CN115622685B

CN115622685B - Method, device and system for homomorphic encryption of private data

Info

Publication number: CN115622685B
Application number: CN202211618803.4A
Authority: CN
Inventors: 涂锟; 王�琦; 柯琪锐; 陆阳; 陈艳晶; 张曙光
Original assignee: Chengfang Financial Technology Co ltd
Current assignee: Chengfang Financial Technology Co ltd
Priority date: 2022-12-16
Filing date: 2022-12-16
Publication date: 2023-04-28
Anticipated expiration: 2042-12-16
Also published as: CN115622685A

Abstract

The invention relates to the technical field of data processing, and provides a homomorphic encryption method, device and system for private data, wherein the method acquires the private data to be encrypted; determining an encryption key and a target multiplier corresponding to the encryption key, and respectively carrying out parallel FFT on the encryption key and the target multiplier based on a stream multiprocessor in a graphics processor to obtain a first transformation result and a second transformation result; determining a target product result of the encryption key and the target multiplier based on the alternative product result of the first transformation result and the second transformation result; and finally, homomorphic encryption is carried out on the private data based on the encryption key and the target product result. The method can ensure the security of the private data by homomorphic encryption of the private data. In addition, the parallel FFT is carried out by utilizing the streaming multiprocessors in the graphic processor, so that the efficiency of determining the target product result of the encryption key and the target multiplier can be greatly improved, and the homomorphic encryption efficiency of the private data can be further improved.

Description

Method, device and system for homomorphic encryption of private data

Technical Field

The present invention relates to the field of data processing technologies, and in particular, to a method, an apparatus, and a system for homomorphic encryption of private data.

Background

Along with the gradual strong consciousness of people on protecting privacy data, homomorphic encryption is used as a widely applied security technology, and has huge functions and practical values in the field of privacy calculation.

The core idea of homomorphic encryption is that ciphertext can be calculated, namely that ciphertext operation is carried out on homomorphic encrypted data to obtain an output, the output is decrypted, and the obtained decryption result is identical with the output result obtained by processing unencrypted original data by the same method. In homomorphic encryption of private data, a large number of multiplication operations and linear combination operations are generally required, and the process is complex, which greatly reduces the encryption efficiency of the private data.

For this reason, it is urgently required to provide a method for homomorphic encryption of private data.

Disclosure of Invention

The invention provides a homomorphic encryption method, device and system for private data, which are used for solving the defects in the prior art.

The invention provides a homomorphic encryption method for private data, which comprises the following steps:

acquiring privacy data to be encrypted;

determining an encryption key and a target multiplier corresponding to the encryption key, and respectively carrying out parallel FFT on the encryption key and the target multiplier based on a stream multiprocessor in a graphics processor to obtain a first transformation result and a second transformation result;

Determining a target product result of the encryption key and the target multiplier based on an alternative product result of the first transform result and the second transform result;

and homomorphic encryption is carried out on the private data based on the encryption key and the target product result.

According to the homomorphic encryption method for the private data, provided by the invention, the first transformation result is obtained based on the following steps:

determining FFT point number and round number of butterfly transformation operation in FFT based on the bit number of the encryption key and the bit number of the target multiplier;

representing the encryption key as a polynomial and assigning each polynomial coefficient of the encryption key to a streaming multiprocessor;

for any round, determining a twiddle factor of each butterfly transformation operation in the any round based on the any round, the FFT point number and the position of a polynomial coefficient distributed in each flow multiprocessor in the polynomial, screening out a plurality of flow multiprocessors, and executing each butterfly transformation operation in the any round in parallel based on the twiddle factor of each butterfly transformation operation in the any round and the plurality of flow multiprocessors.

According to the homomorphic encryption method for private data provided by the invention, the rotation factor of each butterfly transformation operation in any turn is determined based on the position of the polynomial coefficient distributed in any turn, the FFT point number and each streaming multiprocessor, and a plurality of streaming multiprocessors are screened out, comprising:

determining the subscript interval of an input node of each butterfly transformation operation in any round based on the round;

calculating the node scale after any turn based on the input node index interval and the FFT point number, and determining a twiddle factor of each butterfly transformation operation in any turn based on the node scale;

the plurality of streaming multiprocessors is screened out based on the input node index interval and the locations in the polynomial of the polynomial coefficients assigned in each streaming multiprocessor.

According to the homomorphic encryption method for private data provided by the invention, the determining of the encryption key and the target multiplier corresponding to the encryption key comprises the following steps:

selecting the encryption key from an encryption key set and selecting the target multiplier from a target multiplier set;

Wherein the encryption key set is constructed based on an odd number of the exponent of 2 in a random number set generated by a quantum random number generator, and the target multiplier set is constructed based on an integer of the exponent of 2 in the random number set.

According to the homomorphic encryption method for private data provided by the invention, the homomorphic encryption is carried out on the private data based on the encryption key and the target product result, and the homomorphic encryption method comprises the following steps:

generating a target random number based on the encryption key;

and homomorphic encryption is carried out on the privacy data based on the target random number and the target product result.

