KR100939356B1 - Apparatus and method for modular multiplier - Google Patents

Abstract

The present invention relates to a modular multiplication device and method thereof.

In the present invention, data is received from the outside and a control signal is generated using the received data. After selecting one of the at least one functional unit to access the memory using the generated control signal, the selected functional unit is allowed to access the memory. Subsequently, when the selected function unit repeatedly performs a modular multiplication operation in units of words, at least one result value generated during the operation is stored in the memory. Then, the result of the multiplication operation performed is transmitted to the outside.

As such, during the continuous word-based modular multiplication process, by controlling the built-in memory directly, it is possible to eliminate the time delay due to data input and output.

Encryption, Modular, Arithmetic, Exponential, Time Delay, Memory, Interface

Description

Modular multiplication apparatus and its method {APPARATUS AND METHOD FOR MODULAR MULTIPLIER}

The present invention relates to a modular multiplication apparatus and a method thereof, and more particularly, to a modular multiplication apparatus and a method of a mobile communication system.

The present invention is derived from the research conducted as part of the IT growth engine technology development project of the Ministry of Information and Communication and the Ministry of Information and Telecommunication Research and Development. [Task Management Number: 2006-S-041-02, Title: Security and Reliability of Next Generation Mobile Terminals] Develop common security core modules for services.

Recently, with the rapid increase of security threats to various mobile communication terminals including computer systems, solutions have been reviewed and developed from various angles.

Dual, public key cryptographic algorithm, RSA (Rivest-Shamir-Adleman, three co-inventor names, hereinafter referred to as 'RSA') cryptographic algorithm can be implemented through modular exponentiation, which is possible through iterative modular multiplication. .

In general, Montgomery's algorithm is used mainly for fast iteration of modular multiplication. In particular, in order to apply the RSA encryption algorithm on a system with limited hardware resources, such as a mobile Trusted Platform Module (TPM), a word that is calculated by dividing the data into units of words instead of processing all the data at once. The word-base Montgomery algorithm is used.

Accordingly, the modular multiplier designed by applying the word-based Montgomery algorithm also performs operations in units of words. However, in order to calculate the entire data using the modular multiplier, the input and output operations of the system and the modular multiplication period must be repeatedly performed under the control of the system.

However, the time delay caused by repetitive data input / output operations between the system and the modular multiplication period is an important cause of degrading the overall modular multiplication regardless of the performance of the modular multiplier itself.

However, since the time required for data input / output is a unique interface performance of a system that cannot be improved, it is necessary to increase the operation speed of the modular multiplier itself as a method for improving performance, and expect a significant performance improvement of the modular multiplication operation. Is very difficult.

That is, in the case of a system requiring a high speed and a low area at the same time as a mobile communication terminal, the modular multiplier using the Montgomery algorithm of word units as it is, there is a problem that can not show satisfactory performance.

It is an object of the present invention to provide an apparatus and method for eliminating the time delay caused by repetitive data input / output required to perform a modular multiplication operation of the total data size.

Modular multiplication apparatus according to the characteristics of the present invention for achieving this object, the modular multiplication unit for repeatedly performing a modular multiplication operation; A memory configured to store at least one result value generated during the operation process; And after synchronizing with the modular multiplier using any one of the result values, storing a value output from the modular multiplier in the memory according to the matched synchronization, and at least one requesting the modular multiplier. And a modular interface unit for reading a value from the memory and providing the value to the modular multiplier.

In addition, the modular multiplication method according to another aspect of the present invention, after synchronizing the signals input from the outside, generating a signal for accessing the memory through the matched signal; Reading a value stored at an address in the memory requested from the outside using the generated signal, and then outputting a control signal notifying the read value and the read value to the outside; Synchronizing with a function unit that performs a modular multiplication operation through a predetermined value, and storing at least one of output values of the function unit in the memory according to the matched synchronization; Reading a value stored in an address of the memory requested by the function unit and providing the value to the function unit; Generating a control signal using any one of the signals input from the outside, and then selecting any one of the functional units to access the memory using the generated control signals; And transmitting a signal of the selected functional unit to the memory, and transmitting a value output from the memory to any one of the functional units to access the memory.

