KR102649929B1 - Digital signature generation and verification method for low-end PLC - Google Patents

Abstract

The present invention relates to a method for generating and verifying electronic signatures for low-specification PLCs that improves the speed of electronic signature generation and verification while using less memory in order to improve the security of low-specification PCLs (Programmable Logic Controllers) in smart factories.

Description

Digital signature generation and verification method for low-end PLC}

The present invention relates to a method for generating and verifying electronic signatures for low-specification PLCs. More specifically, to improve the security of low-specification PCLs (Programmable Logic Controllers) in smart factories, the speed of electronic signature generation and verification is improved while using less memory. This is about a method of generating and verifying electronic signatures for low-end PLCs.

As the safety of smart factory systems emerges, the need to strengthen security for PLCs (Programmable Logic Controllers) within factories is increasing.

As part of the generation and verification method of electronic signatures performed between PLCs to strengthen the security of the smart factory system, electronic signatures using elliptic curves are conventionally used.

The elliptic curve electronic signature generation and verification algorithm mainly uses a scalar multiplication operation method that refers to a table, and to increase the efficiency of the scalar multiplication operation using a fixed point P, a pre-calculation table for the corresponding coordinates is stored in advance. When creating or verifying an electronic signature, the speed of creating and verifying the electronic signature is improved by using a pre-stored calculation table.

In this way, in order to speed up the creation and verification of electronic signatures using finite field operations, a calculation method based on table references is required, but the specifications of PLCs in smart factories are still mostly low-specification PLCs.

Because these low-end PLC resources are very limited, there is a problem in that it is impossible to store large tables. In the case of the conventional table reference method, the table is created in advance, stored, and used, so the memory required to store the table is fixedly allocated, and the corresponding Since it is only used when performing scalar multiplication operations, there is a problem that memory is wasted.

To solve this problem, if a table is created every time a scalar multiplication operation is performed, the time required for the operation increases and efficiency decreases.

Meanwhile, the above-mentioned background technology is technical information that the inventor possessed for deriving the present invention or acquired in the process of deriving the present invention, and cannot necessarily be said to be known technology disclosed to the general public before filing the application for the present invention. .

Korean Patent No. 10-0341507

One aspect of the present invention is to store only specific coordinate values in advance, expand and complete the table using the specific coordinate values stored in advance during the scalar multiplication operation, and then use the completed table for the scalar multiplication operation, thereby achieving minimal PCL security with only a small amount of memory usage. Provides a method of creating and verifying electronic signatures for low-end PLCs that can guarantee performance.

The technical problem of the present invention is not limited to the technical problem mentioned above, and other technical problems not mentioned will be clearly understood by those skilled in the art from the description below.

The electronic signature generation and verification method for low-specification PLC according to an embodiment of the present invention improves the speed of electronic signature generation and verification while using less memory to improve the security of low-specification PCL (Programmable Logic Controller) in smart factories. .

The electronic signature generation and verification method for the low-end PLC is,

Creating a partial coordinate table in which only some fixed coordinates are stored among all fixed coordinates set for a scalar multiplication operation;

generating an extended coordinate table including all fixed coordinates by referring to the partial coordinate table;

performing a scalar multiplication operation based on the extended coordinate table; and

It includes generating a digital signature based on the result of the scalar multiplication operation.

According to one aspect of the present invention described above, rather than storing all of the feature coordinates, the feature coordinates are derived through an operation that selects the minimum number of bases and combines the selected bases, thereby generating a transfer signature while consuming less memory for data storage. and operation speed for verification can be guaranteed.

Figure 1 is a diagram illustrating a schematic configuration of a method for generating and verifying an electronic signature for a low-end PLC according to an embodiment of the present invention.
Figures 2 to 4 are diagrams showing a specific example of an electronic signature method using an elliptic curve.