According to the homomorphic encryption method for private data provided by the invention, the determining of the target product result of the encryption key and the target multiplier based on the alternative product result of the first transformation result and the second transformation result comprises the following steps:

and performing IFFT on the alternative product result to obtain the target product result.

The invention also provides a privacy data homomorphic encryption device, which comprises:

the data acquisition module is used for acquiring the privacy data to be encrypted;

the transformation module is used for determining an encryption key and a target multiplier corresponding to the encryption key, and respectively carrying out parallel FFT on the encryption key and the target multiplier based on a stream multiprocessor in the graphics processor to obtain a first transformation result and a second transformation result;

A product module for determining a target product result of the encryption key and the target multiplier based on an alternative product result of the first transform result and the second transform result;

and the encryption module is used for homomorphic encryption of the privacy data based on the encryption key and the target product result.

The invention also provides a homomorphic encryption system for the private data, which comprises the following steps: the device comprises a quantum random number generator, a graphic processor and the privacy data homomorphic encryption device;

any two of the quantum random number generator, the graphic processor and the privacy data homomorphic encryption device are connected through an interface;

the quantum random number generator is used for providing an encryption key for the privacy data homomorphic encryption device and a target multiplier corresponding to the encryption key;

the privacy data homomorphic encryption device is used for calling the graphics processor.

The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor realizes the homomorphic encryption method of the privacy data when executing the program.

The present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a method of homomorphic encryption of private data as described in any one of the above.

The invention also provides a computer program product comprising a computer program which when executed by a processor implements a method of homomorphic encryption of private data as described in any one of the above.

The invention provides a homomorphic encryption method, device and system for private data, wherein the method firstly acquires the private data to be encrypted; then determining an encryption key and a target multiplier corresponding to the encryption key, and respectively carrying out parallel FFT on the encryption key and the target multiplier based on a stream multiprocessor in a graphics processor to obtain a first transformation result and a second transformation result; thereafter determining a target product result of the encryption key and the target multiplier based on the alternative product result of the first transform result and the second transform result; and finally, homomorphic encryption is carried out on the private data based on the encryption key and the target product result. The method can ensure the security of the private data by homomorphic encryption of the private data. In addition, the parallel FFT is carried out by utilizing the streaming multiprocessors in the graphic processor, so that the efficiency of determining the target product result of the encryption key and the target multiplier can be greatly improved, and the homomorphic encryption efficiency of the private data can be further improved.

Drawings

In order to more clearly illustrate the invention or the technical solutions of the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious to those skilled in the art that other drawings can be obtained according to these drawings without inventive effort.

FIG. 1 is a schematic flow chart of a method for homomorphic encryption of private data;

FIG. 2 is a corresponding diagram of a thread model and a hardware structure level of a graphics processor employed in the method for homomorphic encryption of private data provided by the present invention;

FIG. 3 is a schematic diagram of an FFT conversion process of 8-point polynomials in the homomorphic encryption method of privacy data provided by the invention;

fig. 4 is a schematic structural diagram of a privacy data homomorphic encryption device provided by the invention;

FIG. 5 is a schematic diagram of a system for homomorphic encryption of private data according to the present invention;

FIG. 6 is a schematic diagram of a second embodiment of a system for homomorphic encryption of private data;

fig. 7 is a schematic structural diagram of an electronic device provided by the present invention.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, 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.

Because the existing homomorphic encryption method generally needs a large amount of multiplication and linear combination operation in the homomorphic encryption process of the private data, the process is complex, and the encryption efficiency of the private data is greatly reduced. Therefore, the embodiment of the invention provides a homomorphic encryption method for private data.

Fig. 1 is a schematic flow chart of a method for homomorphic encryption of private data, in an embodiment of the invention, as shown in fig. 1, the method includes:

s1, acquiring privacy data to be encrypted;

s2, determining an encryption key and a target multiplier corresponding to the encryption key, and respectively carrying out parallel FFT on the encryption key and the target multiplier based on a stream multiprocessor in a graphics processor to obtain a first transformation result and a second transformation result;

s3, determining a target product result of the encryption key and the target multiplier based on an alternative product result of the first transformation result and the second transformation result;

s4, homomorphic encryption is carried out on the private data based on the encryption key and the target product result.

Specifically, in the method for homomorphic encryption of private data provided in the embodiment of the present invention, the execution subject is a device for homomorphic encryption of private data, and the device may be a central processing unit (central processing unit, CPU) and may be configured in a computer, where the computer may be a local computer or a cloud computer, and the local computer may be a computer, a tablet, or the like, and is not limited herein specifically.

First, step S1 is performed to obtain the private data to be encrypted, where the private data may be data that the user needs to encrypt, and the private data may be decimal data. The user can be a person, a company, an enterprise and the like, and the privacy data can be face feature data of the person, an identity card number, a mobile phone number, a bank card password, a web page browsing record and the like, and can also be financial data, fund flow data, important client information and the like of the company or the enterprise.