According to the present invention, through the data input and output between the built-in memory and the modular interface, by directly controlling the memory during the continuous word-based modular multiplication process, it is possible to eliminate the time delay due to the data input and output.

In addition, the modular exponential operation may be sequentially performed by changing or updating a value stored in a segment of an embedded memory.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings so that those skilled in the art may easily implement the present invention. As those skilled in the art would realize, the described embodiments may be modified in various different ways, all without departing from the spirit or scope of the present invention. In the drawings, parts irrelevant to the description are omitted in order to clearly describe the present invention, and like reference numerals designate like parts throughout the specification.

Throughout the specification, when a part is said to "include" a certain component, it means that it can further include other components, except to exclude other components unless specifically stated otherwise. In addition, the terms “… unit”, “… unit”, “module”, etc. described in the specification mean a unit that processes at least one function or operation, which may be implemented by hardware or software or a combination of hardware and software. have.

First, the Montgomery modular multiplication algorithm applied to an embodiment of the present invention will be described. For reference, since the basic equations for RSA (Rivest-Shamir-Adleman, RSA) operation and modular multiplication are easily understood by those skilled in the art, detailed descriptions thereof are omitted.

Montgomery multiplication algorithm is a method of modular multiplication by using the surplus coefficient r to transfer the calculation from the integer Z _n area to the rZ _n area, without using the classical division of quotient and remainder. .

R = A × B × r ^-1 modN

In order to implement Equation 1, a word-base Montgomery algorithm, which is divided into arbitrary word units, is performed by Equation 2 below.

Step 1: R = 0

Step 2: for i = 0 to p-1 {

Step 3: R = R + A × B _i (B _i is w-bit word)

m = R ₀ × N ₀ ^* mod2 ^w (N ₀ × N ₀ ^* = -1 mod2 ^w )

             R = R + N * m

R = R / 2 ^w

       }

Step 4: if (R> N) R = R-N

Step 5: return (R)

In addition, the method of processing the Montgomery algorithm correction factor m in the stepwise calculation without a separate calculation process in Equation 2 is as shown in Equation 3 below.

Step 1: R = 0, T = 0

Step 2: for i = 0 to p-1 {

             Carry_pre = 0, Carry_next = 0

Step 3: for j = 0 to p-1 {

If (i == 0) R _j = 0 (R _j is the size of w + 1 bits)

Else R _j = T _j (T _j is the size of w bits)

Step 4: for b = 0 to w-1 {(where b is bit order)

R _j = R _j + A _{jb ×} B _i

if (j == 0) m _b = R _j0 (m is the size of w bits)

else m _b = m _b

R _j = R _j + m _{b ×} N _j

Shift_data _b = R _j0 (shift_data is the size of w bits)

R _j = R _j / 2

        end for b

Step 5: (Carry_pre, T _j ) = R _j + Carry_pre

(Carry_next, T _j -1) = T _j -1 + Shift_data + Carry_next

        } end for j

 } end for i

Step 6: If (T> N) T = T-N (where T is the size of n + 1 bits including the last carry)

Step 7: return (T)

When determining the arbitrary number of bits w in the equation (3), it can be implemented in the form of n '= w × p with the number of bits n' (n '≥ n + 2) larger than the total bit n as the total number of bits Make sure At this time, p is an arbitrary integer and the value of the bit larger than n is 0.

This allows the resulting values to be represented all within a given bit size since the result of the modular operation is always less than 2N.

And, considering that the modular multiplier according to an embodiment of the present invention is a device for modular exponential power only, if the calculation is performed with a bit number larger than 2 bits, N in each result value when the result of the modular multiplication operation is greater than N The result of the final modular exponential power always results in a value less than N, even if the comparison process without subtracting is performed.

