KR100865678B1 - method and system for fast inversion of high-speed public-key crypto system - Google Patents

Abstract

Fast Multiplication Inverter Method and System of Fast Public Key Cryptosystem in Finite Field GF (p) That Can Improve the Computation Speed of Multiply Inverter by Using Addition / Subtraction and Shift Only This is disclosed. The present invention does not require modular operation or multiplication / division in the multiplication inverse operation operation, which occupies the most in the operation time in the finite field GF (p) during encryption operation, and uses only addition, subtraction, and shift to increase the calculation speed. There is an advantage that can be improved. In addition, the computational speed can be increased by reducing the iterative operation compared to other inverted methods.

Description

Method and system for fast inversion of high-speed public-key crypto system

1 is an overall configuration diagram of a general public key cryptosystem.

2 is a schematic flowchart for performing a fast multiplication inverse in a public key cryptosystem in a finite field GF (p) according to the present invention.

3 is a schematic diagram of a fast multiplication inverse system in a finite field GF (p) according to the present invention.

4 is a flowchart illustrating a method of changing an input / output domain in the fast multiplication inverse circuit of FIG. 3.

 <Explanation of symbols for the main parts of the drawings>

100: public key cryptosystem 110: main controller

120: arithmetic control unit 130: arithmetic unit

140: program memory 150: program memory

201: control unit 202, 206: MUX

204: Register 208: Correction unit

The present invention relates to a fast multiplication inverse method and system of a fast public key cryptosystem in finite field GF (p), and more specifically, to perform a multiplication inverse operation operation using only addition / subtraction and shift. The present invention relates to a fast multiplication inverse method and system of a fast public key cryptosystem that can improve the computation speed of a multiplier inverse.

In general, a public key cryptosystem refers to an asymmetric method that uses different keys during encryption and decryption among encryption methods for maintaining security on the Internet. In other words, the public key cryptosystem consists of a public key used by others to encrypt a message and a private key used to restore a ciphertext to the original message. When sending a message, the message is sent with the private key and the value calculated by the encryption algorithm. The receiver then checks the authenticity of the message by using the public key to reverse the calculation.

These public key cryptosystem operations basically include finite field operations, which determine the efficiency of the cryptosystem. The execution time of the public key cryptosystem is the most frequent multiplication and inversion operation. Among these, inversion operation is the subject of many studies because it has more time complexity than multiplication. In finite field GF (p), the inverse operation is nonzero and the inverse x- ¹ of element x of GF (p) is element y satisfying xy = 1.

The inverse computation of the finite field GF (p) is mainly based on the extended euclidean algorithm and Montgomery inverse algorithm. In 1997 finite field GF (p) presented simple algorithmic methods for modular inversion. It is a binary version of the extended Euclidean modular inversion method. This method calculates the inverse by performing an iteration based on the input value and performing a shift operation, addition or subtraction operation on a given finite field.

The Euclidean modular inversion method is faster than the conventional binary inversion method. In addition, three adders and subtractors can be used to implement the hardware required for the operation of the binary version of the extended Euclidean modular inversion method.

However, the Euclidean modular inversion method has a problem in that unnecessary processing operations and specific processing operations cannot perform any processing operations, resulting in inefficient processing.

The present invention has been invented to solve the above problems, and does not require modular operation or multiplication / division in multiplication inverse operation operation used in public key cryptosystem in finite field GF (p). The purpose of the present invention is to improve the computation speed by using only the shift, and to provide an efficient multiplication inverse method in the finite field GF (p) of the public key cryptosystem, which is an improvement over the conventional multiplication inverse method, and a high speed inverse unit for performing the same. .

The present invention for achieving such an object,

p is a non-zero decimal number, when input value x∈ (0, p), p is u variable, x is v variable, 0 is input to r variable, and 1 is input to s variable;

If the value input to the u variable is even, the result of dividing r by 2 and then modular p for the variable r, and the result of dividing u by 2 for the u variable, and if the value input to the variable v is even, repeating a process of inputting a result of dividing s by 2 and then performing a modular p on the variable s and a result of dividing v by 2 on the variable v;

 If the input of u variable and v variable is odd, and the input of u variable is greater than the input of v variable, input the result of dividing the value of v variable by 2 by subtracting the input value of u variable into the u variable, r-adding the input value of the variable r and the input value of the variable s by r and dividing the result by two and inputting the result of modular p;

If the input of u and v variables is odd and the input of the u variable is less than the input of the variable v, then the input of the variable v is divided by 2 by subtracting the input of the variable u from the input of the variable v. Inputting the result of adding the result of the variable s and the value of the variable r to the variable s, dividing the result by two, and inputting the result of the modular p; And,

If the input value of the v variable is 1, selecting the value of the variable of s as an output value y.

