CN119155037A

CN119155037A - Parallel point adding method of elliptic curve based on AVX512IFMA

Info

Publication number: CN119155037A
Application number: CN202410953512.3A
Authority: CN
Inventors: 姜蕊; 彭聪; 冯琦; 罗敏; 何德彪
Original assignee: Wuhan University WHU
Current assignee: Wuhan University WHU
Priority date: 2024-07-16
Filing date: 2024-07-16
Publication date: 2024-12-17

Abstract

The application discloses a parallel point adding method of an elliptic curve based on AVX512IFMA, and belongs to the technical field of computers. The method comprises the steps of determining each coordinate of a plurality of pairs of point data participating in parallel point addition, determining a target number domain corresponding to the plurality of pairs of point data, determining a large number operation rule corresponding to the target number domain, determining a target point addition formula of the plurality of pairs of point data based on the relation between Z coordinate value Z ₁ of the point data and Z coordinate value Z ₂ of the added point data in each pair of point data, converting the coordinate value of the plurality of pairs of point data into the target data corresponding to a data structure of AVX512IFMA, and processing the target data based on the target point addition formula and the large number operation rule to obtain a point addition result of the plurality of pairs of point data. The method realizes 8X 1 paths of parallel acceleration of elliptic curve point addition, and can obtain great performance optimization and improvement.

Description

Parallel point adding method of elliptic curve based on AVX512IFMA

Technical Field

The application belongs to the technical field of computers, and particularly relates to a parallel point adding method of an elliptic curve based on AVX512 IFMA.

Background

In modern cryptography, elliptic curve cryptography (Elliptic Curve Cryptography, ECC) has been widely used in various fields of information security, such as digital signature, blockchain, SSL/TLS protocols, etc., due to its high security and low computational complexity. Elliptic curve Point Addition (Point Addition) and Point multiplication (Point Multiplication) are basic operations of ECC, whose efficiency directly affects the performance of the entire cryptosystem. Therefore, how to optimize the speed of these basic operations, especially the point-add operation, is a hot problem in research.

Conventional ECC point-and-addition implementations typically rely on large integer operations. Since the points on the elliptic curve are represented as large integer pairs, these operations involve a large number of modulo addition, modulo subtraction, modulo multiplication, etc. Although the computational power of modern processors has increased significantly, there is still a performance bottleneck facing large-scale elliptic curve point operations. In addition, the traditional method has low utilization rate in the aspect of parallel computing, and the advantages of the modern multi-core processor cannot be fully exerted.

AVX512IFMA (AVX-512 Integer Fused Multiply-Add) is a single instruction multiple data (SIMD, single Instruction Multiple Data) instruction set proposed by Intel corporation, which is part of the AVX-512 instruction set. It provides efficient vectorized integer arithmetic capability, in particular supporting Fused Multiply-Add (Fused Multiply-Add), i.e., simultaneous Multiply and Add operations. The operation can obviously reduce the instruction number and improve the operation speed. In addition, the AVX512IFMA supports 512-bit vector registers, so that each instruction can process more data, and the parallel computing efficiency is further improved.

Today, multiple cipher implementations work has begun to utilize SIMD to accelerate operations, such as in encryption, digital signature, TLS protocols, to increase computational efficiency and response speed. The BLS12-381 curve is an elliptic curve with high security intensity, and is widely applied to the field of cryptography, in particular to zero knowledge proof systems and public key cryptography. But there is currently no optimization scheme for the AVX512IFMA instruction set for this curve.

Therefore, there is no problem in the related art that the point addition calculation in the elliptic curve is optimized by using the AVX512IFMA instruction set, and no scheme for realizing the calculation acceleration of the point addition of the elliptic curve by using the parallel data processing advantage of the AVX512IFMA instruction set exists at present.

Disclosure of Invention

The present application is directed to solving at least one of the technical problems existing in the related art. Therefore, the application provides a parallel point adding method of elliptic curve based on AVX512IFMA, which utilizes the characteristic that AVX512IFMA single instruction multiple data instruction sets can process multiple data elements of the same type simultaneously in the same instruction period, realizes 8X 1 paths of parallel acceleration on elliptic curve point adding part, and can obtain great performance optimization and improvement.

In a first aspect, the present application provides a parallel point adding method for elliptic curve based on AVX512IFMA, the method comprising:

determining each coordinate of a plurality of pairs of point data participating in parallel point addition, wherein each pair of point data comprises point addition data and point data to be added;

Determining a target number domain corresponding to the multi-point data, wherein the target number domain is a finite domain of an elliptic curve or a secondary expansion domain of the finite domain;

determining a large number operation rule corresponding to the target number domain;

Determining a target point formulation of the multi-point data based on a relationship between a Z coordinate value Z ₁ of the point data and a Z coordinate value Z ₂ of the added point data in each of the multi-point data;

Converting coordinate values of the multi-point data into target data corresponding to a data structure of the AVX512 IFMA;

And processing the target data based on the target point addition formula and the large number operation rule to obtain a point addition result of the multi-point data.

According to the parallel point addition method of the elliptic curve based on the AVX512IFMA, the characteristics that a plurality of data elements of the same type can be processed simultaneously in the same instruction period by utilizing a single-instruction multi-data instruction set are utilized, the bottom 8X 1 path finite field operation and the upper 8X 1 path point addition operation are realized on the elliptic curve, meanwhile, as the bottom majority operation rule is determined based on a target number field, the point addition formulas are different along with the change of the coordinate relation of point data of the participating point addition calculation, a plurality of types of point addition operation interfaces can be provided, and the AVX512IFMA instruction set is used for realizing 8X 1 path parallel acceleration on the elliptic curve point addition part, so that the great performance optimization promotion can be obtained.

According to one embodiment of the present application, the relationship between the Z coordinate value Z ₁ of the added point data and the Z coordinate value Z ₂ of the added point data in each pair of the pairs of point data includes three types of data:

z ₁＝Z₂＝1、Z₁≠Z₂ = 1, and Z ₁≠Z₂.

According to one embodiment of the present application, converting coordinate values of multi-point data into target data corresponding to a data structure of AVX512IFMA includes:

converting each coordinate value of the coordinates of the plurality of pairs of point data into a coordinate value vector corresponding to a target operand base of AVX512 IFMA;

and forming a vector set by a plurality of coordinate value vectors corresponding to each coordinate value of each point data to obtain target data.

