JP2012032740A - Encryption device and method thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an encryption/decryption method capable of encrypting/decrypting on an integer exceeding a range of an effective number for application/software of personal computers without increasing information giving a hint for deciphering by a third party.SOLUTION: An encryption device 1 has a first encryption section 14 that executes a calculation in which a power having an integer Xsmaller than a predetermined number as a base and an integer E as an index is divided by a product N to obtain a remainder and determines the same as an encryption number Yof the integer X. A second encryption section 15 executes substitution decryption on the encryption number Yto obtain an integer Y'. The first encryption section 14 converts the integer Xinto an expansion formula including plural integers, and using the expansion formula, a power which has the integer Xas the base and the integer E as the index is calculated. The second encryption section 15 converts the encryption number Yto obtain an expansion formula including plural integers, and using the expansion formula, substitution decryption is made on the encryption number Y.

Description

  The present invention relates to an encryption device and a method thereof.

  Conventionally, it is known to use an identifier including a unique integer in order to identify a member in a corporate organization or the like. For example, a number of about 8 digits is used to identify a subscriber in the national health insurance system, or a number of about 3 to 10 digits is used for each bank branch and account to identify a bank account. It is used or a number of about 16 digits is used to identify a credit card member.

  Also, RSA encryption is known as a method for performing encryption and digital signature (see, for example, Patent Document 1). The RSA cryptography is a public key cryptosystem based on the fact that it is difficult to perform a prime factorization problem of a composite number having a large number of digits. That is, in the RSA encryption, at the encryption stage, a power of an appropriate positive integer and a remainder operation that uses a product of two prime numbers as a modulus are used, and a power that requires a prime factor of these two prime products in the decryption. Use roots. As a result, in the RSA cryptography, it is difficult to decrypt without knowing the prime factor, thereby ensuring the security of the cryptography.

  Furthermore, in order to ensure security in transmitting and receiving information via a computer network, an SSL protocol having encryption, authentication, and alteration detection functions is known. For example, RSA encryption is used for authentication based on a public key certificate included in the SSL protocol.

JP 09-107352 A

  However, conventionally, when a secret key paired with a public key is decrypted by using a combination of a format such as a number before encryption and a format such as a number after decryption, the same public key and secret key are decrypted. There is a problem that all ciphers using the combination of these can be deciphered. In addition, RSA encryption is based on the length of time required to specify a prime factor as the basis of encryption security. However, there was a problem that it could be decoded in a shorter time.

  In addition, in application software for personal computers, due to restrictions on the range of numerical values that can be handled internally, for example, when calculation such as a power of a natural number of a 16-digit integer is executed, a processor overflow occurs, and an accurate Calculation results may not be obtained. For this reason, it is necessary to divide the original integer as appropriate within the range of digits where overflow does not occur, and to perform power residue calculation independently for each integer obtained by the division. This is the same as encrypting and decrypting plain text by dividing it by the number of unit bytes in text encryption. However, in this method, a key for encryption and decryption is associated with each divided integer or phrase. As a result, there is a problem that a third party gives more clues for decoding.

  For example, the credit card registration number and expiration date are expressed using 16-digit and 4-digit integer formats. If these integers can be combined to produce a 20-digit integer and a method capable of encrypting and decrypting the integer can be provided, then it is compared with a conventional technique that separates the digits and encrypts multiple integers separately. Thus, it is possible to ensure security without increasing information that becomes a clue for decryption by a third party. That is, as a technique for concealing personal information, a method for encrypting and decrypting a multi-digit integer is required.

  Furthermore, information leakage via voice calls or documents such as printed materials cannot be handled by security technology such as SSL protocol for information transmitted using a computer network, and therefore, in various forms including voice or documents. There was a need for a way to conceal personal information.

  The present invention is an encryption that can encrypt and decrypt integers exceeding the range of significant figures such as application software for personal computers without increasing information that is a key for decryption by a third party. An object of the present invention is to provide an encoding and decoding method.

前記所定数より小さい整数Ｘ_ｉを底とし、前記整数Ｅを指数としたべき乗を前記積Ｎで除算した場合の剰余を算出して前記整数Ｘ_ｉの暗号化数Ｙ_ｉとする第１暗号化手段と、前記暗号化数Ｙ_ｉの換字式暗号化により整数Ｙ_ｉ’を算出する第２暗号化手段と、前記Ｙ_ｉ’から換字式復号により前記暗号化数Ｙ_ｉを復号する第２復号手段と、前記暗号化数Ｙ_ｉを底とし、前記整数Ｆを指数としたべき乗を前記整数Ｎで除算した場合の剰余を算出して前記整数Ｘ_ｉを復号する第１復号手段と、を備え、前記第１暗号化手段は、前記整数Ｘ_ｉを、複数の整数により構成される展開式に変換し、当該展開式により、前記整数Ｘ_ｉを底とし、前記整数Ｅを指数としたべき乗を算出し、前記第１復号手段は、前記暗号化数Ｙ_ｉを、複数の整数により構成される展開式に変換し、当該展開式により、前記暗号化数Ｙ_ｉを底とし、前記整数Ｆを指数としたべき乗を算出し、前記第２暗号化手段は、前記暗号化数Ｙ_ｉを、複数の整数により構成される展開式に変換し、当該展開式により、前記暗号化数Ｙ_ｉを換字式暗号し、前記第２復号手段は、前記整数Ｙ_ｉ’を、複数の整数により構成される展開式に変換し、当該展開式により、前記暗号化数Ｙ_ｉを復号する。 An encryption apparatus according to the present invention is an encryption apparatus that encrypts and decrypts an integer, and generates A and B so that a product N of a first prime number A and a second prime number B exceeds a predetermined number. And a product D of an integer A ′ that is 1 less than the first prime A and an integer B ′ that is 1 less than the second prime B, or a least common multiple of the integer A ′ and the integer B ′ An integer E that is prime with K, the integer E is generated such that the power of the integer E as an exponent exceeds the predetermined number of digits, and the integer E is an encryption key A key generation unit, a decryption key generation unit that generates an integer F so as to satisfy the following expression when an arbitrary integer m is set, and uses the integer F as a decryption key corresponding to the encryption key;

First encryption is performed by calculating a remainder when the power of the integer X _i smaller than the predetermined number and the integer E as an exponent is divided by the product N to be the encrypted number Y _i of the integer X _i means a _'second encrypting means for calculating, the Y _i' integer Y _i by substitution cipher of the encrypted number Y _i second decoding for decoding the encrypted number Y _i by substitution type decoded from and means, to a base of said encrypted number Y _i, and a first decoding means for decoding the integer X _i by calculating the remainder when dividing the power that the integer F as index in the integer N The first encryption means converts the integer X _i into an expansion equation composed of a plurality of integers, and uses the expansion equation to calculate a power with the integer X _i as a base and the integer E as an exponent. The first decryption means calculates the encrypted number Y _i by a plurality of integers. Converted into an expansion formula to be formed, and the expansion formula is used to calculate a power with the encryption number Y _i as a base and the integer F as an exponent, and the second encryption means uses the encryption number Y _i Is converted into an expansion equation composed of a plurality of integers, the encrypted number Y _i is substitution-encrypted by the expansion equation, and the second decryption means converts the integer Y _i ′ into a plurality of integers. into a composed deployable, by the foldout, decrypts the encrypted number Y _i.

