KR100345685B1 - Key generating method, and encryption and decryption system and its method by using the braid operation - Google Patents

Abstract

1. TECHNICAL FIELD OF THE INVENTION

The present invention relates to an encryption / decryption system using a braiding operation, a method thereof, a key generation method therefor, and a computer-readable recording medium having recorded thereon a program for implementing the methods.

2. The technical problem to be solved by the invention

The present invention provides an encryption / decryption system using a conjugacy problem of a braid group, a method thereof, a key generation method therefor, and a computer-readable recording medium recording a program for realizing the methods. Its purpose is to.

3. Summary of Solution to Invention

According to the present invention, in an encryption / decryption system using a braiding operation, a second predetermined braid (b) is conjugated (bab ^-1 ) to a first predetermined braid (a) to obtain a secret key (b) and a public key ( a, bab- ¹ ) key generation means for registering the public key; Authentication means for receiving a public key (a, bab ^-1 ) from the key generation means and transferring it to an encryption means; Converts a predetermined message (M) into a braid (m), and conjugates a third predetermined braid (c) to the public key (a, bab ^-1 ) (cac ^-1 , cbab ^-1 c ^-1 ) The encryption means for encrypting the braid (m) (cac ^-1 , mcbab ^-1 c ^-1 ); And the other part of the ciphertext received from the encryption means by conjugating (bcac- ¹ b ^-1 ) the secret key b to the portion of the ciphertext (cac ^-1 ) received from the encryption means (mcbab ^-1 c- ^{). 1} ) and a calculation means (m = m (cbab- ¹ c- ¹ ) (bcac- ¹ b ^-1 ) ^-1 ) to obtain the braid (m) and to decode.

4. Important uses of the invention

The present invention is used to encrypt or decrypt a message.

Description

Encryption / decryption system using braiding operation and method and key generation method therefor {Key generating method, and encryption and decryption system and its method by using the braid operation}

The present invention relates to a key generation method, an encryption / decryption system using the same, and a method and a computer-readable recording medium recording a program for realizing the method. Particularly, the encryption / decryption system using a braid operation and the method and A method of generating a key therefor and a computer-readable recording medium having recorded thereon a program for realizing the above methods.

The public key encryption / decryption system currently used can be largely divided into a discrete log series represented by El Gamal (E1Gamal) and a factorized series represented by Rist-Shamir-Adleman (RSA). 'Difficult to obtain log' and 'difficult to factor synthetic water'. Until now, the security of the two series has been shown to be similar, and due to the characteristics of each encryption / decryption system, an appropriate encryption / decryption system is selected and used according to the use environment.

However, since such a conventional encryption / decryption system mainly takes a numerical approach, stability is questioned due to the newly developed calculation method and the improvement of the calculation capability. In particular, if a quantum computer under study is developed, the numerical encryption / decryption system is no longer secure. Therefore, the development of a new encryption / decryption system is required.

On the other hand, the braid group proposed by Artin in 1925 has been studied by many mathematicians since, and many studies are still in progress. Of these, the Conjugacy problem is known as one of the most important problems of the braid group, and there have been many studies among mathematicians. However, no efficient solution is known yet, and the complexity of the best algorithm known to date is It is as shown in (1).

[Equation 1]

Where n is the argument of the group of braids, and | W | is the length of the word when the group of braids is represented by the atin generator. In the above Equation (1), even if n | W | is about 10, the complexity is about 10,000 digits. Therefore, it is impossible to solve the problem by computer calculation using an algorithm.

However, no encryption / decryption system has been developed yet, using the difficulty of conjugation of braids.

Therefore, in order to cope with the emergence of new quantum computers, new calculation methods, and the like, there is an urgent need for the development of an encryption / decryption system using the conjugate problem of a braid group.

SUMMARY OF THE INVENTION The present invention has been made to meet the above requirements, and records an encryption / decryption system using the conjugate problem of a braidgroup, a method thereof, a key generation method therefor, and a program for realizing the methods. Its purpose is to provide a computer readable recording medium.

1 is an exemplary view of the braid used in the present invention.

Figure 2 is an example for explaining the transmission and reception structure of the encryption / decryption system using a braiding operation according to the present invention.

