CN104579651B - The method and apparatus of elliptic curve cipher point multiplication operation - Google Patents
The method and apparatus of elliptic curve cipher point multiplication operation Download PDFInfo
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Abstract
A kind of elliptic curve cipher point multiplication operation method and apparatus, the elliptic curve cipher point multiplication operation method include that controller selects data flow to be treated, and the data flow is stored into first memory；Point multiplication operation device is successively read the data bit in first memory, when the value of the data bit is 1, carries out the first operation to the data bit, and the result of the first operation is stored to second memory；When the value of the data bit is 0, the second operation is carried out to the data bit, and the result of the second operation is stored to second memory.Using the above method and device, the power consumption for realizing elliptic curve cipher point multiplication operation can be effectively reduced.
Description
Technical field
The present invention relates to field of data encryption, more particularly to a kind of method and apparatus of elliptic curve cipher point multiplication operation.
Background technology
Elliptic Curve Cryptography（Elliptic Curve Cryptography, ECC）It is one based on elliptic curve mathematics
The method of kind of public key cryptography, ECC is the generally acknowledged at present highest cipher system of every bit security, with safe, speed
Soon, key is short, required the advantages that taking up less resources when realizing.ECC is generally basede on two kinds of finite fields：Binary expands domain and prime field,
Currently used is prime field ECC algorithm.The realization of prime field ECC is based on Large-number operation.
The main operational of prime field ECC algorithm is point multiplication operation, and point multiplication operation is by a series of times of point and point plus cycle
It operates and constitutes, it is by a series of big digital-to-analogue adds, mould subtracts, modular multiplication is constituted that point and point, which add, again.In existing point multiplication operation device, by controlling
Device and arithmetic unit processed realize that point multiplication operation, wherein arithmetic unit realize that moulds several greatly adds, mould subtracts and mould using hardware circuit jointly
Multiply.The realization process of point multiplication operation can be described as follows：Controller chooses binary data stream to be treated, takes data flow first
A data bit, controller judge the value of data bit, if the value of data bit is 1, arithmetic unit calls point doubling in RAM
As a result, point add operation is carried out to the result of point doubling, and will be in the storage to preset purpose RAM of the result of point add operation；If
The value of current data position is 0, and point doubling is carried out to data bit, by the result storage of point doubling to preset purpose
In RAM.Judgement and operation, and the operation knot to being stored in purpose RAM are carried out to other data bit successively using the above scheme again
Fruit is scheduled, to realize point multiplication operation.
From in said program it is known that each data bit in binary data stream, controller is needed to data
The value of position is judged, carries out corresponding operation according to different value scheduling computation devices, the realization of entire point multiplication operation has largely
It is big number calculate, need a large amount of RAM handling processes, cause the power consumption of point multiplication operation device larger.
Invention content
The embodiment of the present invention solves the problems, such as during being elliptic curve cipher point multiplication operation, point multiplication operation device power consumption compared with
Big problem.
To solve the above problems, the embodiment of the present invention provides a kind of method of elliptic curve cipher point multiplication operation, including：Control
Device processed selects data flow to be treated, and will be in data flow storage to first memory；Point multiplication operation device is successively read
Data bit in first memory carries out the first operation, and by first when the value of the data bit is 1 to the data bit
The result of operation is stored to second memory；When the value of the data bit is 0, the second operation is carried out to the data bit, and
By the result storage of the second operation to second memory.
Optionally, the first memory is register, and the second memory is RAM or register.
Optionally, the second memory is RAM, and the result storage of the result of first operation and the second operation is arrived
In the RAM in preset RAM block, the number N of the RAM block is equal to the storage space volume divided by elliptic curve of the RAM
The operation length of crypto-operation.
Optionally, described that first operation is carried out to data bit, including：Point doubling is carried out to the data bit, and to institute
The result for stating point doubling carries out point add operation.
Optionally, the point doubling carries out operation, described times of point public affairs using a times point formula for Jacobi projected coordinate system
The operational parameter of formula is stored in advance in the second memory.
Optionally, the point add operation adds formula to be transported using the point under Jacobi projection-affine mixed proportion
It calculates, the point adds the operational parameter of formula to be stored in advance in the second memory.