The detailed description of the present invention described below refers to the accompanying drawings, which show by way of example specific embodiments in which the present invention may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. It should be understood that the various embodiments of the invention are different from one another but are not necessarily mutually exclusive. For example, specific shapes, structures and characteristics described herein may be implemented in one embodiment without departing from the spirit and scope of the invention. Additionally, it should be understood that the location or arrangement of individual components within each disclosed embodiment may be changed without departing from the spirit and scope of the invention. Accordingly, the detailed description that follows is not intended to be taken in a limiting sense, and the scope of the invention is limited only by the appended claims, together with all equivalents to what those claims assert, if properly described. Similar reference numbers in the drawings refer to identical or similar functions across various aspects.

Hereinafter, preferred embodiments of the present invention will be described in more detail with reference to the drawings.

Figure 1 is a flowchart showing a schematic flow of a method for generating and verifying an electronic signature for a low-end PLC according to an embodiment of the present invention.

The purpose of the electronic signature generation and verification method for low-specification PLC according to the present invention is to improve the speed of electronic signature generation and verification while using less memory in order to improve the security of low-specification PCL (Programmable Logic Controller) in a smart factory.

The currently widely used elliptic curve electronic signature signature generation/verification method often uses a scalar multiplication operation method that refers to a table.

In particular, in order to efficiently perform a scalar multiplication operation using a fixed point P when generating/verifying a signature, a pre-calculation table for the relevant coordinates is stored in advance, and the stored pre-calculation table is used during signature generation/verification operations.

At this time, the more pre-calculated points stored in the table, the faster the signature generation/verification speed.

For example, the memory and operation numbers used when storing a table in the P-256 elliptic curve are as shown in Table 1 below, and the calculation method is as shown in Figure 2.

[Table 1]

As such, in the case of the conventional table reference method, since the table is already created, stored, and used, the memory required to store the table is fixed and used only when performing the corresponding scalar multiplication operation, resulting in memory waste. Even so, there is a problem that if the table is created every time a scalar multiplication operation is performed, the efficiency of the operation decreases.

To solve this problem, the electronic signature generation and verification method for a low-end PLC according to the present invention does not store all feature coordinates, but selects the minimum number of bases and derives feature coordinates through an operation that combines the selected bases. This method is characterized by being able to improve the calculation speed to some extent while taking up less memory.

Specifically, the method for generating and verifying an electronic signature for a low-end PLC according to the present invention includes the steps of generating a partial coordinate table in which only some fixed coordinates are stored among all fixed coordinates set for a scalar multiplication operation (S100); Generating an extended coordinate table including all fixed coordinates by referring to the partial coordinate table (S200); performing a scalar multiplication operation based on the extended coordinate table (S300); and generating a digital signature based on the scalar multiplication operation result (S400).

In one embodiment, in the step of generating a partial coordinate table, (2^x)P is stored according to the window size. For example, if the window size is 4 in the P-256 elliptic curve, feature coordinates with features of (2^192)P, (2^128)P, (2^64)P, and P can be stored. .

In one embodiment, in the step of generating an expanded coordinate table including all fixed coordinates with reference to the partial coordinate table, the table may be expanded using the partial coordinate table previously stored according to the above-described embodiment.

For example, when expanding a table using (2^192)P, (2^128)P, (2^64)P, P, 15 tables are created from 4 coordinate tables as shown in Figure 3. It expands to and requires 11 ADDs. In cases like this, (2^64)P+P, (2^128)P+P, (2^192)P+P, (2^128)P+(2^64)P, (2^192)P+ (2^64)P, (2^192)P+(2^128)P, (2^128)P+(2^64)P+P, (2^192)P+(2^64)P+P, (2^192)P+(2^128)P+P, (2^192)P+(2^128)P+(2^64)P, (2^192)P+(2^128)P+(2^64) )The table can be expanded with P+P.

Specifically, the goal of table creation is to calculate the precomputation values of step 1 shown in Figure 2. When w=4 in Figure 2, the value to be calculated is [a_3, a_2, a_1, a_0]P. and a_3, a_2, a_1, and a_0 are 0 or 1.