3 is a flow diagram of an embodiment of a key generation method for encryption / decryption using a braid operation according to the present invention.

4 is a flowchart illustrating an encryption method using a braid operation according to the present invention.

5 is a flowchart illustrating an embodiment of a decoding method using a braiding operation according to the present invention.

* Explanation of symbols for the main parts of the drawings

21: authentication system (CA) 22: encryption system

23: decryption system

In the encryption / decryption system of the present invention for achieving the above object, in the encryption / decryption system using a braid operation, the second predetermined braid (b) is conjugated to the first predetermined braid (a) (bab ^-1). Key generation means for generating a secret key (b) and a public key (a, bab ^-1 ) to register the public key; Authentication means for receiving a public key (a, bab ^-1 ) from the key generation means and transferring it to an encryption means; Converts a predetermined message (M) into a braid (m), and conjugates a third predetermined braid (c) to the public key (a, bab ^-1 ) (cac ^-1 , cbab ^-1 c ^-1 ) The encryption means for encrypting the braid (m) (cac ^-1 , mcbab ^-1 c ^-1 ); And the other part of the ciphertext received from the encryption means by conjugating (bcac- ¹ b ^-1 ) the secret key b to the portion of the ciphertext (cac ^-1 ) received from the encryption means (mcbab ^-1 c- ^{). 1} ) and a calculation means for obtaining and decoding the braid m by performing operation (m = m (cbab ⁻¹ c ⁻¹ ) (bcac ⁻¹ b ⁻¹ ) ⁻¹ ). in the encoding / decoding method of the present invention, encoding / decoding method applied to the encryption / decryption system using the braids operation, a first predetermined ball braids (a) a second predetermined braids, (b) the liquid (bab ^{- 1} ) a first step of generating a private key (b) and a public key (a, bab- ¹ ) to register the public key; Converts a predetermined message (M) into a braid (m), and conjugates a third predetermined braid (c) to the public key (a, bab ^-1 ) (cac ^-1 , cbab ^-1 c ^-1 ) A second step of encoding the braid (m) (cac ^-1 , mcbab ^-1 c ^-1 ); And the part of the encrypted cipher text ball to the private key (b) to (cac ^-1) liquefaction (bcac ^-1 b ^-1) to the other part of the encrypted cipher text (mcbab ^-1 c ^-1) and operations (m = m (cbab ^-1 c ^-1 ) (bcac ^-1 b ^-1 ) ^-1 ) to obtain and decode the braid (m).

Further, the key generation method of the present invention is a key generation method applied to a key generation device of an encryption / decryption system using a braid operation, wherein the first predetermined braid (a) is obtained and the third predetermined braid (c) is used. A first step of obtaining a second predetermined braid (b) that is a product equivalent; And conjugating (bab- ¹ ) the second predetermined braid (b) to the first predetermined braid (a) to generate a secret key (b) and a public key (a, bab ^-1 ). Characterized in that it comprises a second step of registering.

In addition, the encryption method of the present invention is the encryption method applied to the encryption system using the braiding operation, wherein the first predetermined braid (a) is obtained and the second predetermined that is equal to the product of the third predetermined braid (c). A first step of obtaining the braid (b) of; The first predetermined braids (a) the second predetermined braids, (b) the ball liquefied (bab ^-1) and a private key (b) the public key to generate (a, bab ^-1) on the public key A second step of registering; A third step of converting the predetermined message M into braids m; The fourth predetermined braid (c) to conjugate (cac ^-1 , cbab ^-1 c ^-1 ) the third predetermined braid (c) to the public key (a, bab- ¹ ) step; And multiplying (mcbab ^-1 c ^-1) to cipher text ^{(cac -1, mcbab -1 c -1} ) the braids (m) and the ball liquefied public key (cbab ^-1 c ^-1) the message is converted to It characterized in that it comprises a fifth step of generating.

In addition, the decryption method of the present invention, a decryption method applied to the decryption system using a braid operation, the first step of receiving an encrypted cipher text (cac ^-1 , mcbab ^-1 c ^-1 ) during the encryption process; A second step of conjugating (bcac ^-1 b ^-1 ) the secret key (b) to a portion (cac ^-1 ) of the received cipher text and changing the order of the products of the two braids that are equivalents of the products in the value; And a third step of multiplying the inverse of the value of the multiplication by the other portion of the encrypted ciphertext (mcbab- ¹ c ^-1 ) to obtain a braid (m) and to decrypt a predetermined message (M). It features.

