KR101707334B1 - Apparatus for efficient elliptic curve cryptography processor and method for the same - Google Patents

Abstract

The present invention relates to a method and an apparatus for elliptic curve cryptography reducing unnecessary point addition operations based on corrected Lopez-Dahab and Left-To-Right algorithms. The method for elliptic curve cryptography according to an embodiment includes: a step of converting a point on an affine coordinate elliptic curve to projective coordinates; a step of executing scalar point multiplication operation on the point on the projective coordinates; a step of adjusting the fulfillment value obtained from the scalar point multiplication operation by comparison to a value obtained from Lopez-Dahab algorithm scalar point multiplication operation; a step of obtaining a result value by converting the adjusted fulfillment value to the affine coordinates on the projective coordinates; and a step of calculating an encrypted password value based on the result value obtained from the conversion to the affine coordinates.

Description

[0001] APPARATUS FOR EFFICIENT ELLIPTIC CURVE CRYPTOGRAPHY PROCESSOR AND METHOD FOR THE SAME [0002]

The following description relates to an efficient computation apparatus and method for encryption using elliptic curves. More particularly, to a computing device and method for processing scalar point multiplication, which is a geometric operation for points represented on an elliptic curve for elliptic curve encryption.

As Internet and wireless communications grow, the need for cryptographic systems to protect information is also increasing. In a typical cryptosystem, when a sender enciphers a plaintext to know the meaning of a message and transmits the plaintext, the recipient decrypts the received ciphertext again and restores the plaintext. A certain rule or method used in the encryption and decryption process is called an encryption key.

The key may be divided into a symmetric cipher key having the same encryption key used in the encryption process and a decryption key used in the decryption process, and an asymmetric cipher key having a different encryption key and decryption key. Of the cryptographic systems, the elliptic curve cryptosystem (ECC) has recently attracted a great deal of attention from academia and industry. ECC is a public key cryptosystem that uses a public key for data encryption and a secret key for decryption. It is a cryptographic system that implements encryption / decryption based on a special addition method defined on a mathematical object called an elliptic curve to be. The advantage of ECC is that it uses a significantly smaller key compared to other cryptographic systems such as RSA (Rivest Shamir Adleman), but has the same security.

The elliptic curve on the Galois Field (GF) is a set of solutions satisfying Equation (1).

Equation 1:

The operation result Q on the elliptic curve is performed by scalar point multiplication of the point P on the elliptic curve and the scalar value k. The scalar value k having the size of m-bits on the binary finite field GF () can be expressed by Equation (2).

Equation 2:

The result Q of the scalar point multiplication can be expressed by Equation (3).

Equation (3)

The three main steps for calculating a point multiply operation are as follows.

(1) Converts point P from Affine Coordinate to Projective Coordinate.

(2) Calculate Q = kP on the projection coordinates.

(3) Converts point Q from projected coordinates to affine coordinates.

There are multiplication, squaring, addition, subtraction, and inversion in the finite field operation. Addition and subtraction operations can be calculated using an exclusive OR (XOR) operation. The polynomials of the elements of the binary finite field GF () can be expressed as Equation (4) as a (x) and b (x).

Equation 4:

When a polynomial, which is an element of the binary finite field GF (), is a (x) and b (x) as shown in Equation (4), the multiplication operation of the finite field can be expressed as Equation (5). At this time, the computation used is a modulo operation of the subtotal and irreducible polynomial f (x).

Equation 5:

Commonly used finite-field multiplication operations are Digit-Serial multiplication and Bit-Serial multiplication. Although the Digit-Serial multiplication operation is used to reduce the system delay, the complexity of the hardware increases, while the bit-serial multiplication operation has the feature that the hardware complexity decreases but the system delay increases.

The squaring operation is the same as performing the multiplication operation using the same input. The Lopez-Dahab algorithm is an algorithm used in ECC to perform scalar point multiplication of points on elliptic curves.

The Motgomery Ladder Method is the most commonly used algorithm for scalar point multiplication on an elliptic curve using the Lopez-Dahab algorithm. It can be operated on projected coordinates as well as affine coordinates.

Table 1 below shows the pseudo code of the Montgomery Ladder Method multiplication operation process.

Table 1:

To perform such an operation, the point addition operation and the point double operation must be efficiently combined.

