CN109284082A - A kind of point processing method and device that ECC and SM2 is general - Google Patents
A kind of point processing method and device that ECC and SM2 is general Download PDFInfo
- Publication number
- CN109284082A CN109284082A CN201710601306.6A CN201710601306A CN109284082A CN 109284082 A CN109284082 A CN 109284082A CN 201710601306 A CN201710601306 A CN 201710601306A CN 109284082 A CN109284082 A CN 109284082A
- Authority
- CN
- China
- Prior art keywords
- point
- under
- coordinate system
- algorithm
- modified jacobian
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000003672 processing method Methods 0.000 title claims abstract description 22
- 238000012545 processing Methods 0.000 claims abstract description 98
- PXFBZOLANLWPMH-UHFFFAOYSA-N 16-Epiaffinine Natural products C1C(C2=CC=CC=C2N2)=C2C(=O)CC2C(=CC)CN(C)C1C2CO PXFBZOLANLWPMH-UHFFFAOYSA-N 0.000 claims description 6
- 238000013461 design Methods 0.000 abstract description 7
- 238000000034 method Methods 0.000 description 22
- 230000008569 process Effects 0.000 description 11
- 230000006870 function Effects 0.000 description 7
- 238000012790 confirmation Methods 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 3
- 230000009466 transformation Effects 0.000 description 3
- 230000008859 change Effects 0.000 description 2
- 235000013350 formula milk Nutrition 0.000 description 2
- 230000000694 effects Effects 0.000 description 1
- 230000005611 electricity Effects 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 238000001629 sign test Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 238000007711 solidification Methods 0.000 description 1
- 230000008023 solidification Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
- G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
- G06F7/483—Computations with numbers represented by a non-linear combination of denominational numbers, e.g. rational numbers, logarithmic number system or floating-point numbers
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
- G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
- G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
- G06F7/57—Arithmetic logic units [ALU], i.e. arrangements or devices for performing two or more of the operations covered by groups G06F7/483 – G06F7/556 or for performing logical operations
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computational Mathematics (AREA)
- Computing Systems (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Nonlinear Science (AREA)
- Complex Calculations (AREA)
Abstract
A kind of point processing method and device is disclosed herein, comprising: determines the algorithm types that this point processing uses；When using ECC algorithm, the point add operation circuit or point doubling circuit called directly under modified Jacobian Modified Jacobian projective coordinate system completes this point processing；When using SM2 algorithm, the point doubling circuit under point add operation circuit or Modified Jacobian projective coordinate system under affine-Modified Jacobian mixed proportion is called to complete this point processing.The application realizes the point processing method for being common to ECC algorithm and SM2 algorithm, and the operational performance of SM2 and ECC not only greatly improved.Meanwhile circuit area can be also reduced, operation power consumption is reduced, the design requirement of SoC can be preferably adapted to.
Description
Technical field
The present invention relates to system on chip (SOC, system-on-a-Chip) chip field more particularly to a kind of ECC and SM2
General point processing method and device.
Background technique
Elliptic curve cryptosystems (ECC) are to you can well imagine to come out in 1985 fraction of the year by Neal Koblitz and Victor Miller
A kind of public-key cryptosystem, intractability of the safety based on elliptic curves discrete logarithm problem.It is up to the present every
Key provides a kind of highest public-key cryptosystem of encryption intensity, such as 160 ECC can reach 1024 RSA peaces
It is complete horizontal.The security performance of ECC is higher, calculation amount is smaller, processing speed faster, in the case where security performance is roughly the same,
The key of ECC has more brilliant security performance compared to the key of RSA and block cipher, and the requirement to bandwidth is lower.Therefore, from
Just it is always research and the application foci of public key cryptography after ECC proposition, there is more extensive application prospect.
SM2 ellipse curve public key cipher algorithm is that a kind of fixed ECC of curve of national Password Management office publication in 2010 is calculated
Method, it suitable for commercial cipher application digital signature and certification, key exchange and encryption and decryption processes, with improve peace
The credibility and interoperability of full product.National Password Management office requires oval bent using SM2 in China's commercial cipher system
Line cryptographic algorithm replaces RSA Algorithm.
According to the feature of elliptic curve cryptography, it is substantially at present for the design method of ECC and SM2 using soft or hard
Part is implemented in combination with.Wherein, scalar multiplication (more times of point algorithms) complexity highest, when operation time accounts for entire ECC or SM2 process
Between 80% or so.Scalar multiplication is made of point processing (point adduction times point), and arithmetic of rational point and a times point algorithm are added by modular multiplication, mould
Subtract these basic operations with mould to constitute.
In summary, if there is a kind of high-performance point processing can be compatible with ECC and SM2, it will greatly improve ECC's and SM2
Calculated performance.
Summary of the invention
In order to solve the above-mentioned technical problem, the embodiment of the invention provides a kind of ECC and SM2 general point processing method and
Device.
This application provides following schemes:
A kind of point processing method, comprising:
Determine the algorithm types that this point processing uses；
When using ECC algorithm, modified Jacobian Modified Jacobian projective coordinates are called directly
Point add operation circuit or point doubling circuit under system complete this point processing；
When using SM2 algorithm, the point add operation circuit under affine-Modified Jacobian mixed proportion is called
Or the point doubling circuit under Modified Jacobian projective coordinate system completes this point processing.