Therefore, Step 6 of Equation 3 may be omitted when implemented in hardware. In the case of the system considered in the embodiment of the present invention, a modular multiplication apparatus designed in units of arbitrary words based on Equation 3 is applied.

Then, the system to which the present invention is applied will be described first.

1 is a diagram showing the configuration of a system to which the present invention is applied.

As shown in FIG. 1, the system 100 to which the present invention is applied includes a central control unit (CPU) 110 and a memory (RAM) 120, and according to an embodiment of the present invention, a modular multiplier, 200).

In detail, the central control apparatus 110 obtains necessary data from the memory 120 and transmits the obtained data to the modular multiplication apparatus 200 in order to perform the modular multiplication process.

The modular multiplication apparatus 200 continuously performs word-base modular multiplication based on the received data, and then informs the central control apparatus 110 of the result. Then, the central control unit 110 transfers and stores the received result to the memory 120.

As such, the modular multiplication apparatus 200 according to an embodiment of the present invention performs input / output operations with the central control apparatus 110 only for initial data input and result value transfer. In addition, while continuously performing the word-base modular multiplication process, the input / output operation with the central control unit 110 for outputting the intermediate result value generated after every word-unit modular multiplication and inputting a new word unit is not performed at all. Do not. This may eliminate or reduce the time delay caused by the input / output operation.

Next, the modular multiplication apparatus 200 illustrated in FIG. 1 will be described.

2 is a diagram showing the structure of a modular multiplication apparatus according to an embodiment of the present invention.

As illustrated in FIG. 2, the modular multiplication apparatus 200 according to an exemplary embodiment of the present invention includes a modular interface 210, a modular multiplier 220, and a memory 230 (mmRAM).

The modular interface 210 includes a system input / output control unit 211, a modular input / output control unit 212, and a memory input / output control unit 213. The modular multiplier 220 includes an input register 221, 222, 223, 224, a modular controller 225, a modular hardware core 226, a status register 227, and an output register 228, 229.

Specifically, the modular interface 210 is responsible for the interface between the central control unit 110, the memory 230 and the modular multiplier 220. In addition, the central control apparatus 110 recognizes that the modular multiplication apparatus 200 according to the embodiment of the present invention operates as a normal peripheral device having a memory map as large as the memory 230.

In addition, the modular interface 210 enables the modular multiplier 220 to continuously input and output data, thereby allowing continuous words without a time delay due to data input and output between the modular interface 210 and the modular multiplier 220. Enables word-base modular multiplication.

First, the system input / output control unit 211 of the modular interface unit 210 is responsible for input and output between the system (hereinafter referred to as the 'central control unit') and the modular interface unit 210, the central control unit 110 and the modular interface unit Process various signals input and output between the 210 and 210.

That is, the system input / output control unit 211 synchronizes the control and address signals input from the central control unit 110, and the signals A_bus and C_bus approaching the memory 230 through the synchronized signals. )

For reference, A and C of signals denoted by A_xxx, C_xxx, etc. mean an address and a control signal, respectively.

In addition, the system input / output controller 211 transfers the data Data input from the central controller 110 to the memory input / output controller 213 (Di_bus).

In addition, the system input / output control unit 211 reads a status value input from the modular input / output control unit 212 and a desired address value in the memory 230 at the request of the system output from the memory input / output control unit 213. The input value Do_bus is output to the central control unit 110. Then, the control signal Co_bus informing of this is output to the central control device 110.

For reference, Di and Do of values denoted by Di_xxx and Do_xxx mean input data and output data, respectively. In addition, Co of a value denoted by Co_xxx means an output control signal.

In addition, the system input / output controller 211 reads an initial value from the memory 120 of the system and records the initial value in the memory 230 of the modular multiplication apparatus 200 in the process of modular multiplication. When the modular multiplication is completed, the final output value stored in the memory 230 is read and transmitted to the memory 120 of the system.