,

가 타원곡선 위의 두 점이라고 할 때, 점 A와 B의 x좌표의 합인

와

는 수학식6과 같이 표현 가능하다.point

,

Is the two points on the elliptic curve, it is the sum of the x-coordinates of the points A and B

Wow

Can be expressed by Equation (6).

Equation (6)

를

,

로 다시 표현하면 수학식6은 수학식7로 표현할 수 있다.Using projection coordinates

To

,

Expression (6) can be expressed by Equation (7).

Equation (7)

The scalar point multiply operation is performed using the newly expressed coordinates and the Left-To-Right algorithm as shown in Equation (7).

Table 2 below shows the pseudo code of the left-to-right multiplication operation.

Table 2:

The embodiments propose a new efficient Lopez-Dahab and Left-To-Right algorithm by improving the conventional Lopez-Dahab algorithm and the left-to-right algorithm in designing an elliptic curve cryptosystem device. And provides an efficient elliptic curve encryption apparatus and method therefor with low hardware complexity.

Embodiments provide a elliptic curve encryption device having a low level of hardware complexity using a control signal for controlling a field operation by using a scalar point multiplier of Bit-Serial structure.

According to one embodiment, an elliptic curve encryption method comprises: converting a point on an elliptic curve to projection coordinates in affine coordinates; Performing a scalar point multiply operation on the point on the projection coordinate; Comparing the performance value obtained by performing the scalar point multiplication operation with a value obtained through a scalar point multiply operation of the Lopez-Dahab algorithm; Acquiring a result value by converting the adjusted performance value from the projection coordinate to the affine coordinate; And calculating an encrypted encryption value based on the obtained result by transforming to affine coordinates.

According to one aspect, performing a scalar point multiply operation on the point on the projection coordinate may include using a modified Lopez-Dahab algorithm and a Left-To-Right algorithm to reduce the scalar point addition operation, Lt; RTI ID = 0.0 > a < / RTI >

According to another aspect, performing a scalar point multiply operation on the point on the projection coordinate may include determining the scalar point addition operation and the scalar point multiply operation on the projection coordinate based on a bit value of the key . ≪ / RTI >

According to another aspect, performing a scalar point multiply operation on the point on the projection coordinate may include performing four field squaring operations, one field addition operation, and one field multiplication operation when the bit value of the key is zero Performing a double operation on a point performing the operation and performing a double operation on the point when the bit value of the key is 1 and then performing a field multiplication operation of 4 times and a field addition operation of 2 times and a field square operation of 1 And performing a point addition operation to perform a point addition operation.

According to another aspect, performing the scalar point multiply operation on the point on the projection coordinate may include using a field multiply operator having a Bit-Serial structure to calculate the field multiply operation .

According to another aspect, performing a scalar point multiply operation on the point on the projection coordinate may include calculating a first multiplier and a second multiplier simultaneously and outputting a third multiplier and a fourth multiplier through a first signal and a second signal, Turning the multiplier to an enabled state, and calculating the third multiplier and the fourth multiplier in parallel.

According to another aspect of the present invention, performing the scalar point multiply operation on the point on the projection coordinate may include performing an XOR operation on an output value of the third multiplier and the fourth multiplier through an XOR gate, And obtaining the execution value through the multiplexer and the squared calculator.

According to one embodiment, an elliptic curve encryption apparatus includes: a first conversion unit for converting a point on an elliptic curve to projection coordinates in affine coordinates; An operation unit for performing a scalar point multiply operation on the point on the projection coordinate system; An adjustment unit for comparing the performance value obtained by performing the scalar point multiplication operation with a value obtained through a scalar point multiply operation of the Lopez-Dahab algorithm; A second transform unit for transforming the adjusted performance value from the projection coordinate to the affine coordinate to obtain a result value; And an obtaining unit for calculating an encrypted value based on the result obtained by transforming to affine coordinates.

According to embodiments, an efficient elliptic curve encryption apparatus and method can be provided that can reduce unnecessary scalar point addition operations by using an algorithm proposed in the design of an elliptic curve cryptosystem apparatus.

According to embodiments, an efficient elliptic curve encryption device having a low hardware complexity and reducing a system delay by using a bit-serial structure and a field operation control signal in a scalar point multiply operation unit in the design of an elliptic curve cryptosystem device, and Method can be provided.