In this case, the coordinate values to be stored are [1,0,0,0]P = (2^192)P, [0,1,0,0]P = (2^128)P, [0,0,1 ,0]P = (2^64)P, [0,0,0,1]P = P are stored, and the method of expansion is as follows.

[0,0,1,1]P = (2^64)P+P = [0,0,1,0]P + [0,0,0,1]P

[0,1,0,1]P = (2^128)P+P = [0,1,0,0]P + [0,0,0,1]P

[1,0,0,1]P = (2^192)P+P = [1,0,0,0]P + [0,0,0,1]P

[0,1,1,0]P = (2^128)P+(2^64)P = [0,1,0,0]P + [0,0,1,0]P

[1,0,1,0]P = (2^192)P+(2^64)P = [1,0,0,0]P + [0,0,1,0]P

[1,1,0,0]P = (2^192)P+(2^128)P = [1,0,0,0]P + [0,1,0,0]P

[0,1,1,1]P = (2^128)P+(2^64)P+P = [0,1,1,0]P + [0,0,0,1]P

[1,0,1,1]P = (2^192)P+(2^64)P+P = [1,0,1,0]P + [0,0,0,1]P

[1,1,0,1]P = (2^192)P+(2^128)P+P = [1,1,0,0]P + [0,0,0,1]P

[1,1,1,0]P = (2^192)P+(2^128)P+(2^64)P = [1,1,0,0]P + [0,0,1,0] P

[1,1,1,1]P = (2^192)P+(2^128)P+(2^64)P+P = [1,1,1,0]P + [0,0,0, 1]P

When doing this, the elliptic curve addition operation (ADD) is added 11 times.

Here, the elliptic curve addition operation (ADD) is calculated using the following equation and the algorithm shown in FIG. 4.

[Equation]

In some other embodiments, the method of generating and verifying an electronic signature for a low-end PLC according to the present invention may further include the step of encrypting a pre-stored partial coordinate table (not shown).

The encryption step converts the data constituting the partial coordinate table into a data matrix composed of columns and rows of a predetermined size and sets a two-dimensional coordinate value for each bit listed according to the data matrix.

Afterwards, in the encryption step, a data matrix consisting of columns and rows of a predetermined size is imaged, at least one feature point is extracted from the image, and the partial coordinate table is encrypted by shifting each bit listed according to the data matrix based on the extracted feature point. can do.

Specifically, the encryption step may list the bit strings constituting the partial coordinate table as a matrix of a predetermined size.

For example, in the encryption stage, the bit strings that make up the partial coordinate table are listed so that up to 10 bits are listed horizontally, with the first to tenth bits listed in column 1 and the eleventh to twentieth bits in column two, making n columns. Bits can be arranged according to the constructed matrix.

At this time, the encryption step gives the two-dimensional coordinate value of the first mapped data area (1, 1), and secondly, the two-dimensional coordinate value of (1, 2) is given to the listed data, and in this way, the last Arranged data may be assigned two-dimensional coordinate values of (n, m).

Afterwards, the encryption step may convert the data matrix information into an image.

The encryption step divides the generated (converted) image into at least two regions. In one embodiment, the encryption step may split the image into two regions according to a preset region. In one embodiment, the encryption step generates a first feature point group by extracting at least three feature points from the first area of the generated image, and creates a second feature point group by extracting three feature points from the second region.

The encryption step generates a first feature shape connecting at least three feature points constituting the first feature point group, and generates a second feature figure connecting at least three feature points constituting the second feature point group.

Afterwards, in the encryption step, the center of gravity of the first feature shape is extracted and set as the first center of gravity, and the center of gravity of the second feature figure is extracted and set as the second center of gravity.