Wherein, when using SM2 algorithm, the point add operation under affine-Modified Jacobian mixed proportion is called
Point doubling circuit under circuit or Modified Jacobian projective coordinate system completes this point processing, comprising: judges this
Whether point processing is fixed point scalar multiplication；When this point processing is fixed point scalar multiplication, call it is affine-
Under point add operation circuit or Modified Jacobian projective coordinate system under Modified Jacobian mixed proportion
Point doubling circuit completes this point processing；When this point processing is not fixed point scalar multiplication, Modified is called
Point add operation circuit or point doubling circuit under Jacobian projective coordinate system complete this point processing.
Wherein, when the point representation under Jacobian projective coordinate system is (X, Y, Z), the Modified
Point representation under Jacobian projective coordinate system is (X, Y, Z, aZ4), the Modified Jacobian projective coordinate system
It is to affine coordinate system transformation for mula
Wherein, if The arithmetic of rational point form of expression under the Modified Jacobian projective coordinate system are as follows:
X3=R2-TW2, Y3=R (U1W2-X3)-S1W3, Z3=Z1Z2W,Wherein,W=U1-U2, R=S1-S2, T=U1+U2, M=
S1+S2, V=TW2-2X3；Wherein, P and Q indicates two different points on elliptic curve.
Wherein, ifQ=(X2,Y2),When,
The arithmetic of rational point form of expression under the affine-Modified Jacobian mixed proportion are as follows: X3=R2-TW2,
Y3=R (X1W2-X3)-Y1W3, Z3=Z1WWherein,W=X1-
U2, R=Y1-S2, T=U1+U2；
Wherein, P and Q indicates two different points on elliptic curve.
Wherein, if
The point algorithm form of expression again under the Modified Jacobian projective coordinate system are as follows: X3=M2- 2S, Y3=M
(S-X3)-T, Z3=2Y1Z2,Wherein,
Wherein, Q indicates a point on elliptic curve.
A kind of point processing device, includes at least: point processing unit；
The point processing unit includes: point processing controller, modified Jacobian Modified Jacobian
Point add operation circuit under projective coordinate system, the point add operation circuit under affine-Modified Jacobian mixed proportion,
And the point doubling circuit under Modified Jacobian projective coordinate system；
Wherein, the point processing controller, the algorithm types used for confirming this point processing；Using ECC algorithm
When, call directly point add operation circuit under modified Jacobian Modified Jacobian projective coordinate system or
Point doubling circuit completes this point processing；When using SM2 algorithm, affine-Modified Jacobian hybrid coordinate is called
The point doubling circuit under point add operation circuit or Modified Jacobian projective coordinate system under system completes this point fortune
It calculates.
Wherein, the point processing controller is specifically used for when using SM2 algorithm, judges whether this point processing is solid
Pinpoint scalar multiplication；When this point processing is fixed point scalar multiplication, call affine-Modified Jacobian mixed
The point doubling circuit closed under point add operation circuit or Modified Jacobian projective coordinate system under coordinate system completes this
Point processing；When this point processing is not fixed point scalar multiplication, call under Modified Jacobian projective coordinate system
Point add operation circuit or point doubling circuit complete this point processing.
The application can at least obtain one of following effect:
On the one hand, in one preferred embodiment of the application, ECC algorithm and SM2 algorithm be can be used simultaneously, confirmation need using
It, can be by calling directly point add operation circuit or point doubling under Modified Jacobian projective coordinate system when ECC algorithm
Circuit completes a point processing；When confirmation is needed using ECC algorithm, affine-Modified Jacobian can be called to mix
Point add operation circuit under coordinate system completes this point processing or calls times point under Modified Jacobian projective coordinate system
Computing circuit completes this point processing.In this way, realizing the point processing method for being common to ECC algorithm and SM2 algorithm, not only substantially
Improve the operational performance of SM2 and ECC.Meanwhile circuit area can be also reduced, operation power consumption is reduced, SoC can be preferably adapted to
Design requirement.
On the other hand, in another preferred embodiment of the application, ECC and SM2 algorithm can be supported using same covering device, i.e., it is logical
It crosses the point add operation under Modified Jacobian projective coordinate system and affine-Modified Jacobian mixed proportion
Circuit is multiplexed, and the operational performance of SM2 and ECC not only greatly improved.Meanwhile circuit area is also effectively reduced, it reduces
Operation power consumption can preferably adapt to the design requirement of SoC.
In another aspect, counting this application provides the arithmetic of rational point under Modified Jacobian projective coordinate system and again
Method makes times multiplication number of point algorithm not depend on the value of elliptic curve parameter a, eight multiplyings is fixed as, to a ≠ -3mod
The scalar multiplication operational performance of the curve of P, on-fixed point improves about 10%.
Another aspect, this application provides the arithmetic of rational point under affine-Modified Jacobian mixed proportion, make
The scalar multiplication operational performance of fixed point improves about 10%.