Optionally, the second operation of the progress includes：Point doubling is carried out to the data bit.
Optionally, the second operation of the progress further includes：The result that point doubling is carried out to the data bit carries out redundancy
Operation, and using the result of the point doubling as the result of second operation.
Optionally, the duration for executing the redundant operation is equal with the duration of point add operation is executed.
Optionally, the redundant operation is point add operation.
To solve the above problems, the embodiment of the present invention additionally provides a kind of device of elliptic curve cipher point multiplication operation, packet
It includes：Control unit, for selecting data flow to be treated, and will be in data flow storage to first memory；Dot product is transported
Calculate unit, the data bit for being successively read in first memory judges the value of current data position, point multiplication operation device according to
Data bit in secondary reading first memory carries out the first operation when the value of the data bit is 1 to the data bit, and
By the result storage of the first operation to second memory；When the value of the data bit is 0, the second fortune is carried out to the data bit
It calculates, and the result of the second operation is stored to second memory.
Optionally, the first memory is register, and the second memory is RAM or register.
Optionally, the second memory is RAM, and preset RAM block is used to store the result of the first operation in the RAM
With the second operation as a result, storage space volumes of the number N of the RAM block equal to the RAM divided by elliptic curve cipher fortune
The operation length of calculation.
Optionally, the point multiplication operation unit includes first arithmetic device, and the first arithmetic device is used to carry out the first operation,
Including：Point doubling is carried out to the data bit, and point add operation is carried out to the result of the point doubling.
Optionally, the point multiplication operation unit includes second arithmetic device, and the second arithmetic device is used to carry out the second operation,
Including：Point doubling is carried out to the data bit.
Optionally, the point multiplication operation unit further includes third arithmetic unit, and the third arithmetic unit is used for the data
The result that position carries out point doubling carries out redundant operation, and using the result of the point doubling as the knot of second operation
Fruit.
Optionally, the third arithmetic unit executes the duration of a redundant operation and the second arithmetic device executes primary point
Add the duration of operation equal.
Optionally, the third arithmetic unit is additionally operable to carry out point add operation to the result of the point doubling.
Compared with prior art, the technical solution of the embodiment of the present invention has the following advantages：
For a pending data flow, controller only needs scheduling primary, and the data flow to be treated is deposited
It stores up in first memory, completes to carry out point multiplication operation to each data bit in first memory using point multiplication operation device,
Each data bit is scheduled without controller, therefore the number that controller participates in scheduling can be reduced, is reduced
The process that RAM is carried, so as to reduce the power consumption of point multiplication operation device.
Further, the ram space in existing processor is split into the RAM to match with the operation length of default ECC
Block, since compared to other cipher systems, the operation length of ECC is smaller, therefore when use ECC operations, existing ram space energy
Enough split into more RAM blocks.In addition to the necessary RAM block for being used for storing operation result, the RAM block having more is used for storing dot product
Ephemeral data when operation stores other data so that the RAM in existing processor is fully used, and improves RAM's
Utilization rate.
Further, when the value of data bit is 0, by increasing the point add operation of a redundancy for not influencing operation result,
So that the operation execution duration when value of the operation execution duration and data bit when the value of data bit is 0 is 1 is completely the same, to
So that the realization of data operation flow is full symmetric, power consumption analysis can be effectively prevented.
Description of the drawings
Fig. 1 is the elliptic curves cryptosystem curve point multiplication operation flow chart in the embodiment of the present invention one；
Fig. 2 is the elliptic curves cryptosystem curve point multiplication operation flow chart in the embodiment of the present invention two；
Fig. 3 is the elliptic curves cryptosystem curve point multiplication operation flow chart in the embodiment of the present invention three；
Fig. 4 is the elliptic curves cryptosystem curve point multiplication operation apparatus structure schematic diagram in the embodiment of the present invention four.
Specific implementation mode
To make the above purposes, features and advantages of the invention more obvious and understandable, below in conjunction with the accompanying drawings to the present invention
Specific embodiment be described in detail.
Embodiment one
Present embodiments provide a kind of elliptic curve cipher point multiplication operation method, referring to Fig.1, below by way of specific steps into
Row is described in detail.