According to one embodiment of the present application, converting each coordinate value of coordinates of a plurality of pairs of point data into a coordinate value vector corresponding to a target operand base of AVX512IFMA includes:

determining the data type corresponding to the multi-point data;

if the data type is a standard element corresponding to the finite field where the elliptic curve is located, converting each coordinate value in the coordinates of the multiple pairs of point data into a coordinate value vector corresponding to a target operation base of AVX512IFMA based on a preset rule;

If the data type is a preset data type expressed on the Montgomery domain, each coordinate value in coordinates of the plurality of pairs of point data is converted into a coordinate value vector corresponding to a target operation radix of AVX512IFMA based on a Montgomery domain conversion rule corresponding to the target number domain.

According to one embodiment of the present application, if the data type is a standard element corresponding to a finite field where the elliptic curve is located, converting each coordinate value in coordinates of multiple pairs of point data into a coordinate value vector corresponding to a target operation base of AVX512IFMA based on a preset rule includes:

for any coordinate value F in the coordinate values of the plurality of pairs of point data, determining a coordinate value vector F corresponding to a target operation base of AVX512IFMA and corresponding to any coordinate value F by using the following formula, wherein the data type of any coordinate value F is a standard element corresponding to a finite field in which the elliptic curve is located:

f＝f₀+2⁵²f₁+2¹⁰⁴f₂+2¹⁵⁶f₃+2²⁰⁸f₄+2²⁶⁰f₅+2³¹²f₆+2³⁶⁴f₇

F=[f₀,f₁,f₂,f₃,f₄,f₅,f₆,f₇]

Wherein f _i＜2⁵² is more than or equal to 0 and i 8,i is more than or equal to 0, and the target operation base number is 2 ⁵².

According to an embodiment of the present application, forming a vector set of a plurality of coordinate value vectors corresponding to each coordinate value of each point data includes:

the vector set V is determined by the following formula:

The coordinate value vectors corresponding to any coordinate of any point data are F _a,F_b,F_c,F_d,F_e,F_f,F_g and F _h, any column of the vector set V corresponds to one coordinate value vector, and the i-th row of the vector set V corresponds to one register vector v_i＝[f_i ^a,f_i ^b,f_i ^c,f_i ^d,f_i ^e,f_i ^f,f_i ^g,f_i ^h],0≤i＜8,i as an integer.

In a second aspect, the present application provides a parallel point adding device based on an elliptic curve of AVX512IFMA, the device comprising:

the first determining module is used for determining each coordinate in coordinates of a plurality of pairs of point data participating in parallel point addition, wherein each pair of point data comprises point data and point data to be added;

The second determining module is used for determining a target number domain corresponding to the multi-point data, wherein the target number domain is a finite domain of an elliptic curve or a secondary expansion domain of the finite domain;

A third determining module, configured to determine a big number operation rule corresponding to the target number domain;

A fourth determining module, configured to determine a target point formulation of the multi-point data based on a relationship between a Z coordinate value Z ₁ of the point data and a Z coordinate value Z ₂ of the added point data in each of the multi-point data;

The data arrangement module is used for converting coordinate values of the multi-point data into target data corresponding to a data structure of the AVX512 IFMA;

and the data processing module is used for processing the target data based on the target point addition formula and the big number operation rule to obtain a point addition result of the multi-point data.

According to the parallel point adding device of the elliptic curve based on the AVX512IFMA, the characteristics that a plurality of data elements of the same type can be processed simultaneously in the same instruction period by utilizing a single-instruction multi-data instruction set are utilized, the bottom 8X 1 path finite field operation and the upper 8X 1 path point adding operation are realized on the elliptic curve, meanwhile, as the bottom majority operation rule is determined based on a target number field, the point adding formulas are different along with the change of the coordinate relation of point data of the participating point adding calculation, a plurality of types of point adding operation interfaces can be provided, and the AVX512IFMA instruction set is used for realizing 8X 1 path parallel acceleration on the elliptic curve point adding part, so that the great performance optimization promotion can be obtained.

In a third aspect, the present application provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, the processor implementing the parallel point addition method based on an elliptic curve of AVX512IFMA according to the first aspect as described above when the computer program is executed by the processor.

In a fourth aspect, the present application provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a parallel point-adding method for an AVX512 IFMA-based elliptic curve according to the first aspect described above.

In a fifth aspect, the present application provides a chip, the chip comprising a processor and a communication interface, the communication interface being coupled to the processor, the processor being configured to execute a program or instruction to implement a parallel point addition method based on an elliptic curve of AVX512IFMA as in the first aspect.

In a sixth aspect, the application provides a computer program product comprising a computer program which, when executed by a processor, implements the AVX512 IFMA-based elliptic curve parallel point-adding method of the first aspect as described above.

Additional aspects and advantages of the application will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the application.

Drawings

The foregoing and/or additional aspects and advantages of the application will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:

FIG. 1 is a schematic flow chart of a parallel point addition method of an elliptic curve based on AVX512IFMA according to an embodiment of the present application;

FIG. 2 is a schematic diagram of a parallel point-adding device based on an elliptic curve of AVX512IFMA according to an embodiment of the present application;

FIG. 3 is a schematic diagram of a parallel point-to-point computing engine based on an elliptic curve of AVX512IFMA according to an embodiment of the present application;

fig. 4 is a schematic hardware diagram of an electronic device according to an embodiment of the present application.

Detailed Description

The technical solutions of the embodiments of the present application will be clearly described below with reference to the drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which are obtained by a person skilled in the art based on the embodiments of the present application, fall within the scope of protection of the present application.

The terms first, second and the like in the description and in the claims, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged, as appropriate, such that embodiments of the present application may be implemented in sequences other than those illustrated or described herein, and that the objects identified by "first," "second," etc. are generally of a type, and are not limited to the number of objects, such as the first object may be one or more. Furthermore, in the description and claims, "and/or" means at least one of the connected objects, and the character "/", generally means that the associated object is an "or" relationship.

The parallel point adding method based on the elliptic curve of the AVX512IFMA, the parallel point adding device based on the elliptic curve of the AVX512IFMA, the electronic device and the readable storage medium provided by the embodiment of the application are described in detail below by specific embodiments and application scenes thereof with reference to the accompanying drawings.

The parallel point addition method based on the elliptic curve of the AVX512IFMA can be applied to the terminal, and can be specifically executed by hardware or software in the terminal.

The execution main body of the parallel point adding method of the elliptic curve based on the AVX512IFMA provided by the embodiment of the application can be the electronic equipment or the functional module or the functional entity of the parallel point adding method of the elliptic curve based on the AVX512IFMA, the electronic device in the embodiment of the application includes, but is not limited to, a mobile phone, a tablet computer, a camera, a wearable device and the like, and the parallel point adding method based on the elliptic curve of the AVX512IFMA provided in the embodiment of the application is described below by taking the electronic device as an execution main body as an example.