1 is a block diagram illustrating a configuration of an elliptic curve encryption apparatus according to an embodiment of the present invention.
2 is a diagram illustrating a scalar point multiply operation unit according to an embodiment.
3 is a diagram illustrating a field multiplication operation unit according to an embodiment of the present invention.
4 is a flowchart illustrating a scalar point multiply operation method according to an embodiment of the present invention.
5 is a block diagram illustrating a configuration of an elliptic curve encryption apparatus according to an embodiment of the present invention.

Hereinafter, embodiments will be described in detail with reference to the accompanying drawings.

The elliptic curve cryptosystem according to one embodiment can be equally applied to an elliptic curve cryptosystem for various cryptosystems. In the following, a binary finite element having a size of GF () will be described.

The elliptic curve cryptosystem according to one embodiment is an algorithm for an elliptic curve cryptosystem, and a modified Lopez-Dahab algorithm and a left-to-right algorithm having optimized low hardware complexity can be used when the key length is 163 bits .

1 is a block diagram illustrating a configuration of an elliptic curve encryption apparatus according to an embodiment of the present invention.

An elliptic curve cryptographic device can convert a point on an elliptic curve to a projected coordinate in affine coordinates. An elliptic curve cryptographic device can perform a scalar point multiply operation on a point on a projection coordinate. The elliptic curve encryption device can adjust the performance value obtained by performing the scalar point multiply operation by comparing it with the value obtained through the scalar point multiply operation of the Lopez-Dahab algorithm. The elliptic curve cryptographic device can obtain the result by converting the adjusted performance value from projected coordinates to affine coordinates. The elliptic curve cryptographic device can calculate the encrypted cryptographic value based on the obtained result as it is converted into affine coordinates.

In the present invention, the elliptic curve cryptosystem using the proposed algorithm performs computation efficiently by reducing the unnecessary scalar point multiply operation.

Table 3 below shows the pseudo code of the multiplication operation of the proposed algorithm.

Table 3:

The proposed algorithm performs point multiplication operation through four steps.

(1) Converts the point P on the elliptic curve from Affine Coordinate to Projective Coordinate.

(2) Perform point multiplication operation on projection coordinates.

(3) Obtain accurate values compared with the Lopez-Dahab algorithm.

(4) Transform from projection coordinate to affine coordinate and obtain result Q.

The proposed modified Lopez-Dahab algorithm and Left-To-Right algorithm have the advantage of reducing the number of scalar point addition operations in scalar point multiply operation.

로 초기 값을 설정할 수 있다.

과

값은 키 값의 LSB인

에 의해 결정될 수 있다.

이면

이고

이면

과

은 0이다.In the first step of the proposed algorithm, the point P on the elliptic curve is transformed from affine coordinates to projection coordinates

Can be set to the initial value.

and

The value is the LSB of the key value.

Lt; / RTI >

If

ego

If

and

Is zero.

에 따라 투영 좌표 상에서 스칼라 포인트 덧셈 연산과 스칼라 포인트 곱셈 연산이 결정될 수 있다. 개선된 알고리즘에 의한 이 단계의 장점은 키의 비트 값인

가 0일 경우 불필요한 스칼라 포인트 덧셈 연산을 줄일 수 있다. 그러므로 스칼라 포인트 곱셈 연산을 수행하는데 소요되는 시간이 확연히 줄어들게 된다.In performing the point multiply operation on the projection coordinates,

A scalar point addition operation and a scalar point multiplication operation can be determined on the projection coordinate. The advantage of this step with the improved algorithm is that the bit value of the key

Is 0, it is possible to reduce unnecessary scalar point addition operations. Therefore, the time required to perform the scalar point multiplication operation is significantly reduced.

)과 한 번의 필드 덧셈 연산(

), 한 번의 필드 곱셈 연산(

)을 수행하는 포인트 두 배 연산만을 수행할 수 있다. 타원곡선 암호화 장치는 키의 비트 값이 1일 경우 포인트 두 배 연산을 수행한 뒤, 네 번의 필드 곱셈 연산(

)과 두 번의 필드 덧셈 연산(

), 한 번의 필드 제곱 연산

을 수행하는 포인트 덧셈 연산을 추가로 수행할 수 있다.As shown in Table 3, the elliptic curve cryptosystem can perform four field squared operations (

) And one field addition operation (

), One field multiplication operation

). ≪ / RTI > An elliptic curve encryption device performs a double-point operation if the bit value of the key is 1, and then performs four field multiplication operations

) And two field addition operations (

), One field square operation

A point addition operation can be performed.