Another aspect, the application is by being multiplexed affine-Modified Jacobian mixed proportion and Modified
Point add operation circuit under Jacobian projective coordinate system, further reduces circuit area, reduces operation power consumption.
In another aspect, ECC algorithm and SM2 algorithm use same set of point processing device in the application, reduce circuit face
Product, reduces operation power consumption.
Other features and advantages of the present invention will be illustrated in the following description, also, partly becomes from specification
It obtains it is clear that understand through the implementation of the invention.The objectives and other advantages of the invention can be by specification, right
Specifically noted structure is achieved and obtained in claim and attached drawing.
Detailed description of the invention
Attached drawing is used to provide to further understand technical solution of the present invention, and constitutes part of specification, with this
The embodiment of application technical solution for explaining the present invention together, does not constitute the limitation to technical solution of the present invention.
Fig. 1 is a kind of flow diagram of point processing method of the embodiment of the present application；
Fig. 2 is the exemplary implementation flow chart of some operation methods of embodiment.
Fig. 3 is the structural schematic diagram of two midpoint arithmetic unit of embodiment；
Fig. 4 is the structural schematic diagram of exemplary dots arithmetic facility in embodiment two.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with attached drawing to the present invention
Embodiment be described in detail.It should be noted that in the absence of conflict, in the embodiment and embodiment in the application
Feature can mutual any combination.
Step shown in the flowchart of the accompanying drawings can be in a computer system such as a set of computer executable instructions
It executes.Also, although logical order is shown in flow charts, and it in some cases, can be to be different from herein suitable
Sequence executes shown or described step.
The application provide it is a kind of be common to ECC and SM2, high performance, low-power consumption point processing technical solution, with big
The calculated performance of width raising ECC and SM2.The application can be applied to smart card, mobile payment etc. and want to safety, performance and power consumption
Ask relatively high field.
Since the characteristic of elliptic curve determines that the design method of ECC and SM2 are substantially using software and hardware combining
It realizes.In entire algorithm flow, scalar multiplication computational complexity highest, operation time accounts for entire ECC or SM2 flow time
80% or so.Therefore, it can be said that scalar multiplication operational performance determines the performance of ECC and SM2, it is the key that elliptic curve operations.
Scalar multiplication is made of point processing, in consideration of it, the application provides a kind of point processing device that ECC and SM2 is general to improve mark
Multiplication performance is measured, to promote the performance of ECC and SM2.
Technical scheme is described in detail below.It should be noted that following examples can any combination.
Embodiment one
A kind of point processing method, as shown in Figure 1, may include:
Step 101, the algorithm types that this point processing uses are determined, execute step when confirmation is needed using ECC algorithm
102, step 103 is executed when confirmation is needed using SM2 algorithm；
Step 102, when using ECC algorithm, modified Jacobian (Modified is called directly
Jacobian) the point add operation circuit under projective coordinate system or point doubling circuit complete this point processing；
Step 103, when using SM2 algorithm, the point under affine-Modified Jacobian mixed proportion is called to add
Point doubling circuit under computing circuit or Modified Jacobian projective coordinate system completes this point processing.
In the present embodiment, is realized and be common to by same set of point processing device (passing through same group of computing circuit of multiplexing)
The point processing method of ECC algorithm and SM2 algorithm, not only greatly improved the operational performance of SM2 and ECC.Meanwhile it can also reduce electricity
Road surface product, reduces operation power consumption, can preferably adapt to the design requirement of SoC.
In the present embodiment, determine the mode of algorithm types that local point processing uses can there are many.For example, can basis
This algorithm types that need to automatically determine of current application are ECC or SM2, which is that this point processing uses
Algorithm types.For example, when the point processing method of the present embodiment being applied to smart card, the affiliated terminal needs of the smart card make
Which kind of algorithm just used with the corresponding point processing method of which kind of algorithm.If terminal uses SM2 algorithm, point processing
Method then uses SM2 algorithm, if terminal uses ECC algorithm, point processing method just uses ECC algorithm.
The present embodiment can also include: by Jacobian projective coordinates before using ECC algorithm or SM2 algorithm
The lower point adduction times point algorithm of system optimizes, and obtains arithmetic of rational point under Modified Jacobian projective coordinate system and again
Point algorithm.In a kind of implementation, the point adduction times point algorithm under Jacobian projective coordinate system is optimized, is obtained
The mode of arithmetic of rational point under Modified Jacobian projective coordinate system and times point algorithm can be with are as follows: in Jacobian projection
Point representation when point representation under coordinate system is (X, Y, Z), under the Modified Jacobian projective coordinate system
For (X, Y, Z, aZ4), the Modified Jacobian projective coordinate system is to affine coordinate system transformation for mulaIn this way, times multiplication number put in algorithm under Modified Jacobian projective coordinate system is eight times
(4M+4S) does not depend on the value of elliptic curve parameter a, is more suitable for the unfixed algorithm of this elliptic curve of ECC, each times of point
Algorithm can save multiplying twice.In addition, the arithmetic of rational point under Modified Jacobian projective coordinate system compares Jacobi
Mostly multiplication operates arithmetic of rational point under determinant (Jacobian) projective coordinate system three times.