Step S101, controller select data flow to be treated, and will be in data flow storage to first memory.
In specific implementation, data flow to be treated can be binary bit stream, and first memory can be deposit
Device can also be other kinds of memory for storing data flow to be treated.
Step S102, point multiplication operation device can be successively read the data bit in first memory, when the value of the data bit
When being 1, the first operation is carried out to the data bit, and the result of the first operation is stored to second memory；When the data
When the value of position is 0, the second operation is carried out to the data bit, and the result of the second operation is stored to second memory.
In specific implementation, point multiplication operation device can read the reading of data bit according to the sequence from a high position to low level
It takes, and the value of the current data position read is judged according to this, corresponding operation is carried out according to the value of current data position.
In specific implementation, the first operation may include following operation：Point doubling is carried out to data bit, and to putting fortune again
The result of calculation carries out point add operation.Second operation may include following operation：Point doubling is carried out to data bit.Either execute
First operation still executes the second operation, and the result of operation can be saved in second memory.
In specific implementation, second memory can be register, can also be RAM.Due to the realization in point multiplication operation
In the process, it may appear that more Large-number operation, need larger memory space store operation as a result, therefore in the present embodiment
In, RAM may be used as the second memory.
In specific implementation, point multiplication operation device successively judges the value of data bit in data flow, executes corresponding the
One operation or the second operation, and the result of each data bit arithmetic is stored in second memory successively.When in data flow
Data bit be fully completed judgement and execute operation after, controller can select new data flow, and repeat above-mentioned flow, until institute
There is data processing to finish.
Using the scheme of the present embodiment, for a pending data flow, controller only needs scheduling primary, will be described
In data flow storage to first memory to be treated, completed to each number in first memory using point multiplication operation device
Point multiplication operation is carried out according to position, each data bit is scheduled without controller, therefore controller ginseng can be reduced
With the number of scheduling, the process that RAM is carried is reduced, so as to reduce the power consumption of point multiplication operation device.
It is understood that register can also be used as second memory.When register is as second memory,
Using the scheme of the present embodiment, for a pending data flow, controller only needs scheduling primary, needs to handle by described
Data flow storage in first memory, complete to carry out each data bit in first memory using point multiplication operation device
Point multiplication operation is scheduled each data bit without controller, can equally reduce controller and participate in scheduling
Number reduces the read-write operation of register, so as to reduce the power consumption of point multiplication operation device.
Embodiment two
Present embodiments provide a kind of elliptic curve cipher point multiplication operation method, with reference to figure 2, below by way of specific steps into
Row is described in detail.
Step S201, controller selects data flow to be treated, and the data flow is stored to first memory.
In specific implementation, register may be used and store data flow to be treated as first memory.Data flow
Length be N, the length of a data flow can be a word length, i.e. 32 data bit, can also be 32 integer multiple data
Position.
Step S202 carries out Initialize installation to the counter in point multiplication operation device.
Point multiplication operation device can be successively read the data bit in the first memory.It in specific implementation, can be in point
One counter is set in multiplication device, by the value of counter come the number of the data bit currently-read to point multiplication operation device
It is counted.The length of counter is identical as the length of data flow to be treated, and the value of initialization counter is 1.
Step S203, point multiplication operation device read the data bit in first memory.
Step S204 judges whether the value of data bit is 1, if 1, thens follow the steps S205；If 0, then follow the steps
S207。
Step S205 carries out point doubling to current data position.
Step S206 carries out point add operation to the point doubling result of step S205, and the result of point add operation is stored
Into second memory.
Step S207 carries out point doubling to current data position, and the result of point doubling is stored to second memory
In.
In the present embodiment, times point formula progress operation of Jacobi projected coordinate system may be used in point doubling, described
The operational parameter of point formula is it is known that and the operation flow of point formula again is split as the operation sequence that hardware can identify again
Row.Point add operation may be used the Jacobi point penetrated under mixed proportion of project-walking back and forth and formula added to carry out operation, and the point adds public affairs
The operational parameter of formula is it is known that and the operation flow of point plus formula is split into the sequence of operations that should will be identified.It can be with
Sequence of operations is prestored in RAM, hardware circuit can directly be scheduled sequence of operations, complete point doubling and point
Add operation.