Next, the modular input / output controller 212 performs a function of accurately accessing the memory 330 at an appropriate point in time according to the operation flow of the modular multiplier 220.

That is, the modular input / output controller 212 synchronizes with the modular multiplier 220 based on a status value output from the modular multiplier 220, and a signal for accessing the memory 230 through the synchronization signal. Create (A_mm, C_mm).

The modular input / output controller 212 selects two output values (pre_sum and post_sum) of the modular multiplier 220 as one signal Di_mm according to a synchronization signal, and transmits the selected signals to the memory input / output controller 213. .

In addition, the input data (mm_input_data) of the modular multiplier 220 is converted into a value Do_mm stored at a desired address in the memory 230 at the request of the modular multiplier 220, which is a value output from the memory input / output controller 213. Will output

That is, in the modular multiplication operation, the modular input / output controller 212 reads an input value from the memory 230 and writes an output value in the memory 230 each time the modular word multiplication is performed.

Next, the memory input / output control unit 213 performs a function of selecting one of the memory 230 access request of the system input / output control unit 211 and the memory 230 access request of the modular input / output control unit 212.

First, the memory input / output controller 213 generates a control signal for selection through a specific value input from the central control apparatus 110, and generates a signal mm_input_ctrl driving the modular multiplier 220. Based on the generated control signal, one of two types of input signals related to the memory 230 received from the system input / output controller 211 and the modular input / output controller 212 is selected and transmitted to the memory 230. .

In addition, the memory input / output controller 213 transmits data output from the memory 230 to either the central controller 110 or the modular multiplier 220 based on the control signal.

That is, the memory input / output controller 213 is responsible for access to the memory 230 in the process of modular multiplication, and is responsible for data input / output of the memory 230, and is responsible for driving the modular multiplication unit 220.

Next, the modular multiplier 220 performs an operation according to Equation 3 mentioned above. First, the modular multiplier 200 receives a control signal mm_input_ctrl, which is a signal including information about the number of driving and operations of the modular multiplier 220 from the modular interface 210.

When the received control signal is input to the modular controller 225, the modular controller 225 controls the operation of the entire modular multiplier 220 based on the input control signal.

In addition, when the data (mm_input_data) for performing a word-base operation is input from the modular interface unit 210, the modular controller 225 receives the input data according to the generated signal (input_reg_ctrl). , 222, 223, 224).

For reference, the four input registers 221, 222, 223, and 224 are configured as two stage registers, so that the input data is stored in advance in the next word operation. This minimizes the input / output delay between the modular interface 210 and the modular multiplier 220.

The modular hardware core unit 226 performs a word-based modular multiplication operation based on the input data. In this case, values (pre_sum and post_sum) corresponding to T _j and T _{j −1} of step 5 of Equation 3 described above are generated, respectively. The modular hardware core unit 226 outputs each value to an output register (pre_sum output register). , post_sum output register, 228, 229).

Then, the data is stored in the corresponding area of the memory 230 via the modular interface 210.

In addition, the modular hardware core unit 226 stores all the status values of the calculation process in a status register 227, and transmits the stored values to the modular interface unit 210 to generate a new input signal mm_input_ctrl. To be used. For reference, the above process is repeated to complete the entire modular multiplication process by modular multiplication in word units.

As such, the modular multiplication apparatus according to the embodiment of the present invention separately embeds a memory therein. And, while performing a continuous word-base modular multiplication process, it performs data input and output between the built-in memory and the modular interface. In other words, by directly controlling the memory, a high-speed data input / output processing is possible by eliminating the time delay caused by the data input / output.

In addition, according to an embodiment of the present invention, the modular exponential operation may be sequentially performed by changing or updating a value stored in the segment by optimizing and assigning a segment in the embedded memory to a modular exponential operation for the RSA operation.