Further, the second encryption means adds a value of a key R _i that is an integer randomly selected from a positive integer smaller than the predetermined number to the encrypted number Y _i . It is preferable to perform encryption.

Further, the first encryption means, to the integer X _i, by adding an offset number T, and updates the integer X _i, and the bottom of the integer X _i, which is the updated index the integer E The remainder when the power is divided by the product N is calculated as the encrypted number Y _i of the integer X _i , and the encryption is performed by subtracting the offset number T from the encrypted number Y _i update the number Y _i, the second encryption unit, to the encrypted number Y _i, by adding the number of offset T, encryption update the encrypted number Y _i, are the updated The remainder when the number Y _i is the base and the power of the integer F as an exponent is divided by the integer N is calculated to decode the integer X _i , and the offset number T is calculated for the integer X _i Preferably, the integer X _i is updated by subtraction.

In addition, when there are a plurality of the integers X _{i and the} offset number T is added to each of the integers X _i, each of the integers X _i is greater than or equal to 0 and less than or equal to the predetermined number. It is preferable to set as follows.

  In addition, the encryption apparatus includes the prime number generation unit, the encryption key generation unit, the decryption key generation unit, the first encryption unit, and the second encryption unit. An encryption control unit that executes a predetermined number of times in the order of a key generation unit, the decryption key generation unit, the first encryption unit, and the second encryption unit, the second decryption unit, and the first decryption unit. It is preferable to further comprise decoding control means for executing the predetermined number of times in the order of the second decoding means and the first decoding means.

  Further, when the prime number generating unit is repeatedly executed by the encryption control unit, it is preferable that the A and B are generated so that the A and the B are different in each repeated execution.

前記所定数より小さい整数Ｘ_ｉに対して、オフセット数Ｔを加算して、当該整数Ｘ_ｉを更新し、当該更新された整数Ｘ_ｉを底とし、前記整数Ｅを指数としたべき乗を前記積Ｎで除算した場合の剰余を算出して前記整数Ｘ_ｉの暗号化数Ｙ_ｉとし、当該暗号化数Ｙ_ｉに対して、前記オフセット数Ｔを減算して当該暗号化数Ｙ_ｉを更新する第１暗号化手段と、前記暗号化数Ｙ_ｉに対して、前記オフセット数Ｔを加算して、当該暗号化数Ｙ_ｉを更新し、前記更新された暗号化数Ｙ_ｉを底とし、前記整数Ｆを指数としたべき乗を前記整数Ｎで除算した場合の剰余を算出して前記整数Ｘ_ｉを復号し、当該整数Ｘ_ｉに対して、前記オフセット数Ｔを減算して整数Ｘ_ｉを更新する第１復号手段と、前記素数生成手段と、前記暗号鍵生成手段と、前記復号鍵生成手段と、前記第１暗号化手段とを、前記素数生成手段、前記暗号鍵生成手段、前記復号鍵生成手段、前記第１暗号化手段の順に所定回数実行する暗号化制御手段と、前記第１復号手段を、前記所定回数実行する復号制御手段と、を備え、前記第１暗号化手段は、前記整数Ｘ_ｉを、複数の整数により構成される展開式に変換し、当該展開式により、前記整数Ｘ_ｉを底とし、前記整数Ｅを指数としたべき乗を算出し、前記第１復号手段は、前記暗号化数Ｙ_ｉを、複数の整数により構成される展開式に変換し、当該展開式により、前記暗号化数Ｙ_ｉを底とし、前記整数Ｆを指数としたべき乗を算出する。 An encryption apparatus according to the present invention is an encryption apparatus that encrypts and decrypts an integer, and generates A and B so that a product N of a first prime number A and a second prime number B exceeds a predetermined number. And a product D of an integer A ′ that is 1 less than the first prime A and an integer B ′ that is 1 less than the second prime B, or a least common multiple of the integer A ′ and the integer B ′ An integer E that is prime with K, the integer E is generated such that the power of the integer E as an exponent exceeds the predetermined number of digits, and the integer E is an encryption key A key generation unit, a decryption key generation unit that generates an integer F so as to satisfy the following expression when an arbitrary integer m is set, and uses the integer F as a decryption key corresponding to the encryption key;

For small integer X _i than the predetermined number, by adding an offset number T, and updates the integer X _i, the updated integer X _i and a bottom, said power was the integer E and exponent product calculates a remainder when divided by N and the encryption number Y _i of the integer X _i, with respect to the encrypted number Y _i, and updates the encryption number Y _i by subtracting the offset number T a first encryption unit, to the encrypted number Y _i, by adding the number of offset T, and updates the encrypted number Y _i, and the bottom of the updated encrypted number Y _i, the the power that the integer F as index by calculating the remainder when divided by the integer N decoding the integer X _i, update the integer X _i with respect to the integer X _i, by subtracting the offset number T First decryption means, prime number generation means, encryption key generation means, and decryption An encryption control unit that executes a predetermined number of times in the order of the prime number generation unit, the encryption key generation unit, the decryption key generation unit, and the first encryption unit; Decryption control means for executing the first decryption means a predetermined number of times, wherein the first encryption means converts the integer X _i into an expansion expression composed of a plurality of integers, and the expansion expression To calculate the power with the integer X _i as the base and the integer E as the exponent, and the first decryption means converts the encrypted number Y _i into an expansion formula composed of a plurality of integers, According to the expansion formula, a power is calculated with the encryption number Y _i as a base and the integer F as an exponent.

前記所定数より小さい整数Ｘ_ｉを底とし、前記整数Ｅを指数としたべき乗を前記積Ｎで除算した場合の剰余を算出して前記整数Ｘ_ｉの暗号化数Ｙ_ｉとする第１暗号化ステップと、前記暗号化数Ｙ_ｉを換字式暗号化により整数Ｙ_ｉ’を算出する第２暗号化ステップと、前記整数Ｙ_ｉ’から換字式復号により前記暗号化数Ｙ_ｉを復号する第２復号ステップと、前記暗号化数Ｙ_ｉを底とし、前記整数Ｆを指数としたべき乗を前記積Ｎで除算した場合の剰余を算出して前記整数Ｘ_ｉを復号する第１復号ステップと、を含み、前記第１暗号化ステップは、前記整数Ｘ_ｉを、複数の整数により構成される展開式に変換し、当該展開式により、前記整数Ｘ_ｉを底とし、前記整数Ｅを指数としたべき乗を算出し、前記第１復号ステップは、前記暗号化数Ｙ_ｉを、複数の整数により構成される展開式に変換し、当該展開式により、前記暗号化数Ｙ_ｉを底とし、前記整数Ｆを指数としたべき乗を算出し、前記第２暗号化ステップは、前記暗号化数Ｙ_ｉを、複数の整数により構成される展開式に変換し、当該展開式により、前記暗号化数Ｙ_ｉを換字式暗号し、前記第２復号ステップは、前記整数Ｙ_ｉ’を、複数の整数により構成される展開式に変換し、当該展開式により、前記暗号化数Ｙ_ｉを復号する。 The encryption device according to the present invention encrypts and decrypts an integer by the encryption device encrypting and decrypting the integer, and the product N of the first prime number A and the second prime number B is a predetermined number. A prime number generating step for generating A and B so as to exceed, and a product D of an integer A ′ that is 1 less than the first prime number A and an integer B ′ that is 1 less than the second prime number B, or the integer A least common multiple K of A ′ and the integer B ′ and an integer E that is a prime, and the integer E is generated such that the power of the integer E as an exponent exceeds the predetermined number of digits. Then, an encryption key generation step using the integer E as an encryption key, and an integer F is generated so as to satisfy the following expression when an arbitrary integer m is set, and the integer F is set as a decryption key corresponding to the encryption key A decryption key generation step;