Subsequently, the encryption step displays the first center of gravity and the second center of gravity on the image, sets the horizontal axis pixel coordinate value of the first center of gravity to a first random number, and sets the horizontal axis pixel coordinate value of the first center of gravity to a first random number. The vertical axis pixel coordinate value is set to a second random number, the horizontal axis pixel coordinate value of the second center of gravity is set to a third random number, and the vertical axis pixel coordinate value of the second center of gravity is set to a fourth random number. .

In the encryption step, each bit constituting the data matrix is horizontally shifted by a fourth random number and then vertically shifted by a first random number to generate primary transformation matrix data.

Finally, in the encryption step, each bit string constituting the first transformation matrix data is horizontally shifted by a second random number and then vertically shifted by a third random number to generate secondary transformation matrix data.

In one embodiment, the encryption step may implement an encryption and decryption procedure using a lightweight encryption and decryption algorithm such as ARIA (Academy Research Institute Agency), ECC (Elliptic Curve Cryptosystem), etc.

Meanwhile, in the encryption step, the data matrix is shifted and the encrypted firmware is transmitted, and the four random number information generated by the encryption step are transmitted together to the ECU.

Accordingly, the ECU can perform a firmware update process by demodulating the transformed matrix data into the original matrix based on the received random number information.

As such, the technology according to the present invention may be implemented as an application or in the form of program instructions that can be executed through various computer components and recorded on a computer-readable recording medium. The computer-readable recording medium may include program instructions, data files, data structures, etc., singly or in combination.

The program instructions recorded on the computer-readable recording medium may be those specifically designed and configured for the present invention, or may be known and usable by those skilled in the computer software field.

Examples of computer-readable recording media include magnetic media such as hard disks, floppy disks and magnetic tapes, optical recording media such as CD-ROMs and DVDs, and magneto-optical media such as floptical disks. media), and hardware devices specifically configured to store and perform program instructions, such as ROM, RAM, flash memory, etc.

Examples of program instructions include not only machine language code such as that created by a compiler, but also high-level language code that can be executed by a computer using an interpreter or the like. The hardware device may be configured to operate as one or more software modules to perform processing according to the invention and vice versa.

Although the above has been described with reference to embodiments, those skilled in the art will understand that various modifications and changes can be made to the present invention without departing from the spirit and space of the present invention as set forth in the following patent claims. You will be able to.

Claims (3)

In order to improve the security of low-end PLCs (Programmable Logic Controllers) in smart factories, an electronic signature generation and verification method for low-end PLCs that improves the speed of creating and verifying electronic signatures while using less memory,
The electronic signature generation and verification method for the low-end PLC is,
Creating a partial coordinate table in which only some fixed coordinates are stored among all fixed coordinates set for a scalar multiplication operation;
generating an extended coordinate table including all fixed coordinates by referring to the partial coordinate table;
performing a scalar multiplication operation based on the extended coordinate table; and
Including generating a digital signature based on the result of the scalar multiplication operation,
The step of generating the partial coordinate table is,
The number of feature coordinates is determined according to the window size, but in the P-256 elliptic curve, if the window size is 4, the feature values of (2^192)P, (2^128)P, (2^64)P and P are Characterized by storing feature coordinates,
The step of generating an extended coordinate table containing all fixed coordinates by referring to the partial coordinate table,
Characterized in that the operation result value of the extended coordinate table is determined based on the result of the elliptic curve addition operation according to the following equation,

[Equation]


The electronic signature generation and verification method for the low-end PLC is,
further comprising encrypting the pre-stored partial coordinate table,
The step of encrypting the pre-stored partial coordinate table includes:
The data constituting the partial coordinate table is converted into a data matrix composed of columns and rows of a predetermined size, and two-dimensional coordinate values are set for each bit listed according to the data matrix,
Characterized by imaging a data matrix composed of columns and rows of a predetermined size, extracting at least one feature point from the image, and encrypting the partial coordinate table by shifting each bit listed according to the data matrix based on the extracted feature point. , Electronic signature generation and verification method for low-end PLC.

delete delete