Then, step S2 is executed to determine the encryption key and the target multiplier corresponding to the encryption key, where the encryption key and the target multiplier may be random numbers, and may be generated by a quantum random number generator, which is not specifically limited herein. The encryption key may be a large integer odd number, and the target multiplier corresponding to the encryption key may be a large integer. The large whole odd number is the large integer of the odd number, and the large integer is the number whose range is beyond the range that the basic data type can represent.

Graphics processor (Graphics Processing Unit, GPU) is a special purpose image rendering hardware with better versatility and higher performance for each hardware. The thread model 21 of the GPU shown in fig. 2 may include Grid, block, thread and Warp. Grid, block, thread is a software organization structure, which is three levels of thread organization, corresponding to devices (devices), streaming multiprocessors (Streaming Multiprocessor, SM) and unified computing Device architecture (Compute Unified Device Architecture, CUDA) cores (cores), respectively, of hardware structure level 22.

The smallest unit in which the GPU operates is Thread. Multiple threads may constitute one Block, and multiple blocks executing the same program may constitute Grid. Multiple blocks share memory (Cache), so each inter-Block communication can be considered as a full communication mode.

Based on this, when parallel fast fourier transforms (Fast Fourier Transformation, FFT) are performed on the encryption key and the target multiplier respectively by the SMs in the GPU, parallelized butterfly transform operations of the FFT may be distributed to different SMs in a hierarchical structure to be performed, so as to improve the parallelism of the FFT. The basic idea of parallel FFT is to split FFT according to iterative rounds of butterfly transformation operation, parallelize the same butterfly transformation operation in each round, then use each SM in GPU as a calculation node of parallel calculation, and distribute parallelized butterfly transformation operation to different SMs, thereby improving parallelism of FFT and conversion efficiency.

Before parallel FFT is performed on the encryption key and the target multiplier respectively by SM in the GPU, the encryption key and the target multiplier may be represented as polynomials, respectively, the degree of which may be the number of bits of the encryption key and the target multiplier minus one. Further, a parallel FFT process is performed, that is, a polynomial is converted from a coefficient representation to a point value representation.

Is provided with one

Large integer of bits

，

Can be expressed as one

A sub-polynomial, the polynomial having two representation methods, coefficient representation and point value representation.

Coefficient representation:

wherein, the method comprises the steps of, wherein,

as a function of the amount of the independent variable,

as a function of the variables,

is an index

Independent variable of (2)

Is used to determine the coefficient of the polynomial of (c),

is that

One term of the sub-polynomials, a coefficient vector consisting of the polynomial coefficients of all the terms

Uniquely defining this polynomial, i.e. large integers

. Calculating the multiplication of two large integers, i.e. two, according to the coefficient representation

The complex degree of the polynomial multiplication is that

。

Point value representation: to a group of interpolation nodes different from each other

Respectively take in

Obtaining

Each value is taken

Wherein

. According to algebraic basic theorem, one

The polynomial of degree is in complex domain and is only

Root, thus one

Polynomial of degree

The polynomial is uniquely determined by the different value points.

FFT is a kind of FFT that can be performed at

A discrete fourier transform (Discrete Fourier transform, DFT) algorithm completed in time. The DFT will give coefficient vectors for the polynomial

Is converted into

The calculation formula is as follows:

wherein, the liquid crystal display device comprises a liquid crystal display device,

is that

The root of the secondary unit,

。

the polynomial of the point value representation is converted into the coefficient representation using FFT, a process called inverse discrete fourier transform (Inverse Discrete Fourier Transform, IDFT) whose calculation formula is:

is that

The root of the secondary unit,

。

the polynomial can be obtained by utilizing the periodicity, symmetry and halving property of the unit primitive root

The polynomial sequence of (2) is divided into an even index term and an odd index term according to the index, and FFT is respectively carried out to obtain

And

then

The FFT transform result of the polynomial sequence of (c) is:

thus will

The FFT of the points is broken down into two

FFT of point, let

To the power of 2, so recursively decomposed, the algorithm complexity is

. In the recursion process, the array is continuously split layer by layer from the top, the operation result with the minimum granularity is generated to the lowest layer, and then the final result is formed layer by layer. Additional storage space is needed in the process of separating the subscripts, and space complexity is improved.

To reduce the spatial complexity, special operations are performed layer by layer from the bottom results back to the top. This operation is called butterfly (butterfly) operation, which can be used to sequence a sequence

In situ conversion to

Its space complexity is

. To implement butterfly operations, it is necessary to perform a bit reverse order (bit reverse) on the sequence index,the following index

. After the conversion of the original sequence elements is completed in the bit reverse order, FFT operation is performed layer by layer according to the cycle. The temporal complexity of such an algorithm is

The spatial complexity is

。

The encryption key is subjected to parallel FFT by the SM in the GPU to obtain a first transformation result, and the target multiplier is subjected to parallel FFT by the SM in the GPU to obtain a second transformation result.

After that, step S3 is performed, the first transformation result and the second transformation result may be multiplied first, so as to obtain an alternative product result of the first transformation result and the second transformation result. Since the first transformation result can be regarded as a point value representation of the polynomial of the encryption key and the second transformation result can be regarded as a point value representation of the polynomial of the target multiplier, the first transformation result and the second transformation result are multiplied, i.e. the dot product is calculated for both.