First encryption is performed by calculating a remainder when the power of the integer X _i smaller than the predetermined number and the integer E as an exponent is divided by the product N to be the encrypted number Y _i of the integer X _i step a, _'a second encryption step of calculating, the integer Y _i' integer Y _i by substitution cipher of the encrypted number Y _i second decrypting the encrypted number Y _i by substitution type decoded from a decoding step, the bottom of the encrypted number Y _i, a first decoding step of the power that the integer F as index by calculating the remainder when divided by the product N to decode the integer X _i, the And the first encryption step converts the integer X _i into an expansion equation composed of a plurality of integers, and the expansion equation is a power that uses the integer X _i as a base and the integer E as an exponent. The first decryption step calculates the number of encryptions. The _i, into a deployable composed of a plurality of integers, by the foldout, a bottom said encrypted number Y _i, and calculates the power that the integer F as index, the second encryption step The encrypted number Y _i is converted into an expansion formula composed of a plurality of integers, the encrypted number Y _i is substitution-encrypted by the expansion formula, and the second decryption step includes the integer Y _i 'Is converted into an expansion expression composed of a plurality of integers, and the encrypted number Y _i is decrypted by the expansion expression.

  According to the present invention, it is possible to encrypt and decrypt integers that exceed the range of significant figures such as application software for personal computers without increasing information that is a clue for decryption by a third party. it can.

It is a figure which shows the function structure of the encryption apparatus which concerns on 1st Embodiment. It is a flowchart which shows the flow of a process in the case of encrypting with the encryption apparatus which concerns on 1st Embodiment. It is a flowchart which shows the flow of a process in the case of decoding by the encryption apparatus which concerns on 1st Embodiment. It is a figure which shows the function structure of the encryption apparatus which concerns on 2nd Embodiment. It is a flowchart which shows the flow of a process in the case of encrypting by the encryption apparatus which concerns on 2nd Embodiment. It is a flowchart which shows the flow of a process in the case of performing decoding with the encryption device which concerns on 2nd Embodiment.

<First Embodiment>
Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[Function configuration]
FIG. 1 is a diagram illustrating a functional configuration of the encryption device 1 according to the first embodiment. The encryption device 1 is a device that encrypts and decrypts an arbitrary numerical value within a predetermined range. The encryption device 1 is communicably connected to another encryption device 1 via a communication network N configured by a computer network such as a LAN (Local Area Network) or the Internet.

  The first embodiment is applied to a personal computer (encryption device 1) and its peripheral devices. Each unit in the first embodiment is configured by hardware included in a personal computer and its peripheral devices, and software that controls the hardware.

  The hardware includes a CPU as a control unit, a storage unit, a communication unit, a display unit, and an input unit. Examples of the storage unit include a memory (RAM, ROM, etc.), a hard disk drive (HDD), and an optical disk (CD, DVD, etc.) drive. Examples of the communication unit include various wired and wireless interface devices. Examples of the display unit include various displays such as a liquid crystal display and a plasma display. Examples of the input unit include a keyboard and a mouse.

  The software includes a computer program, application software, and data for controlling the hardware. The computer program, application software, and data are stored in the storage unit, and are appropriately executed and referenced by the control unit. Further, the computer program, application software, and data can be distributed via a communication line, and can be recorded and distributed on a computer-readable medium such as a CD-ROM.

The control unit of the encryption device 1 includes a prime number generation unit 11, an encryption key generation unit 12, a decryption key generation unit 13, a first encryption unit 14, a second encryption unit 15, and an encryption control unit 16. The 2nd decoding part 17, the 1st decoding part 18, and the decoding control part 19 are provided.
Is provided.

  The prime number generation unit 11 generates the first prime number A and the second prime number B so that the product N of the first prime number A and the second prime number B exceeds a predetermined number X. The predetermined number X is, for example, a 20-digit integer, and is an integer exceeding the range in which the multiplication result can be expressed at once by the register. Further, the predetermined number X is a value larger than this integer when the information to be encrypted at a time can be expressed as an integer.

  The encryption key generation unit 12 includes a product D of an integer A ′ that is 1 less than the first prime number A and an integer B ′ that is 1 less than the second prime number B, or a least common multiple K of the integer A ′ and the integer B ′, It is a prime integer E, and the power of the predetermined number X as the base and the integer E as the exponent exceeds the predetermined number of digits larger than the number of digits that can be represented by the register (overflow occurs) An integer E is generated in, and this integer E is used as an encryption key. In other words, the encryption key generation unit 12 randomly generates an integer E that is an integer E that is prime with the product D or the least common multiple K, and whose operation result of the power of the integer X exceeds the predetermined number of digits. Is the encryption key.

  The decryption key generation unit 13 generates an integer F so as to satisfy the following expression (1) when an arbitrary integer m is set, and calculates the integer F as a decryption key corresponding to the encryption key E. The generated integer F is notified to the first decoding unit 18 described later. The integer F may be any number as long as the expression (1) is satisfied, and the decryption key generation unit 13 may randomly generate the integer F.

The first encryption unit 14 calculates an arbitrary positive integer smaller than the predetermined number X, that is, a power that has the integer X _i to be encrypted as a base and the integer E as an exponent, as a first prime number A and a second prime number. by calculating the remainder when divided by the product N with B, and calculates the number of encryption Y _i an integer X _i. That is, the first encryption unit 14 calculates the encryption number Y _i of the integer X _i expressed by the following equation (2). “Mod” shown in the equation (2) is a function for calculating a remainder.

Specifically, the first encryption unit 14 calculates the encrypted number Y _i of the integer X _i using an iterative square method (fast power method). The processing procedure will be described below.

First, the first encryption unit 14 performs the binary expansion of an integer E, the multiplication E integers X _i, to expand the power of the product of the 2 ^k of the integer X _i. Here, k is assumed to be an integer from 0 to n, and n corresponds to the largest number among n whose 2 n powers do not exceed the integer E. For example, when the integer E is 287, the integer X _i is expressed by the following equation (3). In addition, since the power of 2 is the largest number that does not exceed the integer E, n is 8.