In the present embodiment, second memory can be RAM.The memory space of RAM can be split into N number of RAM block, N
Equal to the storage space volume of RAM divided by the operation length of default elliptic curve cipher operation, i.e. the memory space of N=RAM holds
The operation length of amount/elliptic curve cipher.For example, the storage space volume of RAM is 1K bytes, i.e. 8192 bits, elliptic curve
The operation length of password is 512 bits, then the memory space of RAM can be split as to 8192/512=16 RAM block at this time.
In the present embodiment, for example, for step S205, point doubling is carried out to data bit, the result of point doubling can
To be stored in the specified RAM block for being used for storing ephemeral data, such as can be by RAM block 1, i.e. RAM1 is as storage ephemeral data
RAM block.Step S205 is finished, and executes step S206, at this time the knot of point multiplication operation device invocation step S205 from RAM1
Fruit carries out point add operation, and the result of point add operation is possibly stored in purpose RAM block, for example, purpose RAM block can be RAM2；
For step S207, since step S207 only carries out point doubling to data bit, then the result of point doubling is possibly stored to mesh
RAM block RAM2 in.Likewise, RAM block of multiple RAM blocks as storage ephemeral data can also be defined, can also define more
Purpose RAM block of a RAM block as storage operation result.For example, the operation result of step S206 can be stored to purpose RAM
It, will be in the operation result storage to purpose RAM block RAM3 of step S207 in block RAM 2.
Step S208, after the completion of current data bit arithmetic, point multiplication operation device reads next data bit, and the value of counter is corresponding
Add 1.
Step S209, if in the presence of a data bit, repeat step S202 to step S208；If next data are not present
Position, then terminate flow.
Step S209 judges whether the data bit is the last one data by judging whether the value of counter is N+1
Position, if it is the last one data bit, then terminates flow；If not the last one data bit, then next data bit is repeated
Step S202 to step S208.
Using the scheme of the present embodiment, the ram space in existing processor is split into the operation length with default ECC
The RAM block to match, since ECC is the highest cipher system of every bit security generally acknowledged at present, i.e., when required level of encryption
It is required that when identical, there is ECC shorter operation length, the number N of RAM block and the operation length of Encryption Algorithm to be inversely proportional, therefore
Compared to other Encryption Algorithm, more RAM blocks can be split into using RAM when ECC algorithm, are used for storing fortune in addition to necessary
The RAM block of result is calculated, the RAM block having more can be used for ephemeral data when storing point multiplication operation or store other data so that
RAM in existing processor is fully used, and improves the utilization rate of RAM.
Embodiment three
Present embodiments provide a kind of elliptic curve cipher point multiplication operation method, with reference to figure 3, below by way of specific steps into
Row is described in detail.
Step S301, controller selects data flow to be treated, and the data flow is stored to first memory.
Step S302 carries out Initialize installation to preset counter in point multiplication operation device.
Point multiplication operation device can be successively read the data bit in the first memory.It in specific implementation, can be in point
One counter is set in multiplication device, of the currently-read data bit of point multiplication operation device is judged by the value of counter
Number.The length of counter is identical as the length of data flow to be treated, and the value of initialization counter is 1.
Step S303, point multiplication operation device read the data bit in first memory.
Step S304 judges whether the value of data bit is 1, if 1, thens follow the steps S305；If 0, then follow the steps
S307。
Step S305 carries out point doubling to current data position.
In the present embodiment, the result of point doubling can be stored to the RAM block RAM1 to specified storage ephemeral data
In.
Step S306 carries out point add operation to the operation result of step S305, and the result storage of point add operation is arrived
In RAM2.
In the present embodiment, point multiplication operation device can call the operation result in RAM1, to the operation result in RAM1 into
Row point add operation, and will be in the storage to purpose RAM block RAM2 of obtained point add operation result.
Step S307 carries out point doubling to current data position, and will be in the storage to RAM3 of the result of point doubling.
Step S308 carries out redundant operation to the operation result of step S307.