Such as the point representation under Jacobian projective coordinate system be (X, Y, Z) when, Modified Jacobian projection
Point representation under coordinate system can be (X, Y, Z, aZ4), Modified Jacobian projective coordinate system to affine coordinate system
Transformation for mula can beIt is excellent by being carried out to the point adduction times point algorithm under Jacobian projective coordinate system
Change point adduction times point algorithm and the affine-Modified for improving and obtaining under Modified Jacobian projective coordinate system
Arithmetic of rational point under Jacobian mixed proportion.
If P, Q is two points on elliptic curve, the respectively expression under Modified Jacobian projective coordinate system
Are as follows:The two points are added and indicate are as follows:The arithmetic of rational point form of expression under Modified Jacobian projective coordinate system are as follows: X3
=R2-TW2, Y3=R (U1W2-X3)-S1W3, Z3=Z1Z2W,Wherein,W=U1-U2, R=S1-S2, T=U1+U2, M=
S1+S2, V=TW2-2X3。
If P, Q is two points on elliptic curve, respectively in Modified Jacobian projective coordinate system and affine coordinate
Expression under system are as follows:Q=(X2,Y2).The two points are added and indicate are as follows:The arithmetic of rational point form of expression under affine-Modified Jacobian mixed proportion are as follows:
X3=R2-TW2, Y3=R (X1W2-X3)-Y1W3, Z3=Z1WWherein,W=
X1-U2, R=Y1-S2, T=U1+U2。
If Q is the point on elliptic curve, the expression under Modified Jacobian projective coordinate system are as follows:Two identical points, which are added (times point) result, to be indicated are as follows:
The point algorithm form of expression again under Modified Jacobian projective coordinate system are as follows: X3=M2- 2S, Y3=M (S-X3)-T, Z3=
2Y1Z2,Wherein,
Under above-mentioned Modified Jacobian projective coordinate system and affine-Modified Jacobian mixed proportion
Arithmetic of rational point feature is similar, it is therefore possible to use same covering device is realized, saves circuit area.
It as shown in table 1 below, is the operational performance index of arithmetic of rational point and times point algorithm under different coordinates.Wherein, I table
Show that an inversion operation, M indicate multiplication operation, S indicates a square operation.As can be seen from Table 1, scalar multiplication makes
It is better than using affine coordinate system and canonical projection with the performance of arithmetic of rational point and times point algorithm under Jacobian projective coordinate system
Arithmetic of rational point and a times point algorithm under coordinate, wherein since the number dependence of the multiplication in times point algorithm of elliptic curve is oval
Curve y2≡x3The value of the parameter a of+ax+b (modp), if a=-3mod P, a times point algorithm only has eight multiplication operation (4M+
4S), otherwise point algorithm needs ten multiplication operations (4M+6S) again.As can be seen from Table 1, the present embodiment uses Modified
Double-adding method under Jacobian projective coordinate system is fixed as eight multiplication operations, Modified Jacobian projective coordinate system
Jacobian is better than with the performance of arithmetic of rational point and double-adding method under affine-Modified Jacobian mixed proportion
Arithmetic of rational point and a times point algorithm under projective coordinate system.
Table 1
In the present embodiment, point add operation circuit based on affine-Modified Jacobian projective coordinate system and
Point add operation circuit under Modified Jacobian projective coordinate system realizes the above method.It calls according to different conditions not
With point add operation circuit, improve scalar multiplication performance to reduce in scalar multiplication multiplication number, at the same to computing circuit into
Row optimization, by the point add operation circuit and Modified Jacobian under affine-Modified Jacobian projective coordinate system
Point add operation circuit multiplexer under projective coordinate system reduces circuit area, reduces operation power consumption in two kinds of algorithms.This
Outside, the arithmetic of rational point of the point add operation circuit of affine-Modified Jacobian projective coordinate system, can make the mark of fixed point
Measure multiplication performance boost about 10%.
It is fixed curve based on SM2 algorithm curve in the present embodiment, ECC algorithm curve is the characteristic of on-fixed curve.It is right
In fixed point scalar multiplication and on-fixed point scalar multiplication using the point adduction times point algorithm under different coordinate systems.In SM2 algorithm
Including fixed point scalar multiplication and on-fixed point scalar multiplication, ECC algorithm curve is not fixed, and all scalar multiplications are all on-fixed
Point scalar multiplication.Specifically, SM2 algorithm curve is fixed curve, it is based in the signature of SM2, sign test, encryption and decryption process
The scalar multiplication (kG) of basic point G (x, y) and the scalar multiplication of non-basic point.Basic point is fixed in SM2 algorithm, for basic point
Scalar multiplication is known as fixed point scalar multiplication, and the scalar multiplication midpoint of non-basic point is unfixed, referred to as on-fixed point scalar multiplication.
The present embodiment realizes the above method based on the point doubling circuit under Modified Jacobian projective coordinate system,
The multiplication number of this times of point algorithm does not depend on the value of elliptic curve parameter a, only eight multiplyings, and it is this ellipse to be suitable for ECC
The unfixed algorithm of circular curve, a times point algorithm can save multiplying twice every time, to a ≠ -3mod P curve, on-fixed
The scalar multiplication operational performance of point improves about 10%.