Subsequently, the first encryption unit 14, as shown in the following equation (4), the 2 ⁰ square of an integer X _i from the remainder when divided by the product N in order, the product of multiplication 2 ^k integers X _i The remainder when dividing by N is calculated.

Here, since the integer E is generated so that the operation result of the predetermined number X raised to the E power is larger than the number of digits that can be expressed by the register, the integer X _i is calculated to the ^2k power. , Digit overflow may occur. Accordingly, the first encryption unit 14, the integers X _i, using the following equation (5), expanded to an integer, which is divided into digit X _u and lower digit X _d of the upper, the upper digit X _u and based on the lower digit _{X d,} it is calculated up to ^{2 n} square of an integer _{X i.}

Where M is the base and Cd is the number of the lower digits in the integer X _i . Cd is an integer of 1 or more.

For example, when the base M is 2, the number of digits of the integer X _i is 16 digits, and the number of lower digits Cd is 8 digits, the expression (5) is expressed as the following expression (6). .

For example, when the cryptographic apparatus 1 according to the first embodiment includes a 16-bit register CPU, and the value of the integer X _i is a decimal number 65532, the exponent is calculated in the calculation of the power of the integer X _i . As such, when 2 is used, the integer upper limit value 65535 that can be expressed using a 16-bit register is exceeded. That is, simply when implementing the E-th power of the calculation of the integer X _i included in equation (2) on the right side according to conventional calculation method of a power integers X _i, there is a case where the value of an accurate power may not be obtained.

On the other hand, when the upper digit and the lower digit are divided as integer parts using the digit division represented by the equation (6), for example, the integer X _i is a decimal number 65532, that is, a binary number. 1111111111111100 (2) is divided into an integer 11111111 (2) (decimal 255) included in the upper 8 digits and an integer 11111100 (2) (decimal 252) included in the lower 8 digits. In this case, the two divided numbers are smaller than the square of 255, and therefore fall within an integer range that can be expressed by a 16-bit register. Therefore, it is possible to avoid errors due to overflowing digits.

In the first embodiment, as shown in the equation (5), it is divided into two integers. For example, when the integer X _i is 20 digits, as shown in the following equation (7): It is good also as dividing | segmenting into four integers.

_{Wherein, X 15} is 20 digit column 16 integer _{X i, X 10} is 15 digit from 11 digit integer _{X i, X 5} is 10 digit from 6 digit integer _{X i, X 0} is the fifth digit from the first digit of the integer X _i. In addition, when the integer X _i is less than 20 digits, the upper digits may be zero-padded. By doing in this way, the encryption device 1 generates the integer E under the condition that overflow occurs, and then expands the integer X _i using the equations (3) to (5) to obtain the encrypted number Y _i . By calculating, it is possible to accurately calculate the encryption number Y _i while avoiding overflow.
Note that the integer X _i is preferably divided so that the number of digits of the integer after division is equal, as in the equations (6) and (7).

Subsequently, the first encryption unit 14 calculates a remainder of the power of the integer X _i expanded to the product of the power of 2 as the E power. For example, when the integer E is 287, the remainder of the integer X _i raised to the E power is represented by the following equation (8). Therefore, as shown in the equation (4), 2 ^{k of the} integer X _i obtained in advance. It is possible to easily calculate from the remainder when the power is divided by the product N. In this calculation, the remainder may be calculated by dividing the multiplicand into an upper digit and a lower digit in the same manner as equation (5) so as to avoid overflow.

The second encryption unit 15 randomly selects a predetermined number X is smaller than a positive integer, and the integer key R _i. Subsequently, using the key R _i , the second encryption unit 15 performs a substitution encryption of the encrypted number Y based on the following equation (9), and calculates an integer Y _i ′.

In the equation, Rot () is a function for substituting the encrypted number Y _i using the key R _i as a secret key. Specifically, Rot () adds the encrypted number Y _i by the value of the key R _i within the range of the predetermined number X. Also, if the result of adding the key R _i to the encrypted number Y _i exceeds the predetermined number X, Rot () exceeds the predetermined number X by adding R _i to Y _i as an integer Y _i ′ min, _i.e., returns the Y i _{+ R} i -X. The key R _i is notified to the second decryption unit 17.

Further, Rot (), when adding the key _{R i} to encrypt the number _{Y i,} the encryption number _{Y i,} using the following equation (10), the upper digit _{Y u} and lower digit _{Y d} It generates a divided integer portion, with the digit Y _u and lower digit Y _d of the upper, and calculates the integer Y _{i '.}

Similar to equation (5), in equation (10), M is the bottom, and Cd is the number of lower digits in the encrypted number Y _i . Cd is at least 1.

  The encryption control unit 16 controls the execution of the prime number generation unit 11, the encryption key generation unit 12, the decryption key generation unit 13, the first encryption unit 14, and the second encryption unit 15. Specifically, the encryption control unit 16 includes a prime number generation unit 11, an encryption key generation unit 12, a first encryption unit 14, and a second encryption unit 15, a prime number generation unit 11, and an encryption key generation. The unit 12, the first encryption unit 14, and the second encryption unit 15 are executed a predetermined number of times in this order. This predetermined number of times may be a predetermined number of times or an integer randomly generated by the encryption control unit 16. The predetermined number of times is notified to the decoding control unit 19.

The second decryption unit 17 calculates the encryption number Y _i by substitution decryption from the integer Y _i ′ substituted by the second encryption unit 15. Specifically, the second decryption unit 17 performs substitution-type decryption using the following formula (11), and calculates the encryption number Y.

In the equation, the key R _i is an integer used as a secret key for substitution encryption, and is an integer generated by the second encryption unit 15. The key _Ri is notified separately from the data encrypted by the second encryption unit 15.

Rot ⁻¹ () is a value obtained by subtracting the integer Y _i ′ by the value of the key R _i within a predetermined number X. 'If the result of the key _{R i} by subtracting the is less than 0, ^{Rot -1} () is the number of encryption _{Y i,} the integer _{Y i'} Integer _{Y i} less than 0 min by subtracting the _{R i} in A value obtained by subtracting from the predetermined number X, that is, Y _i −R _i + X is returned.

Further, ^{Rot -1} () is 'when subtracting the _{R i,} the integer _{Y i'} Integer _{Y i} for, the expression (10) as well as, divided integer part to the higher digit and lower digit And the encryption number Y _i is calculated using the upper and lower digits.

The first decryption unit 18 uses the integer F as the decryption key notified from the decryption key generation unit 13, and divides the power with the encryption number Y _i as the base and the integer F as the exponent by the product N By calculating the remainder, the original number of the encrypted number Y _i , that is, the integer X _i is calculated. That is, the first decryption unit 18 calculates the original integer X _i of the encrypted number Y _i represented by the following equation (12). Similar to the first encryption unit 14, the first decryption unit 18 calculates the original integer X _i of the encrypted number Y _i by using an iterative square method (fast power method). Detailed processing of the first decryption unit 18 is the same as that of the first encryption unit 14, and thus description thereof is omitted.