In specific implementation, in order to make the result of redundant operation do not influence point multiplication operation as a result, the result of redundant operation
It can abandon, non-purpose RAM block can also be stored in.For example, in the present embodiment, the result storage of redundant operation can be arrived
In RAM1, the result of point multiplication operation is not had an impact as long as meeting.
In the present embodiment, the duration of redundant operation of execution and the when appearance for executing a point add operation can be made
Deng so that execute a redundant operation power consumption with execution the power consumption of point add operation it is equal, prevent power consumption analysis.
In the present embodiment, operation mode identical with step S306 may be used in redundant operation, to the fortune of step S307
Calculate result and carry out point add operation so that execute step S307 and the occupied durations of step S308 with execute step S305 and
The occupied durations of step S306 are equal so that execute step S307 and step S308 power consumption with execute step S305 and
The power consumption of step S306 is equal, can effectively prevent power consumption analysis.
Step S309, after the first data bit completes operation, point multiplication operation device reads next data bit, the value phase of counter
1 should be added.
Step S310, if in the presence of a data bit, repeat step S302 to step S309；If next data are not present
Position, then terminate flow.
Using the scheme of the present embodiment, when the value of data bit is 0, by increasing a redundancy for not influencing operation result
Point add operation so that it is complete that the operation when value that operation when the value of data bit is 0 executes duration and data bit is 1 executes duration
Complete consistent, the realization of data operation flow is full symmetric, can effectively prevent power consumption analysis.
It is understood that redundant operation is not limited to point add operation, other enable to operation duration to add with point
The operation that the duration of operation is equal all can serve as redundant operation.In addition it is also possible to which redundancy fortune is added when the value of data bit is 1
It calculates, if the redundant operation number being added is M, then when the number of the redundancy being added when the value of data bit is 0 equal to data bit is 1
The number of the redundancy of addition adds 1, i.e. M+1.
Example IV
A kind of elliptic curve cipher point multiplication operation device is present embodiments provided, with reference to Fig. 4, the point multiplication operation device packet
It includes：Control unit 401, point multiplication operation unit 402, wherein：
Control unit 401 is stored for selecting data flow to be treated, and by the data flow to first memory
In；
Point multiplication operation unit 402, the data bit for being successively read in first memory carry out the value of current data position
Judge, point multiplication operation device is successively read the data bit in first memory, when the value of the data bit is 1, to the data
Position carries out the first operation, and the result of the first operation is stored to second memory；When the value of the data bit is 0, to institute
It states data bit and carries out the second operation, and the result of the second operation is stored to second memory.
In specific implementation, second memory can be RAM, and RAM can be split into N number of RAM block, including：Purpose is deposited
RAM block is stored up, the result of the second operation of result or storage for storing the first operation；Ephemeral data stores RAM block, for storing
The ephemeral data occurred in first operation or the second calculating process, the number N of RAM block are equal to the storage space volume of the RAM
Divided by the operation length of preset password operation, crypto-operation is it may be said that elliptic curve cipher operation.
In specific implementation, point multiplication operation unit may include：First arithmetic device 4021, for carrying out the first operation, institute
Stating the first operation includes：Point doubling is carried out to the data bit, and point add operation is carried out to the result of the point doubling.
In specific implementation, the point doubling may be used Jacobi projected coordinate system times point formula calculated,
The operational parameter of described times of point formula is stored in advance in the second memory.Jacobi-may be used in the point add operation
Point under affine mixed proportion adds formula to carry out operation, and the point adds the operational parameter of formula to be stored in advance in described second to deposit
In reservoir.
In specific implementation, point multiplication operation unit may include：Second arithmetic device 4022, for carrying out the second operation, institute
Stating the second operation includes：Point doubling is carried out to the data bit.
In specific implementation, point multiplication operation unit can also include：Third arithmetic unit 4023, for carrying out third operation,
The result that the third operation is used to carry out the data bit point doubling carries out redundant operation, and by the point doubling
As a result the result as second operation.
In specific implementation, the third arithmetic unit 4023 carries out the duration of a redundant operation and the second arithmetic device
The duration of 4022 point add operations of progress is equal, and the third arithmetic unit 4023 to the result of the point doubling a little add
Operation.
Although present disclosure is as above, present invention is not limited to this.Any those skilled in the art are not departing from this
It in the spirit and scope of invention, can make various changes or modifications, therefore protection scope of the present invention should be with claim institute
Subject to the range of restriction.