값과 기존의 Lopez-Dahab 알고리즘의

값 사이의 차이가 발생함을 판단할 수 있다. 타원곡선 암호화 장치는 기존의 Lopez-Dahab 알고리즘의 스칼라 포인트 곱셈 연산을 통해 얻은 값과 수정된 Lopez-Dahab 알고리즘의 수행값을 비교함으로써 수행값

값을 정확하게 수정해주는 과정을 수행할 수 있다.The elliptic curve cryptographic device performs the scalar point multiply operation on points and points when the iteration of all operations is completed.

Values of the conventional Lopez-Dahab algorithm

It can be determined that a difference between values occurs. The elliptic curve encryption device compares the value obtained by the scalar point multiply operation of the existing Lopez-Dahab algorithm with the performance value of the modified Lopez-Dahab algorithm,

The process of correcting the value can be performed.

In the elliptic curve cryptosystem according to the embodiment, the structure of the elliptic curve cryptosystem may use five field multipliers in an iteration of the algorithm.

은 제곱 연산 장치1(Squarer1)과 제곱 연산 장치3(Squarer3)에 의해 병렬로 수행되며

과

의 계산은 제곱 연산 장치2(Squarer2)와 제곱 연산 장치4(Squarer4)에 의해 동시에 수행될 수 있다. 제곱 연산 장치2(Squarer2)의 결과

와 제곱 연산 장치4(Squarer4)의 결과

는 곱셈기5에서 곱셈 연산

을 통해 계산될 수 있다. 제곱 연산 장치1(Squarer2)과 제곱 연산 장치3(Squarer3)의 결과는 163비트 XOR게이트에서 XOR연산

에 의해 계산될 수 있다.The elliptic curve cryptographic device may perform a scalar point multiply operation on the points on the modified projection coordinates and perform a double point operation on the projection coordinates. The elliptic curve cryptographic device uses two squared operations

Are performed in parallel by a squaring unit 1 (Squarer 1) and a squaring unit 3 (Squarer 3)

and

Can be performed simultaneously by the squaring apparatus 2 (Squarer 2) and the squaring apparatus 4 (Squarer 4). The result of Squarer 2

And the result of squaring 4 (Squarer 4)

The multiplication operation in the multiplier 5

Lt; / RTI > The results of Squarer 2 and Squarer 3 are multiplied by the XOR operation in a 163 bit XOR gate

Lt; / RTI >

Referring to FIG. 3, a field multiplication operation unit is shown.

The most popular module in designing a scalar point multiplier for an elliptic curve cryptosystem is a field multiplier. When using the Bit-Serial method to compute the field multiply operation, the number of clock cycles is larger than that of using the Digit-Serial method, but the hardware complexity is low. The elliptic curve encryption apparatus according to an embodiment provides an elliptic curve encryption apparatus and a method using the multiplier and the field operation control signal using the Bit-Serial method and having low hardware complexity and low system delay.

2 is a diagram illustrating a scalar point multiply operation unit according to an embodiment.

, 곱셈기2는

를 동시에 계산하고 m_done1신호와 m_done2신호를 통해 곱셈기3과 곱셈기4를 사용 가능(enable)상태로 바꾸며 곱셈기3과 곱셈기4는

와

를 병렬로 계산할 수 있다. As shown in FIG. 2, the multiplier 1 multiplies

, The multiplier 2

And multiplier 3 and multiplier 4 are enabled through enable signals m_done1 and m_done2, and multiplier 3 and multiplier 4 are enabled

Wow

Can be calculated in parallel.

을 하며 결과값은 다중화기(Multiplexer)와 제곱연산장치5(Squarer5)를 통해 새로운

,

값을 출력할 수 있다.The elliptic curve encryption device can provide a way to reduce the execution time of the proposed algorithm to twice. The output values of multiplier 3 and multiplier 4 are multiplied by a 16-bit XOR gate to perform an XOR operation

The result is multiplier and multiplier 5 (Squarer 5)

,

Value can be output.

The elliptic curve cryptosystem according to an embodiment uses a modified Lopez-Dahab algorithm and a left-to-right algorithm, thereby reducing unnecessary calculation processes and reusing modules repeatedly used, resulting in low hardware complexity.

An elliptic curve cryptographic device can return a result as it transforms the projection coordinates into affine coordinates.

4 is a flowchart illustrating a scalar point multiply operation method according to an embodiment of the present invention.

로 초기 값을 설정할 수 있다.