  The decoding control unit 19 controls the execution of the second decoding unit 17 and the first decoding unit 18. Specifically, the decoding control unit 19 executes the second decoding unit 17 and the first decoding unit 18 a predetermined number of times in the order of the second decoding unit 17 and the first decoding unit 18.

[flowchart]
Next, the flow of processing for performing encryption and decryption using the encryption device 1 according to the first embodiment will be described.
FIG. 2 is a flowchart illustrating a processing flow when encryption is performed by the encryption device 1 according to the first embodiment. In this flowchart, it is assumed that encryption is performed A times as the predetermined number of times by the encryption control unit 16.

  In step S1, the control unit (encryption control unit 16) sets the value of the counter c1 provided in the storage unit to 1 to determine whether or not the predetermined number of times.

  In step S2, the control unit (prime generation unit 11) sets the first prime number A and the second prime number B so that the product N of the first prime number A and the second prime number B exceeds a predetermined number X. Generate.

  In step S3, the control unit (encryption key generation unit 12) generates an integer E as an encryption key based on the first prime number A and the second prime number B. Specifically, the control unit (encryption key generation unit 12) calculates the product D of (A-1) and (B-1) or the least common multiple K of (A-1) and (B-1) and the prime. An integer E is generated such that the power of the predetermined number X as the base and the integer E as the exponent exceeds the predetermined number of digits larger than the number of digits that can be represented by the register, This integer E is an encryption key.

  In step S4, the control unit (decryption key generation unit 13) generates a decryption key (integer F) corresponding to the encryption key (integer E). Specifically, an integer F is generated so as to satisfy the above equation (1) when an arbitrary integer m is set, and this integer F is used as a decryption key. For example, the control unit notifies the integer F to the encryption device 1 that performs decryption in association with information indicating the number of times the first encryption unit 14 is associated with the decryption key.

In step S5, the control unit (the first encryption unit 14) performs the binary expansion of an integer E, on the basis of the deployable, the multiplication E integers X _i, a power of 2 ^k of the integer X _i Expand to product.

In step S6, the control unit (first encryption unit 14) sets k to 0.
In step S ^< b> 7, the control unit (first encryption unit 14) calculates the remainder when the integer X _{i to} the ^2k power is divided by the product N. Specifically, the control unit (first encryption unit 14) squares the remainder when the 2k ^-1 power of the integer X _i calculated immediately before is divided by the product N, and further adds this value to the product N Calculate the remainder when dividing by. In addition, the control unit (first encryption unit 14) converts the integer X _i into a sum of a plurality of integers based on the above equation (5) so that overflow does not occur, and converts the integer X _i into the converted integer. Based on this, the remainder when the integer X _{i to} the ^2k power is divided by the product N is calculated.

In step S8, the control unit (first encryption unit 14) adds 1 to k.
In step S9, the control unit (first encryption unit 14) determines whether k is larger than n. When this determination is YES, the control unit (first encryption unit 14) moves the process to step S10, and when this determination is NO, the control unit (first encryption unit 14) moves the process to step S7.

In step S10, the control unit (first encryption unit 14) calculates, as the encryption number Y _i , the remainder when the integer X _i is divided by the product N based on the residue calculated in step S7. To do.

In step S <b> 11, the control unit (second encryption unit 15) generates a key R _i , performs substitution encryption of the encrypted number Y based on the equation (9), and calculates an integer Y _i ′. This key R _i is, for example, by the control unit, associated with the information indicating whether the key according to many times the substitution cipher is notified to the encryption apparatus 1 for decoding.

In step S12, the control unit (encryption control unit 16) determines whether or not the counter c1 is equal to the predetermined number of times A. The control unit (encryption control unit 16) ends the process if this determination is YES, and moves the process to step S13 if this determination is NO.
In step S13, the control unit (encryption control unit 16) adds 1 to the counter c1 and substitutes an integer Y _i ′ for the integer X _i . Thereafter, the control unit (encryption control unit 16) moves the process to step S2.

FIG. 3 is a flowchart showing the flow of processing when decryption is performed by the encryption device 1 according to the first embodiment. The encryption device 1 is notified of the encrypted data, the key R _i used for encryption, and the decryption key (integer F), and is in a state where the encrypted data can be decrypted. And The number of encryption repetitions, that is, the predetermined number is A.

  In step S21, the control unit (decoding control unit 19) sets the value of the counter c2 provided in the storage unit to 1 in order to determine whether or not the predetermined number of times.

In step S <b> 22, the control unit (second decryption unit 17) calculates the encryption number Y _i from the integer Y _i ′ that is substitution-encrypted by the second encryption unit 15 based on the above-described equation (11). To do. Used for decoding, the key R _i, is associated information indicating how many times the substitution type decoding, decoding in order from the key R _i corresponding to a predetermined number of times A is performed.

In step S23, the control unit (first decoding unit 18) performs the binary expansion of the encrypted number Y _i, on the basis of the deployable, the multiplication F encryption number Y _i, the encrypted number Y _i to expand the power of the product of the 2 ^k of.

In step S24, the control unit (first decoding unit 18) sets k to 0.
In step S25, the control unit (first decoding unit 18), the multiplication ^{2 k} encryption number _{Y i,} and calculates a remainder when divided by the product N. Specifically, the control unit (first decryption unit 18) squares the remainder obtained by dividing the 2k ^-1 power of the encrypted number Y _i calculated immediately before by the product N, and further multiplies this value. The remainder when dividing by N is calculated. Further, the control unit (first decryption unit 18) converts the encrypted number Y _i into a sum of a plurality of integers based on the above-described equation (10) so as not to cause overflow, and converts it into the converted integer. based on, calculates a remainder when the multiplication 2 ^k encryption number Y _i divided by the product N.

In step S26, the control unit (first decoding unit 18) adds 1 to k.
In step S27, the control unit (first decoding unit 18) determines whether k is larger than n. The control unit (first decoding unit 18) moves the process to step S28 when this determination is YES, and moves the process to step S25 when this determination is NO.

In step S28, the control unit (first decryption unit 18) calculates the remainder when the encrypted number Y _i is divided by the product N as the integer X _i based on the remainder calculated in step S25 ( Decrypt).

In step S29, the control unit (decoding control unit 19) determines whether or not the counter c2 is equal to the predetermined number A. When this determination is YES, the control unit (decoding control unit 19) ends the process, and when this determination is NO, the process proceeds to step S30.
In step S30, the control unit (decryption control unit 19) adds 1 to the counter c2 and substitutes an integer X _i for the encrypted number Y _i . Thereafter, the control unit (decoding control unit 19) moves the process to step S22.