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

1 is a schematic diagram of a general public key cryptosystem, and FIG. 2 is a schematic flowchart for performing a fast multiplication inverse in a public key cryptosystem in a finite field GF (p) according to the present invention. 3 is a schematic configuration diagram of a fast multiplication inverse circuit in the finite field GF (p) according to the present invention, and FIG. 4 is a flowchart illustrating a method of changing an input / output domain in the fast multiplication inverse circuit of FIG. 3. to be.

As shown in FIG. 1, the public key cryptosystem 100 includes a main controller 110 including a program memory 140, an arithmetic control unit 120, and a computing device 130 including a data memory 150. do. The main controller 110 receives a control signal from a host system (not shown) and controls the operation controller 120. The arithmetic unit 130 under the control of the arithmetic controller 120 performs addition, square power, multiplication, and inversion in GF (p).

Traditional modular inversion methods generally include the modular exponent method and the extended Euclidean method, which include complex computational operations such as multiplication, squares, and division. slow.

As shown in FIG. 2, p is a non-zero prime number in an input condition, and p is a u variable, when the input value x∈ (0, p) is shown in FIG. 2. x is input for v variable, 0 for r variable, and 1 for s variable. (Step S1)
In step S1, if the value input to the u variable is even, the result of dividing r by 2 and then modular p is input to the r variable, and the result of dividing u by 2 is input to the u variable (steps S2 to S3).

In addition, in step S1, if the value input to the v variable is even, the result of dividing s by 2 and then modular p is input to the s variable, and the result of dividing v by 2 is input to the v variable (steps S4 to S5).

delete

If after step S2 and after step S4 the inputs of the u and v variables are not even, that is, when the inputs of the u and v variables are odd, if the input of the u variable is greater than the input of the v variable (step S6), For the u variable, subtract the input value of the v variable from the input value of the u variable and divide the result by 2, and for the r variable, divide the input value of the r variable and the input value of the s variable by 2, and then modular p. The result is entered and the process returns to step 2 (step S7).

When the input of the u variable and the v variable is odd after steps S2 and S4, if the input value of the u variable is smaller than the input value of the v variable (step S6), the input of the v variable is determined from the input value of the v variable. Subtract the input value of the variable u by dividing by 2 and input the result of the variable s and the value of the variable r by adding to the variable s, divide the value by 2, enter the result of modular p, and return to step 4. (Step S8)

Then, after step S4, if the input value of the v variable is 1 (step S9), the value of the variable of s becomes the output value y (step S10).

The fast multiplication method in the public key cryptosystem according to the present invention uses the fact that the result of subtraction of odd data and odd data is even, and when two variables are odd, the median value is reduced by subtraction of two variables. The even middle value generated as a result of subtraction is characterized by the fact that the shift operation is performed all at once in the next iteration operation.

 That is, in the conventional multiplication inverse method, if one of the input values of the u and v variables is even and the other is odd, the above step S2 to S3 or S4 to S5 should be executed once more. When the input value of the u or v variable is divided by 2, only the above steps S2 to S3 or S4 to S5 are executed repeatedly, resulting in a decrease in computational speed, while a fast multiplication station in the finite field GF (p) according to the present invention. The method is to reduce the number of repetitions of the operation by using a structure that can process the shift operation performed in the iterative operation of the next step after subtraction after the input value of the u and v variables is odd.

<Table 1> Comparison of Mean Computations According to Multiplication Inverse Methods

Bits Operation count Efficiency increase rate Sun's Zhou's The present invention Sun (%) Zhou (%) 128 1064 649 424 60.2 34.7 160 1336 816 553 58.6 32.2 192 1607 983 658 59.0 33.1 224 1878 1150 763 59.4 33.7 256 2149 1317 876 59.2 33.5 384 3233 1984 1344 58.4 32.3 521 4425 2723 1715 61.2 37.0

<Table 1> shows the average amount of calculation for the number of bits when comparing the multiplication inverse in the finite field GF (p) according to the present invention and the multiplication inverse developed by the conventional Zhou and Sun. As shown in Table 1, the result of the comparison shows that the multiplication inverse method according to the present invention has a smaller average count than the conventional methods developed by Sun and Zhou.

 As shown in FIG. 3, the multiplicative inverse system for performing the fast multiplication inverse method according to the present invention does not constitute an adder or a subtractor, unlike the conventional inverse device, and has an odd number for fast calculation of input variable values ( A control unit 201 is formed for selecting the calculation method of odd and even discrimination and addition / subtraction. The first to fourth MUXs 202A to 202D receive the decimal value p of the finite field GF (p), the modular inverse x, and the initial variables 0 and 1 which are input variables for the multiplication inverse calculation and are controlled by the controller 201. Print the selected value. On the output side of the first to fourth MUXs 202A to 202D, the control unit 201 receives the selected input variable value, the shifted variable value, and the output value through the correction unit as the variables u, v, r, and s, respectively. First to fourth registers 204A to 204D for storing and shifting operations are connected.