First, the following description is made of the coincidence and corresponding definitions that need to be used in the present application:

The finite field of the BLS12-381 elliptic curve, where p is the modulus of the BLS12-381 elliptic curve.

Finite field of BLS12-381 elliptic curveIs a secondary domain of the (c).

R: BLS12-381 elliptic curve.

P _i coordinates of elliptic curve point i, expressed as (X, Y, Z), P _i ε E where 1.ltoreq.i.ltoreq.n, n being the order of the elliptic curve.

V _i a 512 bit vector.

V is vector set, which is composed of 8V _i (0.ltoreq.i < 8) and can represent 8 big numbers.

A, R, C: three different sets of vectors.

Q is a vector set composed of modulus.

Elliptic curve point groups on the upper surface.

PADD ^* elliptic curve point-add, when Z ₁＝Z₂＝1,Z₁ and Z ₂ are the Z coordinate values of the two points participating in the point-add, respectively.

PADD, elliptic curve point-added, when Z ₁≠Z₂＝1,Z₁ and Z ₂ are the Z coordinates of the two points, respectively.

PADD ⁺ elliptic curve point-added, when Z ₁≠Z₂,Z₁ and Z ₂ are the Z coordinates of the two points, respectively.

As shown in FIG. 1, the parallel point adding method of the elliptic curve based on the AVX512IFMA comprises the steps of 110, 120, 130, 140, 1 and 160.

Step 110, determining each coordinate of a plurality of pairs of point data participating in parallel point addition, wherein each pair of point data comprises point data and point data to be added.

It should be noted that the AVX512IFMA can operate on multiple sets of data in parallel by using one set of instructions, and the AVX512IFMA instruction set is similar in nature to a vector processor that can perform the same operation on one set of data (also referred to as a "data vector") simultaneously, thereby achieving spatial parallelism. Since the AVX-512IFMA instruction set supports multiplication and addition operations on integers in each 64-bit lane of two registers, 8×1-way data arrangement can be realized, that is, at most, 8-way point additions of the same type of point data can be processed simultaneously in the same instruction cycle, therefore, the pairs of the multi-point data on the elliptic curve participating in parallel point additions cannot exceed 8 at a time, and since the AVX-512IFMA instruction set realizes 8×1-way data arrangement, when the pairs of the point data participating in parallel point additions cannot reach 8, for example, only 5-way point data participate in parallel point additions, 0-setting processing can be adopted on the data of the remaining 3 ways, but in general, in order to realize efficient parallel point addition processing, 8-way point data participate in parallel point additions are arranged as much as possible in each instruction cycle. For example, the same type of dot data P1, Q1, P2, Q2, P3, Q3, P4, Q4, P5, Q5, P6, Q6, P7, Q7, P8, and Q8 on the elliptic curve, if dot data P1 and dot data Q1 are to be added, dot data P2 and dot data Q2 are to be added, dot data P3 and dot data Q3 are to be added, dot data P4 and dot data Q4 are to be added, dot data P5 and dot data Q5 are to be added, dot data P6 and dot data Q6 are to be added, dot data P7 and dot data Q7 are to be added, dot data P8 and dot data Q8 are to be added, the above 8 dot data calculation may be processed simultaneously in the same instruction period, and two dot data involved in dot calculation may be divided into two data types, one being the dot data is to be added, and the other is the dot data to be added, and the dot data Q6 is used for the dot data.

It should be noted that, in this embodiment of the present application, the elliptic curve is a specific curve BLS12-381 curve, so it may be determined that the coordinate values of the point data on the elliptic curve are in most cases standard binary large integers represented by 381 bits, and if the determined point data on the elliptic curve is from a special database and the data in the special database is the data type expressed on the montgomery domain, then the montgomery domain conversion is also required for the point data on the elliptic curve participating in point addition, which will be described in detail later.

And 120, determining a target number field corresponding to the plurality of pairs of point data, wherein the target number field is a finite field of an elliptic curve or a secondary expansion field of the finite field.

It should be noted that, the point-adding calculation is performed on the point data on the BLS12-381 curve, which can be divided into two kinds of point data in the target number domain, one is the finite domain of the elliptic curve BLS12-381Elliptic curve point group onThe other is the finite field of elliptic curve BLS12-381Is spread by the second order of (2)Elliptic curve point group onIs included in the data of the point in the image. For different target number domains, the corresponding large number operation rules of the bottom number domain operation layer are also different, namely for a finite fieldThe large number operations of the method comprise modulo addition, modulo subtraction, modulo multiplication addition, modulo multiplication and modulo square, and all have a set of operation rules corresponding to AVX512IFMA, and are applied to the secondary spread domainThe above large number operation also comprises the large number operation of modulo addition, modulo subtraction, modulo multiplication addition, modulo multiplication and modulo square, and is based on finite fieldAn additional set of operation rules extended on the basis of the rules of the large number operation.

Step 130, determining a big number operation rule corresponding to the target number domain.

It will be appreciated that since the target number field includes two types, the finite fields of elliptic curves BLS12-381, respectivelyAnd the finite field of elliptic curve BLS12-381Is spread by the second order of (2)The two number domains are respectively provided with a corresponding large number operation rule.

Step 140, determining a target point formulation of the multi-point data based on the relationship between the Z coordinate value Z ₁ of the point data and the Z coordinate value Z ₂ of the added point data in each of the multi-point data.

It should be noted that, when performing point addition calculation on point data on the BLS12-381 curve, different relationships between Z coordinate values of the added point data and the added point data may result in different point addition calculation formulas. For example, the coordinates of the added point data P are (X1, Y1, Z1), the coordinates of the added point data Q are (X2, Y2, Z2), and if Z ₁＝Z₂ =1, the calculation formula of the coordinates (X3, Y3, Z3) of the point-added result point data R obtained by the point-adding calculation is as follows:

H=X2-X1

HH=H²

I=4*HH

J=H*I

r=2*(Y2-Y1)

V=X1*I

X3=r²-J-2*V

Y3=r*(V-X3)-2*Y1*J

Z3=2*H

In the case of Z ₁≠Z₂ =1, the calculation formula of the coordinates (X3, Y3, Z3) of the dot-added calculation result dot data R is as follows:

Z1Z1=Z1²

U2=X2*Z1Z1

S2=Y2*Z1*Z1Z1

H=U2-X1

HH=H²

I=4*HH

J=H*I

r=2*(S2-Y1)

V=X₁*I

X3=r²-J-2*V

Y3=r*(V-X3)-2*Y1*J

Z3=(Z1+H)²-Z1Z1-HH

in the case of Z ₁≠Z₂, the calculation formula of the coordinates (X3, Y3, Z3) of the dot-added calculation result dot data R is as follows:

Z1Z1=Z1²

Z2Z2=Z2²

U1=Xl*Z2Z2

U2=X2*Z1Z1

S1=Y1*Z2*Z2Z2

S2=Y2*Z1*Z1Z1

H=U2-U1

I=(2*H)²

J=H*I

r=2*(S2-S1)

V=U1*I

X3=r²-J-2*V

Y3=r*(V-X3)-2*S1*J

Z3=((Z1+Z2)²-Z1Z1-Z2Z2)*H

therefore, there is a need to determine the relationship between the Z coordinate values of the added point data and the added point data.