Thereafter, a target product result may be determined from the alternative product results. Since the alternative multiplication result is still in the form of a point value representation, the coefficient representation of the alternative multiplication result can be obtained by performing inverse fast fourier transform (Inverse Fast Fourier Transform, IFFT) on the alternative multiplication result, i.e. the target product result of the encryption key and the target multiplier, which is the product of the coefficient representation of the polynomial of the encryption key and the coefficient representation of the polynomial of the target multiplier.

And finally, executing step S4, and carrying out homomorphic encryption on the private data through a homomorphic encryption algorithm according to the encryption key and the target product result. Homomorphic encryption algorithms may include homomorphic encryption algorithms, partial homomorphic encryption algorithms, approximately homomorphic encryption algorithms, and the like. If ciphertext data obtained by a homomorphic encryption algorithm can execute the operations of addition and multiplication infinitely, the homomorphic encryption algorithm is a complete homomorphic encryption algorithm, and is abbreviated as a homomorphic encryption algorithm.

Taking the full homomorphic encryption scheme (DGHV) on integers as an example, the DGHV belongs to symmetric encryption, and generally includes a key generation stage (KeyGen), an encryption algorithm (Encrypt) stage, a decryption algorithm stage (Decrypt), a homomorphic calculation stage (evaluation), and the like.

In the key generation stage, according to a security parameter lambda, an odd number of N bits is selected as an encryption key p by KeyGen (lambda), and p is a large integer in order to improve algorithm security. The encryption key may be generated by a random number generator.

The encryption scheme in the encryption stage can be expressed as c=p×q+2r+m, m is the private data to be encrypted, p is the encryption key, q is the target multiplier, p×q is the target product result, p and q are both random large integers, r is the target random number, usually a small integer, and can be determined by p. The relationship of r to p can be expressed as |2r| < |p/2|. c is an encryption result obtained by homomorphic encryption of the privacy data m.

In the homomorphic encryption process of the private data, the private data can be homomorphic encrypted according to the bits, namely m is any bit of the private data, the value space of m is {0,1}, and the value space of c is an integer, namely the ciphertext space.

Based on stream type multiprocessor in the graphic processor, parallel FFT is carried out on encryption key and target multiplier to obtain first conversion result and second conversion result, namely, the encryption key and target multiplier are respectively represented as a polynomial by coefficient representation, and the polynomial of the encryption key and the polynomial of the target multiplier are converted from coefficient representation form to point value representation form. The time complexity of the process is

N is the number of polynomial coefficients of the encryption key. Thereafter, an alternative product of the first and second transformation results is determined, i.e. atComputing polynomial multiplication in the form of a point value representation, the process having a temporal complexity of

. Finally, determining the target product result of the encryption key and the target multiplier through the alternative product result, namely converting the point value representation form of the alternative product result into the coefficient representation form through IFFT to obtain the final target product result, wherein the time complexity of the process is as follows

. Through the three processes, the total time complexity in determining the target product result of the encryption key and the target multiplier is

. It can be seen that the time complexity of determining the target product result of the encryption key and the target multiplier can be reduced to

While the prior scheme for determining the product result of two large integers based on divide-and-conquer method has the time complexity as high as

Compared with the existing scheme, the homomorphic encryption method for the private data provided by the embodiment of the invention can greatly improve homomorphic encryption efficiency.

The embodiment of the invention provides a homomorphic encryption method for private data, which comprises the steps of firstly, acquiring the private data to be encrypted; then determining an encryption key and a target multiplier corresponding to the encryption key, and respectively carrying out parallel FFT on the encryption key and the target multiplier based on a stream multiprocessor in a graphics processor to obtain a first transformation result and a second transformation result; thereafter determining a target product result of the encryption key and the target multiplier based on the alternative product result of the first transform result and the second transform result; and finally, homomorphic encryption is carried out on the private data based on the encryption key and the target product result. The method can ensure the security of the private data by homomorphic encryption of the private data. In addition, the parallel FFT is carried out by utilizing the streaming multiprocessors in the graphic processor, so that the efficiency of determining the target product result of the encryption key and the target multiplier can be greatly improved, and the homomorphic encryption efficiency of the private data can be further improved.

On the basis of the above embodiment, in the method for homomorphic encryption of private data provided in the embodiment of the present invention, the first transformation result is obtained based on the following steps:

Specifically, in the embodiment of the present invention, when performing parallel FFT on an encryption key based on SM in a GPU to obtain a first transformation result, the number of FFT points and the number of rounds of butterfly transformation operation in the FFT may be determined based on the number of bits of the encryption key and the number of bits of a target multiplier. For example, the maximum number of bits of the target product result of the encryption key and the target multiplier may be determined based on the number of bits of the encryption key and the number of bits of the target multiplier. Since the FFT point number N needs to be an exponent power of 2, the minimum value among the exponent powers of 2 that is greater than or equal to the maximum number of bits can be selected as the FFT point number N. The number of rounds of butterfly transformation operation in FFT can be directly determined according to the number N of FFT points, namely

。

Thereafter, the encryption key may be expressed as a polynomial having the number of terms equal to the FFT point number N. Correspondingly, each term of the polynomial corresponds to a polynomial coefficient, and the number of the polynomial coefficients is equal to the number of terms of the polynomial.