In addition, when not driving the modular multiplication apparatus according to an embodiment of the present invention, by allowing the system to use the built-in memory, it also has a value as a memory that can be utilized by the system.

Next, a modular exponentiation process according to an embodiment of the present invention will be described based on the modular multiplication apparatus having the above-described structure.

3 is a flowchart sequentially illustrating a process of performing a modular exponential power of the modular multiplication apparatus illustrated in FIG. 2.

For reference, FIG. 3 is a flowchart illustrating a modular exponential calculation process for performing an RSA operation, centering on a segment value in the memory 230.

As shown in FIG. 3, when the modular exponential operation is started, the modular multiplier 220 first stores basic input data in a segment in the designated memory 230 (S301). Here, the memory 230 composed of segments and Equation 4 will be described.

FIG. 4 is a diagram illustrating the structure of a memory illustrated in FIG. 2.

As shown in FIG. 4, the memory 230 according to an embodiment of the present invention basically has seven segments 231, 232, 233, 234, 235, 236, and 237.

For reference, an embodiment of the present invention applies the L-R binary method, which is the most basic modular exponential method.

Specifically, the L-R binary method, which is a modular exponential method, is represented by Equation 4 below.

Inputs: N (modulus), e (exponent), M (message), R2modN (mapping factor)

Step 1: MRmodN = MM (M, R ² modN), C = 1RmodN = MM (1, R ² modN)

Step 2: for i = n-1 to 0 do {

            C = MM (C, C)

If (e _i = 1) then

              C = MM (C, MRmodN)

            else C = C}

Step 3: C = MM (C, 1)

Step 4: return (C)

Output: C = M ^e modN, 0≤C <N

All input and output values and intermediate values generated in the course of the steps of Equation 4 are stored in the memory 230, and the memory 230 is composed of seven segments as mentioned above for storing the corresponding values. do.

Thereafter, the modular multiplier 220 performs two mapping processes performed in step 1 of Equation 4, which will be described later. First, a predetermined value MRmodN is calculated and stored in a segment of the memory (S302).

Thereafter, the modular multiplier 220 calculates a predetermined value 1RmodN and stores the calculated value in the segment 4 235 (S303).

In order to perform the subsequent operation, the modular multiplier 220 initializes a required flag value to 0 and assigns a bit size of an exponent value key to a count (S304).

Subsequently, the modular multiplier 220 performs a square operation performed in step 2 of Equation 4 (S305), and then checks whether the key bit value corresponding to the current count is 1 (S306). If the key bit value is 1 as a result of the check, the predetermined value MRmodN and the current value are modularly multiplied (S307).

On the other hand, if the key bit value corresponding to the current count is not 1, the modular multiplier 220 toggles the flag value (S308).

Thereafter, the modular multiplier 220 checks whether the count value is 0 (S309), and if the counter value is not 0, decreases the counter value by 1 (S310) and performs a square operation (S305). Start over.

On the other hand, when the count value is 0, the modular multiplier 220 has completed all exponential power operations, and thus performs all reprocessing operations (S311) after completing remapping in step 3 of Equation 4 (S311). do.

For reference, in performing step 2 of Equation 4, an operation process when the key bit is 0 and when the key bit is 1 is different. Therefore, in the above operation, the flag value indicates which segment of segment 4 235 and segment 5 236 is the result of the previous execution.

As such, the modular multiplication apparatus according to the embodiment of the present invention embeds a memory therein. Then, word-based modular multiplication is continuously performed through data input / output between the built-in memory and the modular interface. That is, by directly controlling the memory, time delay caused by data input / output is eliminated.

The embodiments of the present invention described above are not implemented only through the apparatus and the method, but may be implemented through a program for realizing a function corresponding to the configuration of the embodiment of the present invention or a recording medium on which the program is recorded. Implementation can be easily implemented by those skilled in the art from the description of the above-described embodiments.

Although the embodiments of the present invention have been described in detail above, the scope of the present invention is not limited thereto, and various modifications and improvements of those skilled in the art using the basic concepts of the present invention defined in the following claims are also provided. It belongs to the scope of rights.