In a kind of implementation, when using SM2 algorithm, call under affine-Modified Jacobian mixed proportion
Point add operation circuit or Modified Jacobian projective coordinate system under point doubling circuit complete this point processing, can
To include: to judge whether this point processing is fixed point scalar multiplication；When this point processing is fixed point scalar multiplication,
Point add operation circuit or Modified Jacobian projection under affine-Modified Jacobian mixed proportion is called to sit
Point doubling circuit under mark system completes this point processing；When this point processing is not fixed point scalar multiplication, call
Point add operation circuit or point doubling circuit under Modified Jacobian projective coordinate system complete this point processing.
As shown in table 2 below, a kind of example implementations of SM2 algorithm and ECC algorithm are common to for the present embodiment.
Table 2
As shown in table 2, in the above-mentioned implementation of the present embodiment, fixed point scalar multiplication is directed in SM2 algorithm,
Using under the arithmetic of rational point and Modified Jacobian coordinate system under affine-Modified Jacobian mixed proportion
Point algorithm again.It is directed to on-fixed point scalar multiplication in SM2 algorithm, uses the point under Modified Jacobian coordinate system
Point algorithm again under computation system and Modified Jacobian coordinate system.In common SM2 and ECC scalar multiplication algorithm (such as
Radix-2 algorithm and sliding window algorithm), it is all to realize scalar multiplication by continuously calling point add operation and point doubling
's.In the present embodiment, it is described in detail by taking sliding window algorithm as an example.Since SM2 algorithm basic point is fixed and invariable, lead to
It crosses if software realization sliding window algorithm and point of invocation arithmetic unit calculate scalar multiplication, it is contemplated that it calculates and does not have to calculate every time, it can be with
Good solidification is calculated in advance in memory, reduces pre-calculation time.Also, the arithmetic of rational point performance under mixed proportion also superior to
Arithmetic of rational point under Modified Jacobian coordinate system.The present embodiment compares point for the scalar multiplication interpretative version of fixed point
Computation system and again point algorithm all use about 10% (window 5) of the scheme performance boost of Jacobian coordinate system.
As shown in table 2, in the above-mentioned implementation of the present embodiment, the scalar multiplication of on-fixed point is directed in ECC algorithm
Operation uses the arithmetic of rational point and a times point algorithm under Modified Jacobian coordinate system.Using sliding window algorithm, in window
Arithmetic of rational point number is 2 in the case that mouth w is 5w-1- 1+n/ (w+1), times putting an algorithm number is that 255 (n is to multiply in scalar multiplication
Several binary lengths, n=256).To a ≠ -3mod P curve, the present embodiment is directed to the scalar multiplication side of on-fixed point
Case compares about 10% (window 5) of the scheme performance boost for using Jacobian coordinate system.
In the above-mentioned implementation of the present embodiment, scalar multiplication, this algorithm can be realized using sliding window algorithm
Each circulation requires to calculate primary times of point algorithm in calculating process, and in the case where window is 5, arithmetic of rational point number is about
The 1/5 of algorithm is put again.It follows that the above-mentioned implementation of the present embodiment can be obvious, reduce multiplication number in times point algorithm,
Reduce the number of multiplication in scalar multiplication, and then effectively improves scalar multiplication operational performance.
As shown in Fig. 2, being the another example implementations of the present embodiment point processing method, in this implementation, point
Calculating process may include steps of:
Step 201, judgement is currently needed using which type of algorithm (ECC or SM2 algorithm), if necessary to use SM2
Algorithm continues step 202, if you do not need to then continuing step 210 using ECC algorithm；
Step 202, SM2 algorithm is executed；
Step 203, judge whether this point processing is fixed point scalar multiplication, if it is continue step 204, otherwise
Continue step 207；
Step 204, judge whether to select point add operation, be to continue step 205, otherwise continue step 206；
Step 205, the point add operation circuit under affine-Modified Jacobian mixed proportion is called to complete this
Point processing, current process terminate.
Step 206, the extraordinarily computing circuit under Modified Jacobian projective coordinate system is called to complete this place fortune
It calculates, current process terminates.
Step 207, judge whether to select point add operation, be to continue step 208, otherwise continue step 209；
Step 208, the point add operation circuit under Modified Jacobian projective coordinate system is called to complete this point fortune
It calculates, current process terminates.
Step 209, the extraordinarily computing circuit under Modified Jacobian projective coordinate system is called to complete this place fortune
It calculates, current process terminates.
Step 210, ECC algorithm is executed；
Step 211, judge whether to select point add operation, be to continue step 212, otherwise continue step 213；
Step 212, the point add operation circuit under Modified Jacobian projective coordinate system is called to complete this point fortune
It calculates, current process terminates.
Step 213, the extraordinarily computing circuit under Modified Jacobian projective coordinate system is called to complete this place fortune
It calculates, current process terminates.
It, can be according to application it needs to be determined that this algorithm types (ECC or SM2 algorithm), then in above-mentioned implementation
Which kind of selected to carry out according to scalar multiplication algorithm a little to add/point doubling, and according to algorithm types selection using under coordinate system
Arithmetic of rational point.