As described above, according to the first embodiment, the encryption device 1 converts the integer X _i into an expansion expression composed of a plurality of integers by the first encryption unit 14, and the integer X _i is converted into the expansion expression by the expansion expression. The power of the base E and the integer E as an exponent is calculated, and the first decryption unit 18 converts the encrypted number Y _i into an expansion expression composed of a plurality of integers. _{The power with i} as the base and the integer F as the exponent is calculated, and the second encryption unit 15 converts the encrypted number Y _i into an expansion expression composed of a plurality of integers. The conversion number Y _i is subjected to substitution encryption, and the second decryption unit 17 converts the integer Y _i ′ into an expansion expression composed of a plurality of integers, and decrypts the encryption number Y _i by the expansion expression.

That is, when the cryptographic apparatus 1 performs computation on the integer X _i , the encrypted number Y _i , and the integer Y _i ′, the computation target integer is divided into integers having the number of digits that do not cause overflow. The integer X _i , the encrypted number Y _i , and the integer Y _i ′ can be accurately calculated. Furthermore, the integer X _i, for each digit constituting the integer X _i, without separate encryption, encrypts the integer X _i itself, and calculates the number of encryption Y _i. That is, when encrypting the integer X _i , the encryption device 1 does not calculate a plurality of results of encryption, for example, by performing encryption for each of a plurality of bytes. Therefore, it is possible to encrypt and decrypt integers exceeding the range of significant figures such as application software for personal computers without increasing information that becomes a clue for decryption by a third party.

Also, the cryptographic device 1 randomly selects a positive integer smaller than the predetermined number X, sets this integer as the key R _i, and adds the value of this key R _i to the encrypted number Y _i . Formula encryption. In the conventional substitution cipher, the number is replaced with another number (for example, 0 is 1, 1 is 2,...), And when a 20-digit integer is substituted by this method, The number of encryption patterns is limited to ten. In the present embodiment, the key R _i is a positive integer equal to or less than the predetermined number X. Therefore, the larger the predetermined number X, the greater the number of encryption patterns. Therefore, the security can be made stronger than that of the conventional substitution encryption.

  In addition, the encryption device 1 includes an encryption control unit 16, and the encryption control unit 16 includes a prime number generation unit 11, an encryption key generation unit 12, a first encryption unit 14, and a second encryption unit 15. Since the prime number generation unit 11, the encryption key generation unit 12, the first encryption unit 14, and the second encryption unit 15 are executed a predetermined number of times in this order, security is further enhanced compared to the case where encryption is performed only once. Can be.

Also, the cryptographic device 1 calculates the power of the integer X _i and the encrypted number Y _i using the above-described equations (5) and (10). For example, if the integer _{X i} is the square, the square of the right side of Formula (5), the square of an integer _{X u,} integer _{X u} · integer _{X d,} and the square of an integer _{X d} are generated, these Since both are integers less than the number of digits of the original integer X _i , overflow is avoided. In this way, the cryptographic apparatus 1 avoids overflow in the power calculation process by repeating the procedures of the equations (5) and (10) at any power of the integer X _i and the encrypted number Y _i. It becomes possible.

<Second Embodiment>
Hereinafter, a second embodiment of the present invention will be described with reference to the drawings. In addition, the same code | symbol is attached | subjected to the structure similar to 1st Embodiment, and description is abbreviate | omitted or simplified.

[Function configuration]
FIG. 4 is a diagram illustrating a functional configuration of the encryption device 100 according to the second embodiment.
The control unit of the encryption device 100 includes a first encryption unit 114 and a first decryption unit 118 instead of the first encryption unit 14 and the first decryption unit 18 included in the control unit of the first embodiment.

  The first encryption unit 114 adds the offset number T to each of the integers to be encrypted included in the set S when the integer set S to be encrypted is outside the range of 0 to the predetermined number X. Thus, each integer to be encrypted is adjusted to be included in the range of 0 to a predetermined number X, and set as a set S ′.

More specifically, the first encryption unit 114, immediately before the encryption, for integer X _i, immediately after updating the integer X _i by adding an offset number T, was encrypted, the encrypted number Y _i, by subtracting the offset number T, and updates the encryption number Y _i.
The first decoding unit 118, immediately before the decoding, the encrypted number Y _i, immediately after updating the encrypted number Y _i by adding an offset number T, was decoded, integer X _The integer X _i is updated by subtracting the offset number T from _i .
Here, the first encryption unit 114 performs encryption after adding the offset number T to the integer X _i , and subtracts the offset number T from the encryption number Y _i . It is also possible to perform encryption after subtracting the offset number T from the integer X _i and add the offset number T to the encrypted number Y _i after encryption. In this case, the first decoding unit 118, the encrypted number Y _i, immediately after updating the encrypted number Y _i by subtracting the offset number T, was decoded, with respect to the integer X _i Then, the offset number T is added to update the integer X _i .

[flowchart]
Next, the flow of processing for performing encryption and decryption using the encryption device 100 according to the second embodiment will be described.
FIG. 5 is a flowchart showing a processing flow when encryption is performed by the encryption device 100 according to the second embodiment. Here, as in the first embodiment, it is assumed that encryption is performed A times as the predetermined number of times by the encryption control unit 16. In this flowchart, it is assumed that the integer X _i included in the set S is encrypted.

  Since the processing from step S101 to step S104 is the same as the processing from step S1 to step S4 of the first embodiment, description thereof will be omitted.

In step S105, the control unit (the first encryption unit 114), for integer _{X i,} by adding an offset number T, and updates the integer _{X i.} The offset number T is set to be within a range from 0 to a predetermined number X when the offset number T is added to all integers included in the set S.

  Since the processing from step S106 to step S111 is the same as the processing from step S5 to step S10 of the first embodiment, description thereof will be omitted.

In step S112, the control unit (first encryption unit 114) subtracts the offset number T from the encrypted number Y _i . This offset number T is the same value as the offset number T used in step S105.

  Since the processing from step S113 to step S115 is the same as the processing from step S11 to step S13 of the first embodiment, description thereof will be omitted.

FIG. 6 is a flowchart showing a flow of processing when decryption is performed by the encryption device 1 according to the second embodiment. Here, as in the first embodiment, the encrypted data, the key R _i used for encryption, and the decryption key (integer F) are notified, and the encrypted data can be decrypted. It is assumed that it is in a state. The number of encryption repetitions, that is, the predetermined number is A. The offset number T is the same value as the offset number T used in step S105 in FIG.

  Since the process of step S121 and step S122 is the same as the process of step S21 and step S22 of 1st Embodiment, description is abbreviate | omitted.

In step S123, the control unit (first decoding unit 118), the encrypted number _{Y i,} by adding an offset number T, and updates the encryption number _{Y i.}

  Since the processing from step S124 to step S129 is the same as the processing from step S23 to step S28 of the first embodiment, description thereof will be omitted.

In step S130, the control unit (first decoding unit 118), for integer _{X i,} by subtracting the offset number T, and updates the integer _{X i.}

  Since the process of step S131 and step S132 is the same as the process of step S29 and step S30 of 1st Embodiment, description is abbreviate | omitted.