Shift values and initial variables of the variables u, v, r, and s stored in the first to fourth registers 204A to 204D in response to the control signal of the control unit 201 on the output side of the first to fourth registers 204A to 204D. Fifth to sixth MUXs 206A to 206B for selecting and outputting 0 and p values are connected. A correction unit 208 that receives the control signal of the control unit 201 and performs addition and subtraction of each variable output from the fifth to sixth MUXs 206A to 206B on the output side of the fifth to sixth MUXs 206A to 206B. Is connected.

The multiplicative inverse system according to the present invention has a simple structure according to the repetition of shift, addition and subtraction operations. The first to fourth registers 204A to 204D, which receive the values of the variables u, v, r, and s for the multiplication inverse, are set to predetermined initial input values, and the first to fourth MUXs 202A to 202D are even. (even) and odd (odd) are discriminated, and the data selected by the control unit 201 is output. In the multiplicative inverse system according to the present invention, the first to fourth registers 204A to 204D use the shift register without using a divider having a large delay to obtain u / 2, v / 2, r / 2, and s / 2 values. To get a fast value. The correction unit 208 is composed of one adder without a separate subtractor to add or subtract two input values. At this time, the controller 201 determines whether to add or subtract data from the first to fourth registers 204A to 204D or output a data value according to the even and odd discrimination conditions. The correction unit 208 outputs through the s register 204D when the condition is satisfied, and inputs to each register otherwise.

The multiplication inverse system in the finite field GF (p) according to the present invention is capable of expanding the input and output domains, as shown in FIG. Do. By default, for integer domain output for integer domain input conditions, x ^-1 , the result of modular inversion for integer domain input x, is determined as integer domain output. Montgomery domain input x2 ⁿ is output to Montgomery domain x ^-1 2 ⁿ by the Montgomery product and modular inversion method. Here, Montgomery Product and Modular Inversion method allow not only I / O between the same domain but also I / O between different domains. It is also possible to extend from an integer domain input to a Montgomery domain output and from a Montgomery domain input to an integer domain output. This extension can increase the efficiency of the public key cryptosystem.

As described above, the fast multiplication inverse method in the finite field GF (p) according to the present invention does not require multiplication inverse operation operation modular operation or multiplication / division in the finite field GF (p). Therefore, there is an advantage that the operation speed can be improved by using only the shift. In addition, it is possible to increase the computation speed by reducing the iterative operation compared to other inverted methods, which can be effectively used for a public key encryption system requiring high speed.

Although the preferred embodiments of the present invention have been described in detail with reference to the accompanying drawings, the present invention is not limited thereto and may be improved or modified by those skilled in the art within the scope of the technical idea of the present invention.

Claims (2)

Ⅰ) p is a nonzero fractional number, when input value x∈ (0, p), p is a u variable, x is a v variable, 0 is input to r variable, and 1 is input to s variable (S1 ); Ii) After step iv, if the value input to the u variable is even, the result of dividing r by 2 and then modular p is input to the r variable, and the result of dividing u by 2 is input to the u variable, and the v If the value input to the variable is even, repeating the process of inputting the result of modular p after dividing s by 2 for the s variable and the result of dividing v by 2 for the v variable (S2 to S5); Iii) after step ii, if the input of the u variable and the v variable is odd and the input of the u variable is greater than the input of the v variable, then the u variable is subtracted from the input value of the u variable. Inputting the result obtained by dividing by 2, adding the input value of the variable r and the input value of the variable s to the variable r, dividing by 2, inputting the result of the modular p, and returning to step ii; (S6 S7) Iii) after step ii, if the input of the u variable and the v variable is odd and the input value of the u variable is less than the input value of the v variable, then the input of the v variable takes the input value of the u variable from the input value of the v variable. Subtracting the result of dividing by 2, inputting the value of the variable s and the value of the variable r into the s variable, dividing by 2, inputting the result of modular p, and returning to step ii; S6, S8) and Iv) after the step ii, if the input value of the v variable is 1, selecting the value of the variable of s as the output value y; (S10). A control unit 201 for determining odd and even of the input variable values, selecting an addition / subtraction operation method, and performing control for multiplicative inverse calculation; First to fourth MUXs 202A to 202D for outputting selected values by receiving non-zero fractional values, input values x, 0, and 1 according to control signals of the control unit 201; It is connected to the output side of the first to fourth MUXs 202A to 202D and receives p, input values x, 0, and 1, respectively, as non-zero fractional values, and stores them as variables u, v, r, and s, respectively, and shifts them. First to fourth registers 204A to 204D for operation; Are connected to the output side of the first to fourth registers 204A to 204D and receive control signals from the controller 201 to store the values of the variables u, v, r, and s stored in the first to fourth registers 204A to 204D. Fifth to sixth MUXs 206A to 206B for selecting and outputting the selected outputs; And, A beam connected to an output side of the fifth to sixth MUXs 206A to 206B and receiving a control signal from the control unit 201 to perform addition and subtraction operations for each variable output from the fifth to sixth MUXs 206A to 206B. A fast multiplication inverse system of a fast public key cryptosystem, including a government (208).

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