Embodiment two
A kind of point processing device, as shown in figure 3, including at least: point processing unit 31；
The point processing unit 31 may include: point processing controller 311, Modified Jacobian projective coordinate system
Under point add operation circuit 311, the point add operation circuit 312 under affine-Modified Jacobian mixed proportion and
Point doubling circuit 313 under Modified Jacobian projective coordinate system；
Wherein, the point processing controller 311 can be used for confirming the algorithm types that this point processing uses；Using ECC
When algorithm, the point add operation circuit 311 or point doubling circuit under Modified Jacobian projective coordinate system are called directly
313 complete this point processing；When using SM2 algorithm, the point under affine-Modified Jacobian mixed proportion is called
The point doubling circuit 313 under computing circuit 312 or Modified Jacobian projective coordinate system is added to complete this point processing.
The present embodiment realizes ECC algorithm and SM2 algorithm using same set of point processing device, by by Modified
Point add operation circuit under Jacobian projective coordinate system and affine-Modified Jacobian mixed proportion is multiplexed,
The operational performance of SM2 and ECC not only greatly improved.Meanwhile circuit area is also effectively reduced, and operation power consumption is reduced, it can
Preferably adapt to the design requirement of SoC.In addition, affine-Modified Jacobian the mixed proportion of the present embodiment also reusable
Point add operation circuit under Modified Jacobian projective coordinate system, reduces circuit area, reduces operation power consumption.
In a kind of implementation, the point processing controller 311 is particularly used in when using SM2 algorithm, judges this
Whether point processing is fixed point scalar multiplication；When this point processing is fixed point scalar multiplication, call it is affine-
Under point add operation circuit 312 or Modified Jacobian projective coordinate system under Modified Jacobian mixed proportion
Point doubling circuit 313 complete this point processing；When this point processing is not fixed point scalar multiplication, call
Point add operation circuit 311 or point doubling circuit 313 under Modified Jacobian projective coordinate system complete this point fortune
It calculates.
In the present embodiment, point processing device includes affine-Modified Jacobian projective coordinate system and Modified
Point add operation circuit under Jacobian projective coordinate system.In this way, point processing device can call according to different conditions it is different
Point add operation circuit improves scalar multiplication performance to reduce in scalar multiplication multiplication number, while carrying out to computing circuit excellent
Change, the point under affine-Modified Jacobian projective coordinate system and Modified Jacobian projective coordinate system is added into fortune
Circuit multiplexer is calculated, reduces circuit area, reduces operation power consumption.
In the present embodiment, point processing device includes the point doubling circuit under Modified Jacobian projective coordinate system,
The multiplication number of the algorithm of point again of the point doubling circuit does not depend on the value of elliptic curve parameter a, is fixed as eight multiplyings,
To a ≠ -3mod P curve, the scalar multiplication operational performance of on-fixed point improves about 10%.
The concrete operation details of the present embodiment is repeated no more referring to embodiment one.
As shown in figure 4, being a kind of exemplary realization structure of the present embodiment point processing equipment.As shown in figure 4, the point processing
Equipment mainly may include: AHB interface, arithmetic and control unit, point processing device, modulo device, RAM data selector (MUX).
Wherein, point processing device may include: point processing controller, point add operation circuit and point doubling circuit；Modulo device can
To include: that mould adds computing circuit, mould to subtract computing circuit, modular multiplication (Montgomery) computing circuit.Wherein, Mod_int indicates mould
Operation interrupt signal, Point_int indicate point processing interrupt signal.
AHB interface module is mainly used for realizing that AHB agreement is hopped storage read-write protocol；Arithmetic and control unit is used for control system
Or hardware operation RAM, point processing and the selection of modular arithmetic；Point processing device major function is to realize affine-Modified
Point under Jacobian and Modified Jacobian projective coordinate system sums it up point doubling circuit, wherein point add operation circuit
Major function is the point add operation realized under affine-Modified Jacobian and Modified Jacobian projective coordinate system
Circuit, point doubling circuit major function are the point doubling circuits realized under Modified Jacobian projective coordinate system；Mould
Arithmetic unit major function is to realize that big data mould adds, mould subtracts and scale multiplying circuit；Basis fortune in point adduction point doubling
Calculation is added by mould, mould subtracts, modular multiplication is constituted, therefore modulo device realizes a basic operations for adduction point doubling.RAM
MUX can be used for the read-write selection of RAM being output to CPU or modulo device.
Those of ordinary skill in the art will appreciate that all or part of the steps in the above method can be instructed by program
Related hardware (such as processor) is completed, and described program can store in computer readable storage medium, as read-only memory,
Disk or CD etc..Optionally, one or more integrated circuits also can be used in all or part of the steps of above-described embodiment
It realizes.Correspondingly, each module/unit in above-described embodiment can take the form of hardware realization, such as pass through integrated circuit
It realizes its corresponding function, can also be realized in the form of software function module, such as be stored in and deposited by processor execution
Program/instruction in reservoir realizes its corresponding function.The application is not limited to the knot of the hardware and software of any particular form
It closes.