As described above, according to the second embodiment, the encryption device 100 updates the integer X _i by adding the offset number T to the integer X _i by the first encryption unit 114 immediately before encryption. and, immediately after performing encryption, the encrypted number Y _i, by subtracting the offset number T, and updates the encryption number Y _i. Therefore, the encryption apparatus 100 can further increase the complexity of the encryption procedure by adding and subtracting the offset number T to perform encryption, thereby further strengthening the security.

Further, the offset number T, when the plurality of integer X _i is present, the offset number T when added to each the integer X _i, as respectively the integer X _i is 0 or more and less than a predetermined number X Since it is set, even if the plurality of integers X _i are not included in the range of 0 or more and the predetermined number X or less, they can be adjusted to be included in the range of 0 or more and the predetermined number X or less. the encryption of X _i can be carried out successfully.

Further, the encryption device 100 encrypts a plurality of integers X _i in an arbitrary range by addition / subtraction with the offset number T, and the encryption control unit 16 repeatedly executes encryption processing. Therefore, even when the combination of prime numbers by the prime number generation unit 11 is randomly generated and the encryption key (integer E) is generated during repeated execution, the plurality of integers X _i can be encrypted.

For the sake of simplicity, it is assumed that overflow is not considered. For example, when the set S of integers X _i is a number from 0 to 31, the cryptographic device 100 uses the prime number 3 and the prime number 11 in the first encryption. Encryption based on the combination, encryption based on the combination of prime 2 and prime 17 in the second encryption, and encryption based on the combination of prime 5 and prime 7 in the third encryption Suppose that

  Here, in the combination of prime number 3 and prime number 11, basically 33 numbers from 0 to 32, and in the combination of prime number 2 and prime number 17, basically 34 numbers from 0 to 33, prime number 5 and prime number 7. In this combination, 35 numbers from 0 to 34 can be basically RSA encrypted. Therefore, in the case of the combination of the prime number 3 and the prime number 11, the offset number T with respect to the range of 1 to 32 (32 pieces) in which 0 is omitted and the range of 0 to 32 (32 pieces) in which 32 is omitted. Can be used to generate the set S and perform RSA encryption. Further, in the case of the combination of prime number 2 and prime number 17, the range of 2 to 33 (32 pieces) in which 0 and 1 are omitted and the range of 1 to 32 (32 pieces) in which 0 and 32 are omitted. The set S can be generated using the offset number T, and RSA encryption can be performed. Further, in the case of the combination of prime number 5 and prime number 7, a set S is generated using the offset number T for a range of 2 to 33 (32 pieces) in which 0, 1 and 34 are omitted, and RSA encryption It can be performed.

In this case, the offset number T is set in the range of −2 to 0. That is, as described above, when the product N in the combination of the three prime numbers is three consecutive integers, the number of encrypted ranges is made the same and the one slided (added or subtracted) by 0 to 2 is encrypted, and then 0 Since the plurality of integers X _i included in the set S are encrypted into integers within the range that the set S can take after being encrypted by sliding (adding / subtracting) at −2 to return to the original, it is possible to perform encryption integer X _i normally, it is possible to diversify the pattern obtained by encrypting.

In the above example, the case of three consecutive integers has been described. However, if a combination of prime numbers obtained from four consecutive integers (difference is within 3), the encryption of a plurality of integers X _i is normally performed. Can be done. For example, 9985 (combination of prime 5 and prime 1997), 9986 (combination of prime 2 and prime 4993), 9987 (combination of prime 3 and prime 3329), 9986 (combination of prime 2 and prime 4993), For 9987 (combination of prime number 3 and prime number 3329) and 9989 (combination of prime number 7 and prime number 1427), by setting the offset number T in the range of −2 to 0, the encryption of a plurality of integers X _i is performed. Can be done normally.

On the other hand, if encryption is performed using a combination of prime numbers that cannot be obtained from four consecutive integers, encryption is not performed to an integer in a range that can be taken by the set S, and encryption cannot be performed correctly. For example, when a plurality of integers X _i included in the set S are set to ₀ to 34, and the 35 integers are encrypted, the combination of the prime numbers 5 and 7 is basically the combination of the prime numbers 5 and 7. 35 numbers from 0 to 34 can be RSA encrypted. On the other hand, in the combination of the prime number 3 and the prime number 13, for example, if a plurality of integers X _i included in the set S are 2 to 36, the encryption is performed when the 35 integers are encrypted. As a result, an integer that is converted to something other than the selected number after encryption is generated no matter how 35 numbers are selected so that an integer exceeding the range of the set S such as 37 is generated. to cause, can not be performed normally encryption of a plurality of integers X _i.

That is, as described above, when RSA is used for repeated encryption, the combination of two prime numbers is changed to the combination of different prime numbers obtained from four consecutive integers (N, N + 1, N + 2, N + 3) by the offset number T. as, by performing a plurality of integers X _i of RSA cryptography as a set S slides (addition and subtraction) with 0 (or 0 to 2) -2, number encryption of the plurality of integer X _i Y _i In the set S, and the encryption can be performed normally, and the pattern obtained by the encryption can be diversified as compared with the case where RSA encryption is repeatedly performed with the same combination of prime numbers. And security can be further strengthened. Furthermore, by performing encryption in combination with substitutional encryption, patterns obtained by encryption can be further diversified, and diversity can be further increased.

As described above, when the RSA encryption is repeatedly performed by a combination of different prime numbers, the value of the key R _i of the second encryption unit 15 may be set to 0. That is, the substitution encryption by the second encryption unit 15 and the second decryption unit 17 may not be performed. In this way, the function of the second encryption unit 15 is disabled to improve the processing speed, and the pattern obtained by encryption is diversified by performing RSA encryption with a combination of different prime numbers. can do.

  The embodiment of the present invention has been described above, but the present invention is not limited to the present embodiment, and modifications, improvements, and the like within the scope that can achieve the object of the present invention are included in the present invention.

DESCRIPTION OF SYMBOLS 1 Encryption apparatus 11 Prime number generation part 12 Encryption key generation part 13 Decryption key generation part 14, 114 1st encryption part 15 2nd encryption part 16 Encryption control part 17 2nd decryption part 18, 118 1st decryption part 19 Decryption Control unit

Claims (8)

An encryption device for encrypting and decrypting an integer,
Prime number generating means for generating A and B so that the product N of the first prime number A and the second prime number B exceeds a predetermined number;
A product D of an integer A ′ that is 1 less than the first prime number A and an integer B ′ that is 1 less than the second prime number B, or a least common multiple K of the integer A ′ and the integer B ′ and an integer that is prime E, wherein the integer E is generated so that a power of the predetermined number as a base and the integer E as an exponent exceeds a predetermined number of digits, and an encryption key generating means using the integer E as an encryption key;
Decryption key generation means for generating an integer F so as to satisfy the following expression when an arbitrary integer m is set, and using the integer F as a decryption key corresponding to the encryption key;