Step 150, converting the coordinate values of the multi-point data into target data corresponding to the data structure of the AVX512 IFMA.

It should be noted that, for the conversion of the data structure of the coordinate values of the multi-point data, it is necessary to perform the conversion according to the characteristics of the AVX512IFMA, and in view of the fact that the AVX-512IFMA instruction set supports multiplication and addition operations on the 52-bit unsigned integers in each 64-bit lane of the two registers, 2 ⁵² can be naturally used as the operation base, each coordinate value in the coordinates of the multi-point data is converted into a coordinate value vector with the operation base of 2 ⁵², and then a plurality of coordinate value vectors corresponding to each coordinate value of each point data form a vector set, so as to obtain the target data.

And 160, processing the target data based on the target point addition formula and the large number operation rule to obtain a point addition result of the multi-point data.

It will be appreciated that, no matter what the target point formula is, the target point formula needs to call the underlying large number operation rule to perform the basic operation, so after the target point formula is determined, and a set of underlying large number operation rules determined by the target number domain to which the point data participating in the point-to-point calculation belongs are determined, a corresponding set of underlying large number operation rules is called based on the target point formula to process the multi-point data.

According to the parallel point addition method of the elliptic curve based on the AVX512IFMA, the characteristics that a plurality of data elements of the same type can be processed simultaneously in the same instruction period by utilizing a single-instruction multi-data instruction set are utilized, the bottom 8X 1 path finite field operation and the upper 8X 1 path point addition operation are realized on the BLS121-381 curve, meanwhile, as the bottom most calculation rule is determined based on a target number field, and the point addition formulas are different according to the change of the coordinate relation of point data calculated along with the participation point addition, a plurality of types of point addition operation interfaces can be provided, and the 8X 1 path parallel acceleration can be realized on the elliptic curve point addition part by utilizing the AVX512IFMA instruction set, so that the great performance optimization improvement can be obtained.

In some embodiments, the relationship between the Z coordinate value Z ₁ of the point data and the Z coordinate value Z ₂ of the added point data in each of the plurality of pairs of point data includes three types of data:

z ₁＝Z₂＝1、Z₁≠Z₂ = 1, and Z ₁≠Z₂.

Specifically, the point data on the BLS121-381 curve is generally represented using elliptic curve points in the jacobian coordinate system, and thus, coordinates of the point data on the BLS121-381 curve include three coordinate values of X, Y and Z, and a relationship between the Z coordinate values of two point data of participating points on the BLS121-381 curve determines a corresponding point addition formula. For example, the coordinates of the added point data P are (X1, Y1, Z1), the coordinates of the added point data Q are (X2, Y2, Z2), and if Z ₁＝Z₂ =1, the calculation formula of the coordinates (X3, Y3, Z3) of the point-added result point data R obtained by the point-adding calculation is as follows:

H=X2-X1

HH=H²

I=4*HH

J=H*I

r=2*(Y2-Y1)

V=X1*I

X3=r²-J-2*V

Y3=r*(V-X3)-2*Y1*J

Z3=2*H

Z1Z1=Z1²

U2=X2*Z1Z1

S2=Y2*Z1*Z1Z1

H=U2-X1

HH=H²

I=4*HH

J=H*I

r=2*(S2-Y1)

V=X1*I

X3=r²-J-2*V

Y3=r*(V-X3)-2*Y1*J

Z3=(Z1+H)²-Z1Z1-HH

Z1Z1=Z1²

Z2Z2=Z2²

U1=X1*Z2Z2

U2=X2*Z1Z1

S1=Y1*Z2*Z2Z2

S2=Y2*Z1*Z1Z1

H=U2-U1

I=(2*H)²

J=H*I

r=2*(S2-S1)

V=U1*I

X3=r²-J-2*V

Y3=r*(V-X3)2*S1*J

Z3=((Z1+Z2)²-Z1Z1-Z2Z2)*H

It will be appreciated that since there are two types of point data for the target number field, the finite fields of the elliptic curves BLS12-381, respectivelyElliptic curve point group onIs included in the elliptic curve BLS12-381, and is limited to the elliptic curve BLSIs spread by the second order of (2)

Elliptic curve point group onIn addition to 3 different point addition formulas corresponding to 3 different situations of the relationship between the two point Z coordinates of the participating point addition, 2×3=6 different point addition operations may actually be implemented, that is, a calculation engine (i.e., a device) corresponding to the parallel point addition method of the elliptic curve based on AVX512IFMA provided by the embodiment of the present invention may include point addition formulas of 3 points of two groups of elliptic curves BLS12-381, that is, 6 different point addition operation interfaces are provided.

In some embodiments, step 150 may include:

It should be noted that, for each pair of point data, including two kinds of point data including point data and point data to be added, each kind of point data is represented by three coordinate values X, Y and Z, each coordinate value is a big number, and since the AVX-512IFMA instruction set supports multiplication and addition operations on 52-bit unsigned integers in each 64-bit channel of two registers, each coordinate value is first converted into a coordinate value vector with an operation base of 2 ⁵².