For having

The FFT of the polynomial of the points has the following characteristics:

1) The FFT process can be divided into

The operations of the butterfly transformation of the wheel are carried out in each round

The butterfly transformation units;

2) In each round, butterfly transformation operations among different butterfly transformation units are executed in parallel;

3) In each round of FFT, unit root

Also known as twiddle factors. The rotation factor of each round is

，

Wherein t refers to the node scale after each round of recursion decomposition, and the value is halved step by step along with the rounds of recursion.

4) Order the

Then at

Wheel, the input nodes of each butterfly conversion unit are separated

The subscript interval of the input nodes of each point, namely butterfly conversion operation, is

。

To have the following

The FFT of the polynomial of the points is for example as shown in fig. 3:

1) The FFT procedure is totally divided into

The butterfly transform units, rectangular boxes in fig. 3.

2) In each round, the calculation among different butterfly transformation units can be carried out in parallel;

3) At the position of

A round corresponding to the lowest level of the recursive decomposition, so that the node scale

I.e.

Thus the rotation factor of the round is

；

At the position of

A round with node size 2 times that of the previous round, so

I.e.

Thus the rotation factor of the round is

、

；

At the position of

A round corresponding to the topmost layer of the recursive decomposition, so the node scale

I.e.

Thus the rotation factor of the round is

；

4) At the position of

Wheel, the input nodes of each butterfly conversion unit are separated

The node subscript interval is that

；

At the position of

Wheels, each butterfly changeThe input nodes of the cells are spaced apart

The node subscript interval is 2;

at the position of

Wheel, the input nodes of each butterfly conversion unit are separated

The node subscript interval is 1 at each point.

In FIG. 3, the following is illustrative

Are coefficient representation forms of polynomial coefficients,

are all point value representation forms of polynomial coefficients.

Thereafter, each polynomial coefficient of the encryption key may be assigned to one of the streaming multiprocessors, e.g., a kth polynomial coefficient of the encryption key may be assigned to a kth streaming multiprocessor

Is a kind of medium.

Further, for any round

Based on either round

FFT point number N, position of polynomial coefficients allocated in each stream multiprocessor in polynomial

Determining a twiddle factor of each butterfly transformation operation in any turn h

And screening out a plurality of streaming multiprocessors.

For example, the twiddle factor of each butterfly transformation operation in any round h can be determined according to any round h and the FFT point number N

And then, according to the position k of the polynomial coefficient distributed in each streaming multiprocessor in the polynomial, screening out a plurality of streaming multiprocessors which can be used for performing butterfly transformation operations in any turn h. The number of the screened stream type multiprocessors is equal to the number of butterfly-shaped conversion operations in any round h.

Finally, the twiddle factor for each butterfly transform operation in any round h

And a plurality of streaming multiprocessors that perform each butterfly transformation operation in any round h in parallel. That is, for any round h, each selected stream-type multiprocessor corresponds to one butterfly transformation unit, butterfly transformation operations of all butterfly transformation units in any round h are executed in parallel by the corresponding stream-type multiprocessor, and each stream-type multiprocessor realizes execution action by the corresponding Block.

In the embodiment of the invention, in each round, the rotation factors of each butterfly transformation operation in each round are combined by the plurality of stream multiprocessors selected through screening, and each butterfly transformation operation in each round is executed in parallel, so that the execution efficiency of the butterfly transformation operation can be greatly improved, and the determination efficiency of the first transformation result is further improved.

On the basis of the above embodiment, the method for homomorphic encryption of private data provided in the embodiment of the present invention, the second transformation result is obtained based on the following steps:

representing the target multiplier as a polynomial and assigning each polynomial coefficient of the target multiplier into a streaming multiprocessor;

Specifically, in the embodiment of the present invention, the step of determining the second transformation result is identical to the step of determining the first transformation result in the above embodiment, and the difference is only that in the above embodiment, the encryption key is represented as a polynomial and the polynomial coefficient is utilized, and in the embodiment of the present invention, the objective multiplier is represented as a polynomial and the polynomial coefficient is utilized, which is not described in detail herein.