과

값은 키 값의 LSB인

에 의해 결정될 수 있다.

이면

이고

이면

과

은 0이다.An elliptic curve cryptographic device may transform a point on the elliptic curve to projection coordinates in affine coordinates (410). The elliptic curve cryptographic apparatus converts the point P on the elliptic curve from affine coordinates to projection coordinates,

Can be set to the initial value.

and

The value is the LSB of the key value.

Lt; / RTI >

If

ego

If

and

Is zero.

에 따라 투영 좌표 상에서 스칼라 포인트 덧셈 연산과 스칼라 포인트 곱셈 연산이 결정될 수 있다. 타원곡선 암호화 장치는 키의 비트 값이 0일 경우, 네 번의 필드 제곱 연산(

)과 한 번의 필드 덧셈 연산(

), 한 번의 필드 곱셈 연산(

)을 수행하는 포인트 두 배 연산만을 수행할 수 있다. 타원곡선 암호화 장치는 키의 비트 값이 1일 경우, 알고리즘은 포인트 두 배 연산을 수행한 뒤, 네 번의 필드 곱셈 연산(

)과 두 번의 필드 덧셈 연산(

), 한 번의 필드 제곱 연산

을 수행하는 포인트 덧셈 연산을 추가로 수행할 수 있다.An elliptic curve encryption device is a key bit value

A scalar point addition operation and a scalar point multiplication operation can be determined on the projection coordinate. An elliptic curve cryptographic device uses four field squared operations when the bit value of the key is zero

) And one field addition operation (

), One field multiplication operation

). ≪ / RTI > An elliptic curve cryptographic device, if the bit value of the key is 1, then the algorithm performs a double-point operation and then performs four field multiplication operations

) And two field addition operations (

), One field square operation

A point addition operation can be performed.

과 종래의 Lopez-Dahab 알고리즘의

값 사이의 차이가 발생한다. 이에 따라 타원곡선 암호화 장치는 종래의 Lopez-Dahab 알고리즘에서 스칼라 포인트 곱셈 연산을 통해 얻은 값과 수정된 Lopez-Dahab 알고리즘에서 스칼라 포인트 곱셈 연산을 통하여 획득된 수행값을 비교하여

값을 정확하게 수정해주는 과정을 수행할 수 있다.The elliptic curve encryption device performs point and scalar point multiply operations on the projection coordinates,

And the conventional Lopez-Dahab algorithm

There is a difference between the values. Accordingly, the elliptic curve encryption device compares the value obtained through the scalar point multiplication operation in the conventional Lopez-Dahab algorithm with the execution value obtained through the scalar point multiply operation in the modified Lopez-Dahab algorithm

The process of correcting the value can be performed.

은 제곱 연산 장치1(Squarer1)과 제곱 연산 장치3(Squarer3)에 의해 병렬로 수행되며

과

의 계산은 제곱 연산 장치2(Squarer2)와 제곱 연산 장치4(Squarer4)에 의해 동시에 수행될 수 있다. 제곱 연산 장치2(Squarer2)의 결과

와 제곱 연산 장치4(Squarer4)의 결과

는 곱셈기5에서 곱셈 연산

을 통해 계산될 수 있다. 제곱 연산 장치1(Squarer2)과 제곱 연산 장치3(Squarer3)의 결과는 163비트 XOR게이트에서 XOR연산

에 의해 계산될 수 있다.For example, an elliptic curve cryptographic device can use five field multipliers. The elliptic curve cryptographic device may perform a scalar point multiply operation on the point on the projection coordinate and perform a point double operation on the projection coordinate. The elliptic curve cryptographic device uses two squared operations

Are performed in parallel by a squaring unit 1 (Squarer 1) and a squaring unit 3 (Squarer 3)

and

Can be performed simultaneously by the squaring apparatus 2 (Squarer 2) and the squaring apparatus 4 (Squarer 4). The result of Squarer 2

And the result of squaring 4 (Squarer 4)

The multiplication operation in the multiplier 5

Lt; / RTI > The results of Squarer 2 and Squarer 3 are multiplied by the XOR operation in a 163 bit XOR gate

Lt; / RTI >

An elliptic curve cryptographic device can use a scalar point multiplier as a field multiplier. The elliptic curve encryption device can use the multiplier and the field operation control signal using the bit-serial method.