And rearranging a plurality of coordinate value vectors corresponding to each coordinate value of each point data to construct a vector set, wherein the point data and the added point data are provided with three coordinate values of X, Y and Z, so that 6 vector sets are provided. For convenience of explanation of parallel processing of 8×1 data, the multi-pair point data participating in parallel point addition is set to 8-pair point data here and hereinafter. For example, the same type of point data P1, Q1, P2, Q2, P3, Q3, P4, Q4, P5, Q5, P6, Q6, P7, Q7 on an elliptic curve, P8 and Q8, if the point addition of the point addition data P1 (X _P1,Y_P1,Z_P1) and the point addition data Q1 (X _Q1,Y_Q1,Z_Q1), the point addition of the point addition data P2 (X _P2,Y_P2,Z_P2) and the point addition data Q2 (X _Q2,Y_Q2,Z_Q2), the point addition of the point addition data P3 (X _P3,Y_P3,Z_P3) and the point addition data Q3 (X _Q3,Y_Q3,Z_Q3), the point addition of the point addition data P4 (X _P4,Y_P4,Z_P4) and the point addition data Q4 (X _Q4,Y_Q4,Z_Q4), the point addition of the point addition data P5 (X _P5,Y_P5,Z_P5) and the point addition data Q5 (X _Q5,Y_Q5,Z_Q5), the point addition of the point addition data P6 (X _P6,Y_P6,Z_P6) and the point addition data Q6 (X _Q6,Y_Q6,Z_Q6), the point addition of the point addition data P7 (X _P7,Y_P7,Z_P7) and the point addition data Q7 (X _Q7,Y_Q7,Z_Q7), the point addition data P8 (X _P8,Y_P8,Z_P8) and the point addition data Q8 (X _Q8,Y_Q8,Z_Q8) are first converted from a total of X_P1,Y_P1,Z_P1,X_Q1,Y_Q1,Z_Q1,X_P2,Y_P2,Z_P2,X_Q2,Y_Q2,Z_Q2,X_P3,Y_P3,Z_P3,X_Q3,Y_Q3,Z_Q3,X_P4,Y_P4,Z_P4,X_Q4,Y_Q4,Z_Q4,X_P5,Y_P5,Z_P5,X_Q5,Y_Q5,Z_Q5,X_P6,Y_P6,Z_P6,X_Q6,Y_Q6,Z_Q6,X_P7,Y_P7,Z_P7,X_Q7,Y_Q7,Z_Q7,X_P8,Y_P8,Z_P8,X_Q8,Y_Q8,Z_Q8 X2=48 to a vector of coordinate values ⁵², respectively, for example, the converted coordinate value vectors are VX_P1,VY_P1,VZ_P1,VX_Q1,VY_Q1,VZ_Q1,VX_P2,VY_P2,VZ_P2,VX_Q2,VY_Q2,VZ_Q2,VX_P3,VY_P3,VZ_P3,VX_Q3,VY_Q3,VZ_Q3,VX_P4,VY_P4,VZ_P4,VX_Q4,VY_Q4,VZ_Q4,VX_P5,VY_P5,VZ_P5,VX_Q5,VY_Q5,VZ_Q5,VX_P6,VY_P6,VZ_P6,VX_Q6,VY_Q6,VZ_Q6,VX_P7,VY_P7,VZ_P7,VX_Q7,VY_Q7,VZ_Q7,VX_P8,VY_P8,VZ_P8,VX_Q8,VY_Q8,VZ_Q8; respectively, then the 8 coordinate value vectors corresponding to each coordinate value of each point data are rearranged to construct a vector set, which is equivalent to constructing a vector set for the 8 coordinate value vectors of the X coordinate value in the point data, constructing a vector set for the 8 coordinate value vectors of the Y coordinate value in the point data, constructing a vector set for the 8 coordinate value vectors of the Z coordinate value in the point data, constructing a vector set for the 8 coordinate value vectors of the X coordinate value in the point data, constructing a vector set for the 8 coordinate value vectors of the Y coordinate value in the point data, constructing a vector set for 8 coordinate value vectors of Z coordinate value in the added point data, 6 vector sets in total, followed by the above example, namely constructing 6 vector sets V1, V2, V3, V4, V5 and V6, wherein ,V1＝<VX_P1,VX_P2,VX_P3,VX_P4,VX_P5,VX_P6,VX_P7,VX_P8>,V2＝<VY_P1,VY_P2,VY_P3,VY_P4,VY_P5,VY_P6,VY_P7,VY_P8>,V3＝<VZ_P1,VZ_P2,VZ_P3,VZ_P4,VZ_P5,VZ_P6,VZ_P7,VZ_P8>,V4＝<VX_Q1,VX_Q2,VX_Q3,VX_Q4,VX_Q5,VX_Q6,VX_Q7,VX_Q8>,V5＝<VY_Q1,VY_Q2,VY_Q3,VY_Q4,VY_Q5,VY_Q6,VY_Q7,VY_Q8>,V6＝<VZ_Q1,VZ_Q2,VZ_Q3,VZ_Q4,VZ_Q5,VZ_Q6,VZ_Q7,VZ_Q8>.

In some embodiments, converting each coordinate value of the coordinates of the plurality of pairs of point data into a coordinate value vector corresponding to a target operand base of AVX512IFMA includes:

determining the data type corresponding to the multi-point data;

It should be noted that, since the obtained point data to be added may originate from databases of different data structures, it is also necessary to determine the data type of the point data to be added and calculated first, which generally corresponds to the elliptic curve BLS12-381, and the obtained point data to be added and calculated is 381-bit binary, then each coordinate value in the coordinate values of 8 pairs of point data may be converted into a coordinate value vector with an operation base of 2 ⁵² directly based on the preset rule, but there are other cases where the point data to be added and calculated is from a database of a specific montgomery domain, and therefore, for such other cases, each coordinate value in the coordinate values of 8 pairs of point data is converted into a coordinate value vector with an operation base of 2 ⁵² based on the montgomery domain conversion rule corresponding to the target number domain. For example, in most cases, modern computer architectures are 64-bit, and 2 ⁶⁴ is often used as the operand base in large-number operations, but in the present application, the operand base of AVX512IFMA is 2 ⁵², so that when performing a point-add operation, a montgomery domain conversion may be required. The conversion of one domain is essentially a Montgomery multiplication process, e.g., a is a large number of 381 bits, R ₁ is a first Montgomery domain, R ₂ is a second Montgomery domain, and the conversion of aR ₁ to aR ₂ is performed only once on R ₂ domain by performing aR ₁ and aRIn the finite fieldMontgomery multiplication on, converting aR ₂ to aR ₁, only by performing one time on R ₂ domain with aR ₂ and R ₁ in finite domainMontgomery multiplications thereon.