On the basis of the foregoing embodiments, the method for homomorphic encryption of private data provided in the embodiments of the present invention determines a twiddle factor of each butterfly transformation operation in any round based on the round, the FFT point number, and a position of a polynomial coefficient allocated in each streaming multiprocessor in the polynomial, and screens out a plurality of streaming multiprocessors, including:

Specifically, in the embodiment of the present invention, when determining the twiddle factor of each butterfly transformation operation in any round and screening out multiple streaming multiprocessors, the subscript interval s of the input node of each butterfly transformation operation in any round h, that is, the subscript interval of the input node of each butterfly transformation unit, may be determined according to any round h, for example

。

Thereafter, the node scale t after any round h can be calculated according to the input node index interval s and the FFT point number N, for example, there can be

. From the node size t, a twiddle factor for each butterfly transformation operation in any round h can be determined

。

Finally, a plurality of streaming multiprocessors can be screened out according to the input node subscript interval t and the position k of the polynomial coefficient allocated in each streaming multiprocessor in the polynomial. For example, for the kth streaming multiprocessor

The screening conditions may be

If you are

Satisfying the screening condition, then explain

Can pass through the corresponding in any round h

Performing butterfly transformation of a butterfly transformation unitOperating, wherein all the streaming multiprocessors meeting the screening conditions in any round h pass through the corresponding

And executing the butterfly conversion operation of each butterfly conversion unit in any round h in parallel.

Based on the above embodiments, the pseudo code of the parallel FFT algorithm can be expressed as:

/(and/or (V)/will be

In (a) and (b)

Numbering in order

Input array

Polynomial coefficients for storing encryption keys or target multipliers

Array of results

For storing the first or second conversion result

/(and/or distribution)

To the point of

In (3) distribution of

To the point of

In the process, the liquid crystal display device comprises a liquid crystal display device,

is that

Defined variables are used to assist in computation

{

/(all)

Parallel execution

Hybrid/fast Fourier transform

Wheel

//

The index interval of the input node of the butterfly conversion unit of the round is represented;

//

representing the node scale of the recursion decomposition corresponding to the current round;

of the round//

Screening out that the round meets the screening condition

Each of which is

Corresponding to one butterfly transformation unit in the round, performing butterfly transformation operations of all butterfly transformation units in parallel

Is that

Bit inversion of (a)

Is that

Bit inversion of (a)

The method comprises the steps of carrying out a first treatment on the surface of the The first transformation result or the second transformation result is stored in the array B,

is that

Bit inversion of (a)

}

Time complexity analysis of parallel FFT algorithm: the parallel FFT algorithm realizes parallelization aiming at butterfly transformation operation of each iteration round, and the time complexity is constant, namely

Recursively iterate in dichotomy

Wheels, thus of complexity of

。

On the basis of the above embodiment, the method for homomorphic encryption of private data provided in the embodiment of the present invention, where determining an encryption key and a target multiplier corresponding to the encryption key includes:

Specifically, in the embodiment of the present invention, when determining the encryption key and the target multiplier corresponding to the encryption key, the encryption key may be directly selected from the encryption key set, and the target multiplier may be selected from the target multiplier set. The encryption key set and the target multiplier set are all sets formed by random large integers.

The encryption key set can be obtained by constructing an odd number of the exponent power of 2 in the random number set generated by the quantum random number generator, namely the encryption keys in the encryption key set are all the odd numbers of the exponent power of 2 in the bit number and are random numbers. The target multiplier set is obtained by constructing integers with the exponent power of 2 in the random number set generated by the quantum random number generator, namely the target multipliers in the target multiplier set are all integers with the exponent power of 2 in number and are random numbers.

It is understood that the set of random numbers stores therein the quantum random numbers generated by the quantum random number generator. In contrast to pseudo-random numbers, the randomness of quantum random numbers is derived from a classical physical random source that can produce a completely unpredictable random sequence. The quantum random number generator adopts laser phase fluctuation as a random source, the laser phase fluctuation is essentially derived from spontaneous radiation, the quantum random number generator belongs to nondeterministic quantum noise, and a measurement result accords with Gaussian distribution and is a good quantum random source.

The quantum random number generator works independently after being electrified, and can continuously output a binary random number sequence to the outside after being electrified without any external trigger signal source.

In the embodiment of the invention, the odd number with the digit of 2 exponentiation can be screened from the random number set and used as the encryption key to be stored in the encryption key set, and the integer with the digit of 2 exponentiation can be screened from the random number set and used as the target multiplier to be stored in the target multiplier set.

In the embodiment of the invention, the encryption key can be directly read from the encryption key set in the homomorphic encryption process, and the target multiplier is read from the target multiplier set, so that the random number generation efficiency is improved while the physical true random number is generated, and the homomorphic encryption efficiency is further improved.

On the basis of the foregoing embodiment, the method for homomorphic encryption of private data according to the embodiment of the present invention, where the homomorphic encryption of the private data based on the encryption key and the target product result includes:

generating a target random number based on the encryption key;

Specifically, in the embodiment of the invention, when the encryption key and the target product result are combined to homomorphic encrypt the private data, the target random number can be generated according to the encryption key. That is, as for the encryption key p, since the relation between the target random number r and the encryption key p is |2r| < |p/2|, the encryption key p is needed to be used when the target random number r is generated, so long as the small integer satisfying the relation can be met, and the homomorphic encryption result can be ensured to be correctly decrypted.

Thereafter, the private data m may be homomorphically encrypted according to the target random number r and the target product result p×q, i.e., the homomorphically encrypted result c of the private data m is calculated using the formula c=p×q+2r+m.

In the embodiment of the invention, the introduction of the target random number can further ensure the encryption effect on the private data.