, 곱셈기2는

를 동시에 계산하고 m_done1신호와 m_done2신호를 통해 곱셈기3과 곱셈기4를 사용 가능(enable)상태로 바꾸며 곱셈기3과 곱셈기4는

와

를 병렬로 계산할 수 있다. The multiplier 1

, The multiplier 2

And multiplier 3 and multiplier 4 are enabled through enable signals m_done1 and m_done2, and multiplier 3 and multiplier 4 are enabled

Wow

Can be calculated in parallel.

을 수행할 수 있으며, 결과값은 다중화기(Multiplexer)와 제곱연산장치5(Squarer5)를 통해 새로운

,

값을 출력할 수 있다. The elliptic curve cryptosystem uses the 163-bit XOR gate to XOR the output values of the multipliers 3 and 4

, And the resultant value is multiplied by a multiplexer and a square calculator 5 (Squarer 5)

,

Value can be output.

The elliptic curve cryptographic device may obtain the result by transforming the adjusted performance value from projected coordinates to affine coordinates (420). The elliptic curve encryption device can obtain the result value Q. Thus, the elliptic curve cryptosystem can calculate the encrypted cryptographic value based on the acquired result as it is converted into affine coordinates.

5 is a block diagram illustrating a configuration of an elliptic curve encryption apparatus according to an embodiment of the present invention.

The elliptic curve cryptographic apparatus may include a first transform unit 510, an operation unit 520, an adjusting unit 530, a second transform unit 540, and an obtaining unit 550.

The first transform unit 510 may transform a point on the elliptic curve to projection coordinates in affine coordinates.

The operation unit 520 may perform a scalar point multiply operation on the point on the projection coordinate. The operation unit 520 can reduce the execution time of the scalar point multiply operation by reducing the scalar point addition operation by using the modified Lopez-Dahab algorithm and the Left-To-Right algorithm.

The arithmetic operation unit 520 may determine a scalar point addition operation and a scalar point multiplication operation on the projection coordinate based on the bit value of the key. When the bit value of the key is 0, the arithmetic operation unit 520 performs a double operation of performing a field square operation of 4 times, a field addition operation of 1 field and a field multiplication operation of 1, and if the bit value of the key is 1 , A point addition operation may be performed to perform four times field multiplication operation, two field addition operation and one field square operation after performing point double operation.

The operation unit 520 may use a field multiplication operator having a bit-serial structure to calculate a field multiplication operation.

The operation unit 520 calculates the first multiplier and the second multiplier at the same time and turns the third multiplier and the fourth multiplier into the enabled state through the first signal and the second signal. The third multiplier and the fourth multiplier Can be calculated in parallel. The operation unit 520 may perform the XOR operation on the output values of the third multiplier and the fourth multiplier through the XOR gate, and may obtain the operation value through the multiplexer and the squared operator on the output value on which the XOR operation is performed.

The adjusting unit 530 may adjust the value by comparing the value obtained through the scalar point multiplication operation of the Lopez-dahab algorithm that performed the scalar point multiply operation.

The second transform unit 540 may obtain the resultant value by transforming the adjusted performed value from the projected coordinates to the affine coordinates.

The acquiring unit 550 may calculate an encrypted password value based on the obtained result as it is converted into affine coordinates.

The apparatus described above may be implemented as a hardware component, a software component, and / or a combination of hardware components and software components. For example, the apparatus and components described in the embodiments may be implemented within a computer system, such as, for example, a processor, a controller, an arithmetic logic unit (ALU), a digital signal processor, a microcomputer, a field programmable gate array (FPGA) , A programmable logic unit (PLU), a microprocessor, or any other device capable of executing and responding to instructions. The processing device may execute an operating system (OS) and one or more software applications running on the operating system. The processing device may also access, store, manipulate, process, and generate data in response to execution of the software. For ease of understanding, the processing apparatus may be described as being used singly, but those skilled in the art will recognize that the processing apparatus may have a plurality of processing elements and / As shown in FIG. For example, the processing unit may comprise a plurality of processors or one processor and one controller. Other processing configurations are also possible, such as a parallel processor.

The software may include a computer program, code, instructions, or a combination of one or more of the foregoing, and may be configured to configure the processing device to operate as desired or to process it collectively or collectively Device can be commanded. The software and / or data may be in the form of any type of machine, component, physical device, virtual equipment, computer storage media, or device , Or may be permanently or temporarily embodied in a transmitted signal wave. The software may be distributed over a networked computer system and stored or executed in a distributed manner. The software and data may be stored on one or more computer readable recording media.

