one shown), an operating system 531 and executable programs 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 for implementing a quantum homomorphic encryption and decryption method based on a multiple-valued single quantum state provided in the embodiment of the present invention. The processor 510 is used to provide computing and control capabilities, supporting the operation of the overall computer device. The internal memory 550 of the computer device provides an environment for the operating system 531 and executable programs 532 in the memory 530 to run, and the input/output interface 540 is used for network or other device communication with the outside.
It will be understood by those skilled in the art that the structure shown in fig. 3 is a block diagram of only a part of the structure related to 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 combine some components, or have a different arrangement of components.
The processor 510 may be a Central Processing Unit (CPU), a Network Processor (NP), or a combination of a CPU and an 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 (PLD), or a combination thereof. The PLD may be a Complex Programmable Logic Device (CPLD), a field-programmable gate array (FPGA), a General Array Logic (GAL), or any combination thereof.
The memory 530 may also include volatile memory (volatile memory), such as random-access memory (RAM); the memory may also include a non-volatile memory (non-volatile memory), such as a flash memory (flash memory), a Hard Disk Drive (HDD) or a solid-state drive (SSD); the memory may also comprise a combination of memories of the kind described above.
Optionally, the memory is also used for storing 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 (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of illustration, only one thick line is shown in FIG. 3, but this does not indicate only one bus or one type of bus.
It is to be understood that the terminal structure shown in fig. 3 is only an illustration, the terminal may also include more or less components than those shown in fig. 3, or have a different configuration than that shown in fig. 3, and 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 the executable program 532;
a processor 510 for calling said executable 532 in said memory 530, the execution of which comprises:
the encryption client randomly generates two random keys and stores the random keys locally;
the encryption client executes a public key encryption algorithm, encrypts a random key and sends the encrypted random key to the decryption client;
the encryption client executes a quantum one-time pad 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 security channel;
the server determines parameters of an 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 are 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 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 otherwise expressly stated or limited, the terms "mounted," "disposed," "connected," "fixed," "rotated," and the like are to be construed broadly, e.g., as meaning fixedly connected, detachably connected, or integrally formed; can be mechanically or electrically connected; the term "a" or "an" refers to a term that can be used in a generic sense, and includes, but is not limited to, a generic term, a specific term or a specific term.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (9)

1. A quantum homomorphic encryption and decryption method based on a multi-value single quantum state is characterized by comprising 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 a random key and sends the encrypted random key to the decryption client;
the encryption client executes a quantum one-time pad 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;
the server determines parameters of an 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 are 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 decryption client executes a private key decryption algorithm, decrypts the received random key ciphertext and the 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.
2. The quantum homomorphic encryption and decryption method based on the multivalued single quantum state as claimed in claim 1, wherein the evaluation operator is expressed as:
Figure FDA0003312588970000011
wherein the content of the first and second substances,
Figure FDA0003312588970000012
representing the evaluation parameter alphai,βiCorresponding evaluation operator, αi∈{0,1,...,d-1},βiE is e {0, 1., d-1}, (1 ≦ i ≦ n); n represents the number of evaluation operators required by the specified calculation task of the encryption client; | x>Representing the xth d-dimensional plaintext quantum state,<x | represents | x>The conjugate transpose of (1); x ∈ {0,1, …, d-1 }.
3. The quantum homomorphic encryption and decryption method based on the multiple-valued single quantum state as claimed in claim 2, wherein the preparation process of the evaluation operator comprises giving out any two evaluation parameters α and β, and different values of the two evaluation parameters correspond to different evaluation operators, wherein:
when the first evaluation parameter α is 0, the corresponding d-dimensional evaluation operator is represented as a phase transformation-based evaluation operator
Figure FDA0003312588970000021
n represents the value of the second evaluation parameter, and n represents any real number;
when the second evaluation parameter β is 0, the corresponding d-dimensional evaluation operator is a state-transformation-based evaluation operator, denoted as
Figure FDA0003312588970000022
m represents the value of the first evaluation parameter, m is any natural number,
when α is 0 and β is 0, the corresponding d-dimensional evaluation operator is the unit gate I in the two-dimensional quantum state, denoted as
Figure FDA0003312588970000023
When α ≠ 0, β ≠ 0, the corresponding d-dimensional evaluation operator is an operator based on phase and state transformations, denoted as
Figure FDA0003312588970000024
Beta is any real number;
wherein, | x>Representing the xth d-dimensional plaintext quantum state,<x | represents | x>The conjugate transpose of (1); x ∈ {0,1, …, d-1 }; e ═ e2 πi/d。
4. The quantum homomorphic encryption and decryption method based on multiple-valued single quantum states as claimed in claim 1, wherein the d-dimensional plaintext quantum state is encrypted into d-dimensional ciphertext quantum state by an encryption operator using a locally stored random key as represented by:
Figure FDA0003312588970000025
wherein, | ρ>Representing d-dimensional ciphertext quantum states; xaRepresents the encryption operator using the first random key a, i.e. the encryption operator X raised to the power a; zbRepresents the encryption operator using the second random key b, i.e. the encryption operator Z raised to the power b; i sigma>Represents d-dimensional plaintext quantum state, | σ, generated by encryption client>＝t0|0>+t1|1>+…+td-1|d-1>，txRepresenting coefficients among different quantum states of the x d-dimension plaintext quantum state; | x>Representing the xth d-dimensional plaintext quantum state,<x | represents | x>The conjugate transpose of (1); x ∈ {0,1, …, d-1 }; e ═ e2πi/d。
5. The quantum homomorphic encryption and decryption method based on the multivalued single quantum state as claimed in claim 4, wherein the coefficients between different quantum states of each plaintext quantum state satisfy
Figure RE-FDA0003341721760000031
6. The quantum homomorphic encryption and decryption method based on the multivalued single quantum state as claimed in claim 4, wherein the measurement basis of the plaintext quantum state is expressed as:
Figure FDA0003312588970000032
7. the method according to claim 6, wherein the performing of the evaluation operation on the received d-dimensional ciphertext quantum state is represented as:
Figure FDA0003312588970000033
wherein the content of the first and second substances,
Figure FDA0003312588970000034
representing the result quantum state of the evaluation operation directly carried out on the ciphertext quantum state sent by the encryption client.
8. The quantum homomorphic encryption and decryption method based on the multivalued single quantum state as claimed in claim 6 or 7, wherein the random key ciphertext and the evaluation parameter ciphertext are decrypted and a new key represented by using the key update operation is generated as follows:
key＝-a(β1+β2+…+βn)+b(α1+α2+…+αn)
where key represents the newly generated key and the "+" symbol represents the modulo d addition operation.
9. The quantum homomorphic encryption and decryption method based on the multivalued single quantum state as claimed in claim 8, wherein the evaluation result is decrypted by using the updated decryption key, and the decryption result is expressed as:
Figure FDA0003312588970000035
wherein, | σ > ' represents a d-dimensional plaintext quantum state decrypted by the decryption client, a ' represents a first random key after inversion, a ' ═ a, b ' represents a second random key after inversion, and b ' ═ b.
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