In some embodiments, if the data type is a standard element corresponding to the finite field where the elliptic curve is located, converting each coordinate value in coordinates of the multiple pairs of point data into a coordinate value vector corresponding to a target operation radix of AVX512IFMA based on a preset rule includes:

F=[f₀,f₁,f₂,f₃,f₄,f₅,f₆,f₇]

Specifically, the 8×1 way data arrangement of the point data of the participating point addition is realized based on the AVX-512IFMA instruction set, and first, the point data of 381 bit integers is expressed by using an operation base 2 ⁵². Since the AVX-512IFMA instruction set supports multiply and add operations on 52-bit unsigned integers within each 64-bit lane of two registers, 2 ⁵² can naturally be used as the radix. For example, in the BLS12-381 curve, the 381-bit integer f represented using radix 2 ⁵² may be represented as follows, where 0.ltoreq.f _i＜2⁵² and 0.ltoreq.i <8.

f＝f₀+2⁵²f₁+2¹⁰⁴f₂+2¹⁵⁶f₃+2²⁰⁸f₄+2²⁶⁰f₅+2³¹²f₆+2³⁶⁴f₇.

In some embodiments, forming a vector set from a plurality of coordinate value vectors corresponding to each coordinate value of each point data includes:

the vector set V is determined by the following formula:

Specifically, in the 8×1-way parallel computation of the present application, the main data structure is vector set V, which consists of 8 vectors V _i (0+.i < 8). Each v _i consists of eight elements with radix 2 ⁵², which can be stored in a 512-bit register for computation. Here again, the logarithmic setting for the multi-point data involved in parallel point addition is exactly equal to 8, thus for eight integersThe vector set V is defined as follows, where each vector v_i＝[f_i ^a,f_i ^b,f_i ^c,f_i ^d,f_i ^e,f_i ^f,f_i ^g,f_i ^h].

Based on this data structure, the present application can implement basic finite field operation in 8×1 mode using AVX-512 IFMA. If the number of pairs of point data participating in parallel point addition is smaller than 8, for example, 5 pairs of point data are subjected to parallel point addition calculation, then F _a,F_b,F_c,F_d and F _e in the vector set V sequentially correspond to 5 coordinate value vectors, respectively, which are determined based on any coordinate value of any point data in the 5 pairs of point data, and the remaining vectors F _f,F_g and F _h in the vector set V are processed with 0.

Continuing with the description of the large number operations for the different target number fields, the finite field is described firstThe large number operation includes modular addition, modular subtraction, modular multiplication addition, modular multiplication and modular square.

For modulo addition, modulo subtraction, and modulo multiple addition operations: modulo addition, which can be denoted as C++A+B mod Q, includes three steps: first, a and B are added, and the result of their sum is stored in C; next, Q is subtracted from C, but some lanes in C may appear negative, thus creating a 512-bit mask vector in which each 64-bit element corresponds to 8 integers in C, the corresponding 64-bit element being set to all 1's if the integer in the lane is negative, and all 0's if it is non-negative, bitwise and-ing Q with the mask vector, and then adding Q to the negative integer in C instead of the negative integer plus 0 has no effect on the result. Based on a similar principle of the above steps, modulo subtraction C≡A-B mod Q involves only two steps, first subtracting Y from X, then processing the negative part with a mask. Modulo addition is the same as modulo addition, except that the X and Y addition portions of the first stage are shifted left.

Modular multiplication and modular square, where modular multiplication uses the method of Montgomery multiplication, is divided into two stages, integer multiplication and Montgomery reduction. Montgomery multiplications use a modified coarse-integration hybrid scanning (CIHS) method. The modular square is the same as the reduced part of the modular multiplication, and the calculation part is changed from multiplication to square.The above operation is based onIs calculated by finite field operation. For the followingThe 8 multiplied by 1 path can be accelerated by using Karatuba algorithm, and the result is thatThe number of multiplications is reduced from four to three, and for modulo squaring, one can reduceThe number of multiplications is reduced from three to two.

According to the parallel point adding method of the elliptic curve based on the AVX512IFMA provided by the embodiment of the application, the execution main body can be a parallel point adding device of the elliptic curve based on the AVX512 IFMA. In the embodiment of the application, the parallel point adding device based on the elliptic curve of the AVX512IFMA is taken as an example to execute the parallel point adding method based on the elliptic curve of the AVX512IFMA, and the parallel point adding device based on the elliptic curve of the AVX512IFMA provided by the embodiment of the application is described.

The embodiment of the application also provides a parallel point adding device of the elliptic curve based on the AVX512 IFMA.

As shown in fig. 2, the parallel point adding apparatus for an elliptic curve based on AVX512IFMA includes a first determining module 210, a second determining module 220, a third determining module 230, a fourth determining module 240, a data arranging module 250 and a data processing module 260, wherein,

A first determining module 210, configured to determine each coordinate of a plurality of pairs of point data participating in parallel point addition, where each pair of point data includes two kinds of point data, namely point data and point data to be added;

a second determining module 220, configured to determine a target number field corresponding to the plurality of pairs of point data, where the target number field is a finite field of an elliptic curve or a secondary expansion field of the finite field;

a third determining module 230, configured to determine a big number operation rule corresponding to the target number domain;

A fourth determining module 240, configured to determine a target point formulation of the multi-point data based on a relationship between a Z coordinate value Z ₁ of the point data and a Z coordinate value Z ₂ of the added point data in each of the multi-point data;

A data arrangement module 250 for converting coordinate values of the multi-point data into target data corresponding to a data structure of the AVX512 IFMA;

the data processing module 260 is configured to process the target data based on the target point addition formula and the big number operation rule, so as to obtain a point addition result of the multi-point data.

According to the parallel point adding device of the elliptic curve based on the AVX512IFMA, the characteristics that a plurality of data elements of the same type can be processed simultaneously in the same instruction period by utilizing a single-instruction multi-data instruction set are utilized, the bottom 8X 1 path finite field operation and the upper 8X 1 path point adding operation are realized on the BLS121-381 curve, meanwhile, as the bottom most calculation rule is determined based on a target number field, and the point adding formulas are different according to the change of the coordinate relation of point data calculated along with the participation point adding, a plurality of types of point adding operation interfaces can be provided, and the 8X 1 path parallel acceleration can be realized on the elliptic curve point adding part by utilizing the AVX512IFMA instruction set, so that the great performance optimization improvement can be obtained.

z ₁＝Z₂＝1、Z₁≠Z₂ = 1, and Z ₁≠Z₂.

determining the data type corresponding to the multi-point data;

F=[f₀,f₁,f₂,f₃,f₄,f₅,f₆,f₇]

the vector set V is determined by the following formula:

The coordinate value vectors corresponding to any coordinate of any point data are F _a,F_b,F_c,F_d,F_e,F_f,F_g and F _h, any column of the vector set V corresponds to one coordinate value vector, and the i-th row of the vector set V corresponds to one register vector v_i＝[f_i ^a,f_i ^b,f_i ^e,f_i ^d,f_i ^e,f_i ^f,f_i ^g,f_i ^h],0≤i＜8,i as an integer.