1 is a diagram showing the configuration of a system to which the present invention is applied.

2 is a diagram showing the structure of a modular multiplication apparatus according to an embodiment of the present invention.

3 is a flowchart sequentially illustrating a process of performing a modular exponential power of the modular multiplication apparatus illustrated in FIG. 2.

FIG. 4 is a diagram illustrating the structure of a memory illustrated in FIG. 2.

Claims (9)

A modular multiplier that repeatedly performs a modular multiplication operation; A memory configured to store at least one result value generated during an operation performed by the modular multiplier; And At least one of synchronizing with the modular multiplier using any one of the result values stored in the memory, storing a value output from the modular multiplier in the memory according to the synchronized synchronization, and requesting the modular multiplier Modular interface unit for reading the value of from the memory to the modular multiplier Modular multiplication device comprising a. According to claim 1, The modular interface unit, After synchronizing the signals input from the outside, and generates a signal for accessing the memory using the matched signal, and after reading the value stored in the address in the memory requested from the outside through the generated signal, A system input / output control unit configured to output a control signal informing of the read value and the read value to the outside Modular multiplication device comprising a. The method of claim 2, The modular interface unit, After synchronizing with the modular multiplier by using the state value output from the modular multiplier, the operation result value output from the modular multiplier is stored in the memory according to the matched synchronization, and the modular multiplier requests A modular input / output controller for reading a value stored at a predetermined address in a memory and providing the value to the modular multiplier; And Generate a control signal through data input from the outside, select one of the at least one functional unit to access the memory based on the generated control signal, and then allow the selected functional unit to access the memory; A memory input / output controller which drives the modular multiplier using the generated control signal Modular multiplication device further comprising. The method according to any one of claims 1 to 3, The modular multiplier, A predetermined number of input registers for receiving and storing data input from the outside from the modular interface unit; A modular hardware core unit repeatedly performing a modular multiplication operation of a predetermined unit by using the stored data; A predetermined number of output registers for storing at least one output value generated during the modular multiplication process; And A status register for storing at least one status value generated during the modular multiplication process Modular multiplication device comprising a. The method of claim 4, wherein The memory, Includes a certain number of segments, And the segment stores a value output from the modular multiplier. Synchronizing signals input from the outside, and generating a signal for accessing a memory through the matched signal; Reading a value stored at an address in the memory requested from the outside using the generated signal, and then outputting a control signal notifying the read value and the read value to the outside; Synchronizing with a function unit that performs a modular multiplication operation through a predetermined value, and storing at least one of output values of the function unit in the memory according to the matched synchronization; Reading a value stored in an address of the memory requested by the function unit and providing the value to the function unit; Generating a control signal using any one of the signals input from the outside, and then selecting any one of the functional units to access the memory using the generated control signals; And Transmitting a signal of the selected functional unit to the memory, and transmitting a value output from the memory to any one of the functional units to access the memory Modular multiplication method comprising a. The method of claim 6, Organizing the memory into a predetermined number of segments; And Selecting and storing a result value to be stored in the memory from the result value generated during the modular exponential operation and input / output process in the configured segment Modular multiplication method further comprising. The method of claim 7, wherein Storing basic data in a designated segment, and calculating a predetermined value and storing the basic data in the corresponding segment; After initializing a flag value, assigning a bit size of an index value key to a counter, and then performing a square operation; Checking a key bit value corresponding to a current count and then modularly multiplying the predetermined value and the current value according to the checked value; Toggling a flag value according to the identified value; After checking the count value, decreasing the count value according to the checked value and performing the square operation again; And Calculating a final result according to the identified count value Modular multiplication method further comprising. The method of claim 8, Informing, according to the identified key bit value, in which segment the result value performed in the previous step is stored; And Selecting one of the segments to store the result value Modular multiplication method further comprising.

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