On the basis of the foregoing embodiment, the method for homomorphic encryption of private data provided in the embodiment of the present invention, where determining, based on an alternative product result of the first transformation result and the second transformation result, a target product result of the encryption key and the target multiplier includes:

Specifically, in the embodiment of the present invention, since the first transformation result and the second transformation result are both obtained by parallel FFT, the result of the alternative multiplication of the first transformation result and the second transformation result needs to be subjected to inverse fast fourier transform (Inverse Fast Fourier Transform, IFFT), so as to obtain the result of the target multiplication of the encryption key and the target multiplier.

On the basis of the above embodiment, an operation example of the parallel FFT algorithm is given in the embodiment of the present invention, in which only the multiplication of small integers is calculated as an example, but the same is used for large integers, and the acceleration effect is more obvious.

For example: by passing throughParallel FFT algorithm, computation

。

31 and 24, the maximum number of bits of the result is 4, i.e

. For a 4-bit integer, this can be expressed as

. The polynomial coefficient expression vector of the multiplicand 31 is therefore:

the method comprises the steps of carrying out a first treatment on the surface of the The polynomial coefficient expression vector of multiplier 24 is:

。

the parallel FFT algorithm is performed as follows:

initially:

all blocks execute the assignment operation in parallel,

in (a)

；

In (a)

；

In (a)

；

In (a)

。

First, the

Round:

the method comprises the steps of carrying out a first treatment on the surface of the Satisfy the following requirements

Block of (2) is

And

；

in (a)

；

In (a)

；

First, the

Wheel:

Block of (2) is

And

；

in (a)

，

；

In (a)

，

；

The operation result of the parallel FFT algorithm is as follows:

，

，

，

。

i.e. according to the parallel FFT algorithm,

the polynomial coefficients of (a) are converted into point value expression representations as:

At this time

。

Thus, the parallel FFT result of the multiplicand 31 is

The method comprises the steps of carrying out a first treatment on the surface of the The parallel FFT result of multiplier 24 is

。

Dot product is performed on the parallel FFT result of the multiplicand 31 and the parallel FFT result of the multiplier 24 to obtain a dot product result of

。

Performing IFFT (algorithm process is similar to FFT algorithm process) on dot product result, and transforming into a formula

。

The IFFT result calculation formula can be expressed as:

，

，

，

。

at this time, the liquid crystal display device,

，

，

，

，

the IFFT result is brought into an IFFT result calculation formula, and the IFFT result can be obtained as

。

Namely there is

。

As shown in fig. 4, on the basis of the above embodiment, in an embodiment of the present invention, a device for homomorphic encryption of private data is provided, including:

a data acquisition module 41, configured to acquire private data to be encrypted;

the transformation module 42 is configured to determine an encryption key and a target multiplier corresponding to the encryption key, and perform parallel FFT on the encryption key and the target multiplier based on a stream multiprocessor in a graphics processor, to obtain a first transformation result and a second transformation result;

a product module 43 for determining a target product result of the encryption key and the target multiplier based on an alternative product result of the first transform result and the second transform result;

and an encryption module 44, configured to homomorphically encrypt the private data based on the encryption key and the target product result.

On the basis of the above embodiment, the privacy data homomorphic encryption device provided in the embodiment of the present invention, the transformation module is specifically configured to:

the privacy data homomorphic encryption device further comprises a set construction module, which is used for:

the encryption key set is constructed based on an odd number of the exponent power of 2 in a random number set generated by a quantum random number generator, and the target multiplier set is constructed based on an integer of the exponent power of 2 in the random number set.

On the basis of the above embodiment, the privacy data homomorphic encryption device provided in the embodiment of the present invention, the encryption module is specifically configured to:

Generating a target random number based on the encryption key;

On the basis of the foregoing embodiments, the privacy data homomorphic encryption device provided in the embodiments of the present invention, the product module is specifically configured to:

Specifically, the functions of each module in the privacy data homomorphic encryption device provided in the embodiment of the present invention are in one-to-one correspondence with the operation flows of each step in the above method embodiment, and the achieved effects are consistent.

The CPU-level main program of the privacy data homomorphic encryption device may include:

main()

selecting N-bit encryption keys from the encryption key set

Selecting an N-bit target multiplier from a set of target multipliers

The method comprises the steps of carrying out a first treatment on the surface of the v/N bit encryption key

The method comprises the steps of carrying out a first treatment on the surface of the the/N-bit target multiplier Q

The method comprises the steps of carrying out a first treatment on the surface of the The// array A is used for storing the encryption key

Polynomial coefficients of (a)

The method comprises the steps of carrying out a first treatment on the surface of the The// array B is used for storing the encryption key

Polynomial coefficients of the first transform result of (a)

The method comprises the steps of carrying out a first treatment on the surface of the The// array C is used for storing polynomial coefficients of the second conversion result of the target multiplier Q

Will be

The polynomial coefficients of (a) are stored in A, i.e

；

The method comprises the steps of carrying out a first treatment on the surface of the Conversion of multipliers using parallel FFT

Will be

The polynomial coefficients of (a) are stored in A, i.e

；

Alternate product result obtained by multiplying/calculating dot product:////// is%

IFFT is carried out on the result of the alternative multiplication to obtain a conversion result which is stored in an array C

And expressing the array C by using a coefficient expression to obtain a target product result.