The parallel point adding device based on the elliptic curve of the AVX 512 IFMA in the embodiment of the application can be electronic equipment, and can also be a component in the electronic equipment, such as an integrated circuit or a chip. The electronic device may be a terminal, or may be other devices than a terminal. The electronic device may be a Mobile phone, a tablet computer, a notebook computer, a palm computer, a vehicle-mounted electronic device, a Mobile internet appliance (Mobile INTERNET DEVICE, MID), an augmented reality (augmented reality, AR)/Virtual Reality (VR) device, a robot, a wearable device, an ultra-Mobile personal computer (UMPC), a netbook or a Personal Digital Assistant (PDA), etc., and may also be a server, a network attached storage (Network Attached Storage, NAS), a personal computer (personal computer, PC), a Television (TV), a teller machine, a self-service machine, etc., which are not particularly limited in the embodiments of the present application.

The parallel point adding device based on the elliptic curve of the AVX5 12IFMA in the embodiment of the application can be a device with an operating system. The operating system may be a microsoft (Windows) operating system, an Android operating system, a 1OS operating system, or other possible operating systems, which is not particularly limited in the embodiments of the present application.

The parallel point adding device based on the elliptic curve of the AVX512IFMA provided by the embodiment of the present application can implement each process implemented by the method embodiment of fig. 1, and in order to avoid repetition, a detailed description is omitted herein.

Based on the above embodiment, the embodiment of the application also provides a method and a device for rapidly realizing points of elliptic curve based on the AVX512IFMA instruction set, which accelerate the realization of elliptic curve points on a CPU platform, and provide an engine computing interface, which can be used for digital signature, privacy protection, zero knowledge proof and other application scenes. In this example, the BLS12-381 curveGroup(s)The point addition of the group is divided into three cases according to the Z coordinate, and six calculation engines are realized.

In this embodiment, as shown in fig. 3, the scheme may be divided into three parts of 8×1 path data arrangement, finite field operation and point operation, which are described in detail as follows:

And part 1:8×1 paths of data are distributed.

Since the AVX-512IFMA instruction set supports multiply and add operations on 52-bit unsigned integers within each 64-bit lane of two registers, 2 ⁵² can naturally be used as the radix. For example, in the BLS12-381 curve, the 381-bit integer f represented using radix 2 ⁵² may be represented as follows, where 0.ltoreq.f _i＜2⁵² and 0.ltoreq.i <8.

In our 8 x 1-way parallel computation, the main data structure is vector set V, which consists of 8 vectors V _i (0.ltoreq.i < 8). Each v _i consists of eight elements with radix 2 ⁵², which can be stored in a 512-bit register for computation. For eight integersThe vector set V is defined as follows, where each vector v_i＝[f_i ^a,f_i ^b,f_i ^c,f_i ^d,f_i ^e,f_i ^f,f_i ^g,f_i ^h].

Based on this data structure, the basic finite field operation in 8×1 mode can be implemented using AVX-512 IFMA.

Part 2, finite field operation.

The part can realizeDomain and its secondary domain expansionThe large number operation mainly comprises modulo addition, modulo subtraction, modulo multiplication, modulo square and Montgomery domain conversion.

Montgomery domain conversion in most cases, modern computer architectures are 64-bit, often with 2 ⁶⁴ as the operand radix in large number operations, but in the present application, the operand radix of AVX512IFMA is 2 ⁵², so Montgomery domain conversion is sometimes required in performing point addition operations. The conversion of one domain is essentially a Montgomery multiplication process, e.g., a is a large number of 381 bits, R ₁ is a first Montgomery domain, R ₂ is a second Montgomery domain, and the conversion of aR ₁ to aR ₂ is performed only once on R ₂ domain by performing aR ₁ and aRIn the finite fieldMontgomery multiplication on, converting aR ₂ to aR ₁, only by performing one time on R ₂ domain with aR ₂ and R ₁ in finite domainMontgomery multiplications thereon.

And part 3, point operation.

The elliptic curve points under the jacobian coordinate system can be expressed as (X, Y, Z). For points P ₁ and P ₂, the point addition formula can be divided into three cases, PADD ^*, PADD, and PADD ⁺, according to Z ₁＝Z₂＝1、Z₁≠Z₂ =1 and Z ₁≠Z₂. For the 8×1-way point operation part, the 8×1-way finite field operation of the bottom layer can be directly called, and the results are respectively calculated according to a point addition formula.

In some embodiments, as shown in fig. 4, an electronic device 400 is further provided in the embodiments of the present application, which includes a processor 401, a memory 402, and a computer program stored in the memory 402 and capable of running on the processor 401, where the program, when executed by the processor 401, implements each process of the above embodiment of the parallel point adding method based on the elliptic curve of the AVX512IFMA, and the same technical effects can be achieved, so that repetition is avoided and no further description is given here.

The electronic device in the embodiment of the application includes the mobile electronic device and the non-mobile electronic device.

The embodiment of the application also provides a non-transitory computer readable storage medium, on which a computer program is stored, which when executed by a processor, implements each process of the above embodiment of the parallel point adding method based on the elliptic curve of AVX512IFMA, and can achieve the same technical effect, so that repetition is avoided and redundant description is omitted.

The processor is a processor in the electronic device in the above embodiment. Readable storage media include computer readable storage media such as computer readable memory ROM, random access memory RAM, magnetic or optical disks, and the like.

The embodiment of the application also provides a computer program product, which comprises a computer program, wherein the computer program realizes the parallel point adding method based on the elliptic curve of the AVX512IFMA when being executed by a processor.

The embodiment of the application further provides a chip, the chip comprises a processor and a communication interface, the communication interface is coupled with the processor, the processor is used for running programs or instructions, the parallel point adding method embodiment based on the elliptic curve of the AVX512IFMA is realized, the same technical effect can be achieved, and the repetition is avoided, and the description is omitted here.

It should be understood that the chips referred to in the embodiments of the present application may also be referred to as system-on-chip chips, chip systems, or system-on-chip chips, etc.

It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element. Furthermore, it should be noted that the scope of the methods and apparatus in the embodiments of the present application is not limited to performing the functions in the order shown or discussed, but may also include performing the functions in a substantially simultaneous manner or in an opposite order depending on the functions involved, e.g., the described methods may be performed in an order different from that described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

From the above description of the embodiments, it will be clear to those skilled in the art that the above-described embodiment method may be implemented by means of software plus a necessary general hardware platform, but of course may also be implemented by means of hardware, but in many cases the former is a preferred embodiment. Based on such understanding, the technical solution of the present application may be embodied essentially or in a part contributing to the related art in the form of a computer software product stored in a storage medium (e.g., ROM/RAM, magnetic disk, optical disk), including several instructions for causing a terminal (which may be a mobile phone, a computer, a server, or a network device, etc.) to perform the method of the embodiments of the present application.