The advantages of basic principles and main features and the application of the application have been shown and described above.The application is not by upper
The limitation for stating embodiment, the above embodiments and description only describe the principles of the application, are not departing from the application
Under the premise of spirit and scope, the application be will also have various changes and improvements, these changes and improvements both fall within claimed
Within the scope of the application.
Claims (8)
1. a kind of point processing method, comprising:
Determine the algorithm types that this point processing uses；
When using ECC algorithm, call directly under modified Jacobian Modified Jacobian projective coordinate system
Point add operation circuit or point doubling circuit complete this point processing；
When using SM2 algorithm, call point add operation circuit under affine-Modified Jacobian mixed proportion or
Point doubling circuit under Modified Jacobian projective coordinate system completes this point processing.
2. point processing method according to claim 1, which is characterized in that when using SM2 algorithm, call it is affine-
Under point add operation circuit or Modified Jacobian projective coordinate system under Modified Jacobian mixed proportion
Point doubling circuit completes this point processing, comprising:
Judge whether this point processing is fixed point scalar multiplication；
When this point processing is fixed point scalar multiplication, call under affine-Modified Jacobian mixed proportion
Point doubling circuit under point add operation circuit or Modified Jacobian projective coordinate system completes this point processing；
When this point processing is not fixed point scalar multiplication, the point under Modified Jacobian projective coordinate system is called
Computing circuit or point doubling circuit is added to complete this point processing.
3. point processing method according to claim 1, which is characterized in that
When point representation under Jacobian projective coordinate system is (X, Y, Z), the Modified Jacobian projection is sat
Point representation under mark system is (X, Y, Z, aZ4), the Modified Jacobian projective coordinate system to affine coordinate system becomes
Changing formula is
4. point processing method according to any one of claims 1 to 3, which is characterized in that
If
The arithmetic of rational point form of expression under the Modified Jacobian projective coordinate system are as follows:
X3=R2-TW2, Y3=R (U1W2-X3)-S1W3, Z3=Z1Z2W,
Wherein,W=U1-U2, R=S1-S2, T=
U1+U2, M=S1+S2, V=TW2-2X3；
Wherein, P and Q indicates two different points on elliptic curve.
5. point processing method according to any one of claims 1 to 3, which is characterized in that
IfQ=(X2,Y2),When,
The arithmetic of rational point form of expression under the affine-Modified Jacobian mixed proportion are as follows: X3=R2-TW2, Y3=R
(X1W2-X3)-Y1W3, Z3=Z1WWherein,W=X1-U2, R=
Y1-S2, T=U1+U2；
Wherein, P and Q indicates two different points on elliptic curve.
6. point processing method according to any one of claims 1 to 3, which is characterized in that
If
The point algorithm form of expression again under the Modified Jacobian projective coordinate system are as follows: X3=M2- 2S, Y3=M (S-
X3)-T, Z3=2Y1Z2,Wherein,
Wherein, Q indicates a point on elliptic curve.
7. a kind of point processing device, which is characterized in that include at least: point processing unit；
The point processing unit includes: point processing controller, modified Jacobian Modified Jacobian projection
Point add operation circuit under coordinate system, the point add operation circuit under affine-Modified Jacobian mixed proportion and
Point doubling circuit under Modified Jacobian projective coordinate system；
Wherein, the point processing controller, the algorithm types used for confirming this point processing；When using ECC algorithm, directly
It connects the point add operation circuit under the modified Jacobian Modified Jacobian projective coordinate system of calling or point is transported again
It calculates circuit and completes this point processing；When using SM2 algorithm, call under affine-Modified Jacobian mixed proportion
Point doubling circuit under point add operation circuit or Modified Jacobian projective coordinate system completes this point processing.
8. point processing device according to claim 7, which is characterized in that
The point processing controller is specifically used for judging whether this point processing is fixed point scalar multiplication when using SM2 algorithm
Operation；When this point processing is fixed point scalar multiplication, call under affine-Modified Jacobian mixed proportion
Point add operation circuit or Modified Jacobian projective coordinate system under point doubling circuit complete this point processing；?