First encryption is performed by calculating a remainder when the power of the integer X _i smaller than the predetermined number and the integer E as an exponent is divided by the product N to be the encrypted number Y _i of the integer X _i Means,
Second encryption means for calculating an integer Y _i ′ by substitutional encryption of the encrypted number Y _i ;
Second decryption means for decrypting the encrypted number Y _i from the Y _i ′ by substitutional decryption;
The encrypted number Y _i and a bottom, and a first decoding means for decoding the integer X _i by calculating the remainder when the power that the integer F as index divided by the integer N,
The first encryption means converts the integer X _i into an expansion equation composed of a plurality of integers, and calculates a power that uses the integer X _i as a base and the integer E as an exponent by the expansion equation. And
The first decryption means converts the encrypted number Y _i into an expansion equation composed of a plurality of integers, and based on the expansion equation, the encrypted number Y _i is a base and the integer F is an exponent. Calculate the power,
The second encryption means converts the encrypted number Y _i into an expansion formula composed of a plurality of integers, and subtracts the encrypted number Y _i by the expansion formula,
The second decryption unit is an encryption device that converts the integer Y _i ′ into an expansion equation composed of a plurality of integers, and decrypts the encrypted number Y _i by the expansion equation. The second encryption means adds a value of a key R _i that is an integer randomly selected from a positive integer smaller than the predetermined number to the encrypted number Y _i , thereby performing a substitution cipher. The encryption device according to claim 1, wherein the encryption device is performed. Wherein the first encryption means, to the integer X _i, by adding an offset number T, and updates the integer X _i, and the bottom of the integer X _i, which is the updated, was exponential the integer E The remainder when the power is divided by the product N is calculated to obtain the encrypted number Y _i of the integer X _i , and the encrypted number Y _i by subtracting the offset number T from the encrypted number Y _i update _i ,
The second encryption unit, to the encrypted number Y _i, by adding the number of offset T, and updates the encrypted number Y _i, and the bottom of the updated encrypted number Y _i, the power of that the exponent integer F by calculating the remainder when divided by the integer N decoding the integer X _i, with respect to the integer X _i, the integer X _i by subtracting the offset number T The encryption device according to claim 1 or 2, which is updated. The offset number T is such that, when there are a plurality of the integers X _i, when the offset number T is added to each of the integers X _i, each of the integers X _i is greater than or equal to 0 and less than or equal to the predetermined number. The encryption apparatus according to claim 3, which is set. The prime number generation unit, the encryption key generation unit, the decryption key generation unit, the first encryption unit, and the second encryption unit are combined with the prime number generation unit, the encryption key generation unit, and the decryption unit. An encryption control unit that executes a predetermined number of times in the order of a key generation unit, the first encryption unit, and the second encryption unit;
5. The decoding control unit according to claim 1, further comprising: a decoding control unit that executes the second decoding unit and the first decoding unit a predetermined number of times in the order of the second decoding unit and the first decoding unit. The encryption device described.   6. The encryption apparatus according to claim 5, wherein when the prime number generation unit is repeatedly executed by the encryption control unit, the A and the B are generated so that the A and the B are different in each repeated execution. An encryption device for encrypting and decrypting an integer,
Prime number generating means for generating A and B so that the product N of the first prime number A and the second prime number B exceeds a predetermined number;
A product D of an integer A ′ that is 1 less than the first prime number A and an integer B ′ that is 1 less than the second prime number B, or a least common multiple K of the integer A ′ and the integer B ′ and an integer that is prime E, wherein the integer E is generated so that a power of the predetermined number as a base and the integer E as an exponent exceeds a predetermined number of digits, and an encryption key generating means using the integer E as an encryption key;
Decryption key generation means for generating an integer F so as to satisfy the following expression when an arbitrary integer m is set, and using the integer F as a decryption key corresponding to the encryption key;

For small integer X _i than the predetermined number, by adding an offset number T, and updates the integer X _i, the updated integer X _i and a bottom, said power was the integer E and exponent product calculates a remainder when divided by N and the encryption number Y _i of the integer X _i, with respect to the encrypted number Y _i, and updates the encryption number Y _i by subtracting the offset number T First encryption means;
The encrypted number Y _i is added to the offset number T to update the encrypted number Y _i , the updated encrypted number Y _i is a base, and the integer F is an exponent the by calculating the remainder when divided by the integer N decoding the integer X _i, a first decoding means for updating the integer X _i with respect to the integer X _i, by subtracting the offset number T,
The prime number generation means, the encryption key generation means, the decryption key generation means, and the first encryption means are connected to the prime number generation means, the encryption key generation means, the decryption key generation means, and the first encryption key. Encryption control means for executing a predetermined number of times in the order of encryption means;
Decoding control means for executing the first decoding means a predetermined number of times,
The first encryption means converts the integer X _i into an expansion equation composed of a plurality of integers, and calculates a power that uses the integer X _i as a base and the integer E as an exponent by the expansion equation. And
The first decryption means converts the encrypted number Y _i into an expansion equation composed of a plurality of integers, and based on the expansion equation, the encrypted number Y _i is a base and the integer F is an exponent. A cryptographic device that calculates a power. An encryption device encrypts and decrypts an integer,
A prime number generating step of generating the A and the B so that a product N of the first prime number A and the second prime number B exceeds a predetermined number;
A product D of an integer A ′ that is 1 less than the first prime number A and an integer B ′ that is 1 less than the second prime number B, or a least common multiple K of the integer A ′ and the integer B ′ and an integer that is prime E, generating the integer E such that a power of the predetermined number as a base and the integer E as an exponent exceeds a predetermined number of digits, and an encryption key generating step using the integer E as an encryption key;
A decryption key generation step of generating an integer F so as to satisfy the following expression when an arbitrary integer m is satisfied, and using the integer F as a decryption key corresponding to the encryption key;

First encryption is performed by calculating a remainder when the power of the integer X _i smaller than the predetermined number and the integer E as an exponent is divided by the product N to be the encrypted number Y _i of the integer X _i Steps,
A second encryption step of calculating an integer Y _i ′ by substitutional encryption of the encrypted number Y _i ;
A second decryption step of decrypting the encrypted number Y _i by substituting decryption from the integer Y _i ′;
A first decryption step of decrypting the integer X _i by calculating a remainder when the power of the integer F as an exponent is divided by the product N with the encrypted number Y _i as a base,
In the first encryption step, the integer X _i is converted into an expansion equation composed of a plurality of integers, and the expansion equation is used to calculate a power with the integer X _i as a base and the integer E as an exponent. And
In the first decryption step, the encrypted number Y _i is converted into an expansion equation composed of a plurality of integers, and the expansion number Y _i is used as a base and the integer F is an exponent according to the expansion equation. Calculate the power,
In the second encryption step, the encrypted number Y _i is converted into an expansion formula composed of a plurality of integers, and the encryption number Y _i is substitutively encrypted by the expansion formula,
The second decryption step is a method of converting the integer Y _i ′ into an expansion equation composed of a plurality of integers, and decrypting the encrypted number Y _i by the expansion equation.

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