Claims (10)
1. a kind of elliptic curve cipher point multiplication operation method, which is characterized in that including：
Controller selects data flow to be treated, and will be in data flow storage to first memory；
Point multiplication operation device is successively read the data bit in first memory, when the value of the data bit is 1, to the data bit
The first operation is carried out, and the result of the first operation is stored to second memory；When the value of the data bit is 0, to described
Data bit carries out the second operation, and the result of the second operation is stored to second memory；It is described that the is carried out to the data bit
One operation includes：Point doubling is carried out to the data bit, and point add operation is carried out to the result of the point doubling；It is described right
The data bit carries out the second operation：Point doubling is carried out to the data bit, and a times point is carried out to the data bit and is transported
The result of calculation carries out redundant operation, and the duration and power consumption that execute the duration and the execution point add operation of the redundant operation are equal
It is equal, and using the result of the point doubling as the result of second operation.
2. elliptic curve cipher point multiplication operation method as described in claim 1, which is characterized in that the first memory is to post
Storage, the second memory are RAM or register.
3. elliptic curve cipher point multiplication operation method as claimed in claim 2, which is characterized in that the second memory is
RAM stores the result of first operation and the result of the second operation into preset RAM block in the RAM, the RAM
Storage space volumes of the number N of block equal to the RAM divided by the operation length of elliptic curve cipher operation.
4. elliptic curve cipher point multiplication operation method as described in claim 1, which is characterized in that the point doubling is using refined
Gram operation is carried out than times point formula of projected coordinate system, the operational parameter of described times of point formula is stored in advance in second storage
In device.
5. elliptic curve cipher point multiplication operation method as described in claim 1, which is characterized in that the point add operation is using refined
Gram formula is added to carry out operation than the point under projection-affine mixed proportion, the point adds the operational parameter of formula to be stored in advance in
In the second memory.
6. elliptic curve cipher point multiplication operation method as described in claim 1, which is characterized in that the redundant operation is that point adds
Operation.
7. a kind of elliptic curve cipher point multiplication operation device, which is characterized in that including：
Control unit, for selecting data flow to be treated, and will be in data flow storage to first memory；
Point multiplication operation unit, the data bit for being successively read in first memory judge the value of current data position, point
Multiplication device is successively read the data bit in first memory, and when the value of the data bit is 1, the is carried out to the data bit
One operation, and the result of the first operation is stored to second memory；
When the value of the data bit is 0, the second operation carried out to the data bit, and by the result of the second operation storage to the
Two memories；It is described to include to the data bit the first operation of progress：Point doubling is carried out to the data bit, and to described times
The result of point processing carries out point add operation；It is described to include to the data bit the second operation of progress：The data bit is carried out again
Point processing, and the result that point doubling is carried out to the data bit carries out redundant operation, and execute the duration of the redundant operation
It is equal with the duration and power consumption for executing the point add operation, and using the result of the point doubling as second operation
As a result.
8. elliptic curve cipher point multiplication operation device as claimed in claim 7, which is characterized in that the first memory is to post
Storage, the second memory are RAM or register.
9. elliptic curve cipher point multiplication operation device as claimed in claim 8, which is characterized in that the second memory is
In RAM, the RAM preset RAM block be used to store the first operation result and the second operation as a result, the RAM block it is a
Storage space volumes of the number N equal to the RAM divided by the operation length of elliptic curve cipher operation.
10. elliptic curve cipher point multiplication operation device as claimed in claim 7, which is characterized in that the redundant operation is a little
Add operation.
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| CN108875416B (en) | 2018-06-22 | 2020-05-19 | 北京智芯微电子科技有限公司 | Elliptic curve multiple point operation method and device |
| CN113014388B (en) * | 2021-03-30 | 2022-06-28 | 浙江萤火虫区块链科技有限公司 | Scalar multiplication acceleration system in elliptic curve cryptographic algorithm |
| CN113472540B (en) * | 2021-07-01 | 2023-05-09 | 罗克佳华(重庆)科技有限公司 | Method, device, electronic equipment and storage medium for generating ciphertext |
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