The method according to an embodiment may be implemented in the form of a program command that can be executed through various computer means and recorded in a computer-readable medium. The computer-readable medium may include program instructions, data files, data structures, and the like, alone or in combination. The program instructions to be recorded on the medium may be those specially designed and configured for the embodiments or may be available to those skilled in the art of computer software. Examples of computer-readable media include magnetic media such as hard disks, floppy disks and magnetic tape; optical media such as CD-ROMs and DVDs; magnetic media such as floppy disks; Magneto-optical media, and hardware devices specifically configured to store and execute program instructions such as ROM, RAM, flash memory, and the like. Examples of program instructions include machine language code such as those produced by a compiler, as well as high-level language code that can be executed by a computer using an interpreter or the like. The hardware devices described above may be configured to operate as one or more software modules to perform the operations of the embodiments, and vice versa.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. For example, it is to be understood that the techniques described may be performed in a different order than the described methods, and / or that components of the described systems, structures, devices, circuits, Lt; / RTI > or equivalents, even if it is replaced or replaced.

Therefore, other implementations, other embodiments, and equivalents to the claims are also within the scope of the following claims.

Claims (8)

In an elliptic curve encryption method,
Transforming a point on the elliptic curve to a projective coordinate in Affine Coordinate;
Performing a scalar point multiply operation on the point on the projection coordinate;
Comparing the performance value obtained by performing the scalar point multiplication operation with a value obtained through a scalar point multiply operation of the Lopez-Dahab algorithm;
Acquiring a result value by converting the adjusted performance value from the projection coordinate to the affine coordinate; And
Calculating an encrypted password value based on the obtained result value by transforming to affine coordinates
Lt; / RTI >
Wherein performing a scalar point multiply operation on the point on the projection coordinate comprises:
Performing a scalar point multiply operation on the point on the projection coordinate using a control signal using a Bit-Serial structured multiplication operator and a field operation, and performing a point double operation on the projection coordinate
/ RTI > The method according to claim 1,
Wherein performing a scalar point multiply operation on the point on the projection coordinate comprises:
A modified Lopez-Dahab algorithm and a Left-To-Right algorithm are used to reduce the execution time of the scalar point multiply operation by reducing the scalar point addition operation
/ RTI > 3. The method of claim 2,
Wherein performing a scalar point multiply operation on the point on the projection coordinate comprises:
Wherein the scalar point addition operation and the scalar point multiply operation are determined on the projection coordinate based on a bit value of a key
/ RTI > The method of claim 3,
Wherein performing a scalar point multiply operation on the point on the projection coordinate comprises:
When the bit value of the key is 0, performing a field double operation that performs four field squaring operations, one field addition operation and one field multiplication operation,
If the bit value of the key is 1, performing a point addition operation that performs four times field multiplication operation, two field addition operation and one field square operation after performing the point double operation,
/ RTI > delete The method according to claim 1,
Wherein performing a scalar point multiply operation on the point on the projection coordinate comprises:
The first multiplier and the second multiplier are simultaneously calculated and the third multiplier and the fourth multiplier are enabled through the first signal and the second signal, and the third multiplier and the fourth multiplier are connected in parallel Steps to calculate
/ RTI > The method according to claim 6,
Wherein performing a scalar point multiply operation on the point on the projection coordinate comprises:
Performing an XOR operation on an output value of the third multiplier and the fourth multiplier through an XOR gate, and obtaining an output value of the XOR operation through a multiplexer and a squared operator
/ RTI > In an elliptic curve cryptosystem,
A first conversion unit for converting a point on the elliptic curve to projection coordinates in affine coordinates;
An operation unit for performing a scalar point multiply operation on the point on the projection coordinate system;
An adjustment unit for comparing the performance value obtained by performing the scalar point multiplication operation with a value obtained through a scalar point multiply operation of the Lopez-Dahab algorithm;
A second transform unit for transforming the adjusted performance value from the projection coordinate to the affine coordinate to obtain a result value; And
An acquiring unit for calculating an encrypted value based on the acquired result by transforming the affine coordinate into an affine coordinate,
Lt; / RTI >
The operation unit,
Performing a scalar point multiply operation on the point on the projection coordinate using a control signal using a bit-serial structure multiplier and a field operation, and performing a point double operation on the projection coordinate
Elliptic curve encryption device.

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