As shown in fig. 5, on the basis of the above embodiment, in an embodiment of the present invention, a system for homomorphic encryption of private data is provided, including: a quantum random number generator 51, a graphic processor 52, and a privacy data homomorphic encryption device 53 provided in the above embodiments;

any two of the quantum random number generator 51, the graphic processor 52 and the privacy data homomorphic encryption device 53 are connected through interfaces;

the quantum random number generator 51 is used for providing an encryption key for the privacy data homomorphic encryption device and a target multiplier corresponding to the encryption key;

the privacy data homomorphic encryption device 53 is used to invoke the graphics processor 52.

Specifically, in the embodiment of the present invention, as shown in fig. 6, a Quantum Random Number Generator (QRNG) 51 may be configured in a random number generating device (generator) 61, where the random number generating device 61 further includes a judging unit (Judge) 611, a storing unit (Memory) 612, and a first I/O interface 613, and the judging unit 611 performs judgment screening on the random number generated by the quantum random number generator 51, so as to determine an encryption key set, a target multiplier set, and a target random number set, and store the encrypted key set, the target multiplier set, and the target random number set in the storing unit 612.

The privacy data homomorphic encryption device 53 may be configured in a computer (Host) 62, where the computer 62 further includes a memory (DRAM) 621 and a second I/O interface 622, and the encryption key, the target multiplier, and the target random number may be selected from the encryption key set, the target multiplier set, and the target random number set stored in the storage unit 612 through the second I/O interface 622 and the first I/O interface 613, respectively.

The graphics processor 52 may be configured in the graphics processor apparatus 63, and the graphics processor apparatus 63 further includes a storage (GDRAM) 631 and a third I/O interface 632, and the privacy data homomorphic encryption device 53 may invoke the graphics processor 52 through the second I/O interface 622 and the third I/O interface 632.

The privacy data homomorphic encryption system provided by the embodiment of the invention can realize parallel FFT (fast Fourier transform) in the homomorphic encryption process of the privacy data by combining the quantum random number generator, the graphic processor and the privacy data homomorphic encryption device provided by the embodiments, and can greatly improve the homomorphic encryption efficiency. Moreover, the quantum random number generator is introduced, so that homomorphic encryption effect can be ensured.

Fig. 7 illustrates a physical schematic diagram of an electronic device, as shown in fig. 7, which may include: processor (Processor) 710, communication interface (Communications Interface) 720, memory (Memory) 730, and communication bus 740, wherein Processor 710, communication interface 720, memory 730 communicate with each other via communication bus 740. The processor 710 may invoke logic instructions in the memory 730 to perform the privacy data homomorphic encryption methods provided in the embodiments described above.

Further, the logic instructions in the memory 730 described above may be implemented in the form of software functional units and may be stored in a computer readable storage medium when sold or used as a stand alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a magnetic disk, or an optical disk, or other various media capable of storing program codes.

In another aspect, the present invention also provides a computer program product, where the computer program product includes a computer program, where the computer program can be stored on a non-transitory computer readable storage medium, and when the computer program is executed by a processor, the computer can perform the privacy data homomorphic encryption method provided in the foregoing embodiments.

In yet another aspect, the present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, is implemented to perform the privacy data homomorphic encryption method provided in the above embodiments.

The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.

From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.

Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for homomorphic encryption of private data, comprising:

acquiring privacy data to be encrypted;

homomorphic encryption is carried out on the privacy data based on the encryption key and the target product result;

The first transformation result is obtained based on the following steps:

2. The method according to claim 1, wherein the determining a twiddle factor of each butterfly transformation operation in any round based on the round, the FFT point number, and a position of a polynomial coefficient allocated in each streaming multiprocessor in the polynomial, and screening out a plurality of streaming multiprocessors includes:

3. The method for homomorphic encryption of private data according to claim 1, wherein said determining an encryption key and a target multiplier corresponding to the encryption key comprises:

4. A method of homomorphic encryption of private data according to any one of claims 1-3, wherein homomorphic encrypting the private data based on the encryption key and the target product result comprises:

Generating a target random number based on the encryption key;

5. A method of homomorphic encryption of private data according to any one of claims 1-3, wherein said determining a target product result of said encryption key and said target multiplier based on an alternative product result of said first transform result and said second transform result comprises:

6. A privacy data homomorphic encryption device, comprising:

The encryption module is used for homomorphic encryption of the privacy data based on the encryption key and the target product result;

the transformation module is specifically used for:

7. A system for homomorphic encryption of private data, comprising: a quantum random number generator, a graphics processor and the privacy data homomorphic encryption device according to claim 6;

8. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of homomorphic encryption of private data as claimed in any one of claims 1-5 when the program is executed by the processor.

9. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the method of homomorphic encryption of private data according to any one of claims 1-5.