When this point processing is not fixed point scalar multiplication, the point add operation under Modified Jacobian projective coordinate system is called
Circuit or point doubling circuit complete this point processing.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710601306.6A CN109284082A (en) | 2017-07-21 | 2017-07-21 | A kind of point processing method and device that ECC and SM2 is general |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201710601306.6A CN109284082A (en) | 2017-07-21 | 2017-07-21 | A kind of point processing method and device that ECC and SM2 is general |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN109284082A true CN109284082A (en) | 2019-01-29 |
Family
ID=65185340
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201710601306.6A Pending CN109284082A (en) | 2017-07-21 | 2017-07-21 | A kind of point processing method and device that ECC and SM2 is general |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109284082A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110048844A (en) * | 2019-03-29 | 2019-07-23 | 网御安全技术（深圳）有限公司 | Realize more times of point calculating methods, devices of SM2 algorithm |
| CN114205085A (en) * | 2021-12-03 | 2022-03-18 | 东北大学 | Optimization processing method of SM2 and transformation method of super book fabric platform |
| CN114594925A (en) * | 2022-03-17 | 2022-06-07 | 安徽师范大学 | Efficient modular multiplication circuit suitable for SM2 encryption operation and operation method thereof |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102609239A (en) * | 2011-09-01 | 2012-07-25 | 北京华大信安科技有限公司 | ECC (elliptic curve cryptography) coprocessor |
| CN103631660A (en) * | 2013-09-23 | 2014-03-12 | 中国科学院数据与通信保护研究教育中心 | Method and device for distributing storage resources in GPU in big integer calculating process |
| CN104503730A (en) * | 2014-10-24 | 2015-04-08 | 山东华芯半导体有限公司 | Instruction-based large-number point addition and point multiplication operation circuit and realization method |
| WO2016091166A1 (en) * | 2014-12-10 | 2016-06-16 | 山东华芯半导体有限公司 | Arithmetic circuit and data transfer method |
| US20170187530A1 (en) * | 2015-12-23 | 2017-06-29 | Intel Corporation | Elliptic curve hardware integrated circuit |
-
2017
- 2017-07-21 CN CN201710601306.6A patent/CN109284082A/en active Pending
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102609239A (en) * | 2011-09-01 | 2012-07-25 | 北京华大信安科技有限公司 | ECC (elliptic curve cryptography) coprocessor |
| CN103631660A (en) * | 2013-09-23 | 2014-03-12 | 中国科学院数据与通信保护研究教育中心 | Method and device for distributing storage resources in GPU in big integer calculating process |
| CN104503730A (en) * | 2014-10-24 | 2015-04-08 | 山东华芯半导体有限公司 | Instruction-based large-number point addition and point multiplication operation circuit and realization method |
| WO2016091166A1 (en) * | 2014-12-10 | 2016-06-16 | 山东华芯半导体有限公司 | Arithmetic circuit and data transfer method |
| US20170187530A1 (en) * | 2015-12-23 | 2017-06-29 | Intel Corporation | Elliptic curve hardware integrated circuit |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110048844A (en) * | 2019-03-29 | 2019-07-23 | 网御安全技术（深圳）有限公司 | Realize more times of point calculating methods, devices of SM2 algorithm |
| CN110048844B (en) * | 2019-03-29 | 2020-09-11 | 网御安全技术（深圳）有限公司 | Multi-point calculation method and device for realizing SM2 algorithm |
| CN114205085A (en) * | 2021-12-03 | 2022-03-18 | 东北大学 | Optimization processing method of SM2 and transformation method of super book fabric platform |
| CN114594925A (en) * | 2022-03-17 | 2022-06-07 | 安徽师范大学 | Efficient modular multiplication circuit suitable for SM2 encryption operation and operation method thereof |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| JP4067818B2 (en) | Elliptic curve cryptography apparatus, elliptic curve cryptography program, and elliptic curve cryptography calculation method | |
| Pelzl et al. | Hyperelliptic curve cryptosystems: Closing the performance gap to elliptic curves | |
| JP4752313B2 (en) | Cryptographic processing operation method, cryptographic processing apparatus, and computer program | |
| EP1306750A2 (en) | Multi-scalar multiplication computation in elliptic curve signature verification | |
| JP4682852B2 (en) | Cryptographic processing apparatus, cryptographic processing method, and computer program | |
| Kocabaş et al. | Implementation of binary Edwards curves for very-constrained devices | |
| CN101834723A (en) | RSA (Rivest-Shamirh-Adleman) algorithm and IP core | |
| CN101371285B (en) | Encryption processing device, encryption processing method | |
| CN101221491B (en) | Point addition system of elliptic curve cipher system | |
| CN100428140C (en) | Implement method of elliptic curve cipher system coprocessor | |
| CN109284082A (en) | A kind of point processing method and device that ECC and SM2 is general | |
| CN101262345A (en) | Time point system for ellipse curve password system | |
| CN105790939A (en) | Prime number field elliptic curve cryptography system of VLSI realization accelerator | |
| CN109145616A (en) | The realization method and system of SM2 encryption, signature and key exchange based on efficient modular multiplication | |
| CN110704109B (en) | Elliptic curve password coprocessor | |
| JP3794266B2 (en) | Elliptic curve scalar multiplication method and apparatus, and storage medium | |
| KR101223498B1 (en) | Method for generating public key in elliptic curve cryptography and system for executing the method | |
| CN103888246A (en) | Low-energy-consumption small-area data processing method and data processing device thereof | |
| CN113467752B (en) | Division operation device, data processing system and method for private calculation | |
| Zeidler et al. | Design of a low-power asynchronous elliptic curve cryptography coprocessor | |
| JP2004125891A (en) | Power remainder computer | |
| KR20080050054A (en) | Method for generating sparse w-naf key, method for processing and method for encrypting thereof | |
| JP4599859B2 (en) | Cryptographic processing operation method, cryptographic processing apparatus, and computer program | |
| Adachi et al. | Combination of mixed coordinates strategy and direct computations for efficient scalar multiplications | |
| KR100974624B1 (en) | Method and Apparatus of elliptic curve cryptography processing in sensor mote and Recording medium using it |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| WD01 | Invention patent application deemed withdrawn after publication | ||
| WD01 | Invention patent application deemed withdrawn after publication |
Application publication date: 20190129 |