The embodiments of the present application have been described above with reference to the accompanying drawings, but the present application is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present application and the scope of the claims, which are to be protected by the present application.

In the description of the present specification, reference to the terms "one embodiment," "some embodiments," "illustrative embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, schematic representations of the above terms do not necessarily refer to the same embodiments or examples. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

Although embodiments of the present application have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the spirit and scope of the application as defined by the appended claims and their equivalents.

Claims

1. A parallel point addition method for elliptic curve based on AVX512IFMA, characterized by comprising:

Determine each coordinate of the plurality of pairs of point data participating in parallel point addition, each pair of point data includes two types of point data: adding point data and added point data;

Determine a target number field corresponding to the plurality of pairs of point data, the target number field being a finite field of the elliptic curve or a quadratic extension field of the finite field;

Determine a large number operation rule corresponding to the target number domain;

Determine a target point adding formula for the plurality of pairs of point data based on a relationship between a Z coordinate value _Z1 of the adding point data and a Z coordinate value _Z2 of the added point data in each pair of point data in the plurality of pairs of point data;

Convert the coordinate values of the plurality of pairs of point data into target data corresponding to the data structure of the AVX512IFMA;

The target data is processed based on the target point addition formula and the large number operation rule to obtain the point addition results of the multiple pairs of point data.

2. The parallel point adding method of elliptic curve based on AVX512IFMA according to claim 1 is characterized in that the relationship between the Z coordinate value _Z1 of the adding point data and the Z coordinate value _Z2 of the added point data in each pair of point data in the multiple pairs of point data includes three types, namely:

Z ₁ =Z ₂ =1, Z1≠Z ₂ =1, and Z ₁ ≠Z ₂ .

3. The parallel point addition method of elliptic curve based on AVX512IFMA according to claim 2, characterized in that the step of converting the coordinate values of the plurality of pairs of point data into target data corresponding to the data structure of the AVX512IFMA comprises:

Convert each coordinate value in the coordinates of the plurality of pairs of point data into a coordinate value vector corresponding to the target operation base of the AVX512IFMA;

Multiple coordinate value vectors corresponding to each coordinate value of each point data form a vector set to obtain target data.

4. The parallel point addition method of elliptic curve based on AVX512IFMA according to claim 3, characterized in that the step of converting each coordinate value in the coordinates of the plurality of pairs of point data into a coordinate value vector corresponding to a target operation base of the AVX512IFMA comprises:

Determine the data types corresponding to the multiple pairs of point data;

If the data type is a standard element corresponding to the finite field where the elliptic curve is located, each coordinate value in the coordinates of the multiple pairs of point data is converted into a coordinate value vector corresponding to the target operation base of the AVX512IFMA based on a preset rule;

If the data type is a preset data type expressed on a Montgomery domain, each coordinate value in the coordinates of the multiple pairs of point data is converted into a coordinate value vector corresponding to the target operation base of the AVX512IFMA based on the Montgomery domain conversion rule corresponding to the target number domain.

5. The parallel point addition method of elliptic curve based on AVX512IFMA according to claim 4 is characterized in that if the data type is a standard element corresponding to the finite field where the elliptic curve is located, then each coordinate value in the coordinates of the multiple pairs of point data is converted into a coordinate value vector corresponding to the target operation base of the AVX512IFMA based on a preset rule, including:

For any coordinate value f among the coordinate values of the multiple pairs of point data, the data type of the any coordinate value f is a standard element corresponding to the finite field where the elliptic curve is located, and the coordinate value vector F corresponding to the target operation base of the AVX512IFMA corresponding to the any coordinate value f is determined by the following formula:

f＝f ₀ +2 ⁵² f ₁ +2 ¹⁰⁴ f ₂ +2 ¹⁵⁶ f ₃ +2 ²⁰⁸ f ₄ +2 ²⁶⁰ f ₅ +2 ³¹² f ₆ +2 ³⁶⁴ f ₇

F＝[f ₀ , f ₁ , f ₂ , f ₃ , f ₄ , f ₅ , f ₆ , f ₇ ]

Wherein, 0≤f _i <2 ⁵² and 0≤i<8, i is an integer, and the target operation base is 2 ⁵² .

6. The parallel point addition method of elliptic curve based on AVX512IFMA according to claim 5, characterized in that the multiple coordinate value vectors corresponding to each coordinate value of each point data constitute a vector set, comprising:

The vector set V is determined by the following formula:

Among them, the multiple coordinate value vectors corresponding to any coordinate of any type of point data are _Fa , _Fb , _Fc , _Fd , _Fe , _Ff , _Fg and _Fh respectively, any column of the vector set V corresponds to a coordinate value vector, and the i-th row of _the vector set V corresponds to a register vector _vi = [ _fia ^, _fib ^,fic ^, ^fid,fie _, ^fif _, ^fig,fih _] _, _0≤i ^< ⁸ , i is an integer.

7. A parallel point addition device for elliptic curve based on AVX512IFMA, characterized by comprising:

A first determination module is used to determine each coordinate of the coordinates of the plurality of pairs of point data participating in the parallel point addition, each pair of point data includes two types of point data: adding point data and added point data;

A second determination module is used to determine a target number field corresponding to the plurality of pairs of point data, wherein the target number field is a finite field of the elliptic curve or a quadratic extension field of the finite field;

A third determination module is used to determine a large number operation rule corresponding to the target number domain;

a fourth determination module, for determining a target point addition formula for the plurality of pairs of point data based on a relationship between a Z coordinate value _Z1 of the added point data and a Z coordinate value _Z2 of the added point data in each pair of point data in the plurality of pairs of point data;

A data arrangement module, used for converting the coordinate values of the plurality of pairs of point data into target data corresponding to the data structure of the AVX512IFMA;

The data processing module is used to process the target data based on the target point addition formula and the large number operation rules to obtain the point addition results of the multiple pairs of point data.

8. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the parallel point addition method for elliptic curves based on AVX512IFMA as described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the parallel point addition method for elliptic curves based on AVX512IFMA as described in any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that when the computer program is executed by a processor, the parallel point addition method of the elliptic curve based on AVX512IFMA as described in any one of claims 1 to 6 is implemented.