On the other hand, in the present invention, in order to encrypt / decrypt a message using a braiding operation, a second predetermined braid (b) is conjugated to a first predetermined braid (a) in an encryption / decryption system having a processor ( bab- ¹ ) to generate a secret key (b) and a public key (a, bab- ¹ ) to register the public key; Converts a predetermined message (M) into a braid (m), and conjugates a third predetermined braid (c) to the public key (a, bab ^-1 ) (cac ^-1 , cbab ^-1 c ^-1 ) A second function of encoding the braid (m) (cac ^-1 , mcbab ^-1 c ^-1 ); And the part of the encrypted cipher text ball to the private key (b) to (cac ^-1) liquefaction (bcac ^-1 b ^-1) to the other part of the encrypted cipher text (mcbab ^-1 c ^-1) and operations (m providing a computer-readable recording medium having recorded thereon a program for realizing a third function of obtaining and decoding the braid (m) by performing m (cbab ^-1 c ^-1 ) (bcac ^-1 b ^-1 ) ^-1 ). do.

In addition, the present invention, in order to generate a key used for encryption / decryption using a braid operation, a first predetermined braid (a) is obtained in a key generation device having a processor, and the third predetermined braid (c) and A first function of obtaining a second predetermined braid (b) that is a product equivalent; And conjugating (bab- ¹ ) the second predetermined braid (b) to the first predetermined braid (a) to generate a secret key (b) and a public key (a, bab ^-1 ). A computer readable recording medium having recorded thereon a program for realizing a second function of registering the present invention is provided.

In addition, the present invention obtains a first predetermined braid (a) in a key generation and encryption system provided with a processor, in order to encrypt a message using a braid operation, and equals the product with the third predetermined braid (c). A first function of obtaining a second predetermined braid (b) to be; The first predetermined braids (a) the second predetermined braids, (b) the ball liquefied (bab ^-1) and a private key (b) the public key to generate (a, bab ^-1) on the public key A second function to register; A third function of converting a predetermined message M into braids m; The fourth predetermined braid (c) to conjugate (cac ^-1 , cbab ^-1 c ^-1 ) the third predetermined braid (c) to the public key (a, bab- ¹ ) function; And multiplying (mcbab ^-1 c ^-1) to cipher text ^{(cac -1, mcbab -1 c -1} ) the braids (m) and the ball liquefied public key (cbab ^-1 c ^-1) the message is converted to A computer readable recording medium having recorded thereon a program for realizing a fifth function to be generated is provided.

The present invention also provides a decryption system having a processor for decrypting a message using a braid operation, comprising: a first function of receiving an encrypted cipher text (cac ^-1 , mcbab ^-1 c ^-1 ) encrypted during an encryption process; A second function of conjugating a secret key (b) to a portion (cac ^-1 ) of the received ciphertext (bcac ^-1 b ^-1 ) to change the order of the products of two braids that are equivalents of the products in the value; And multiplying the inverse of the order of the product by another portion of the encrypted ciphertext (mcbab- ¹ c ^-1 ) to obtain a braid (m) to decrypt a predetermined message (M). A computer readable recording medium having recorded a program is provided.

That is, the present invention relates to a public key encryption / decryption system using a conjugacy problem of a braid group and a method thereof, and a method for generating a key therefor, in particular, a one-way function in the form of a discrete log rather than an RSA. It is similar to, but the form of discrete log uses 'difficulty of obtaining conjunctive log on Yuhan'.

In particular, the encryption / decryption system such as the discrete log series and RSA is an integer-based encryption / decryption system, whereas the present invention relates to an encryption / decryption system based on a geometric approach, and an encryption / decryption system of a similar approach. Has not been developed yet.

The above objects, features and advantages will become more apparent from the following detailed description taken in conjunction with the accompanying drawings. Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is an exemplary view of the braid used in the present invention.

As shown in Figure 1, the group of braids is to represent the braided braids in a logarithmic group, such as braiding the hair when there are several strands of strings.

There are several ways to express the group of braids. The most representative and intuitively easy way is to express the group's generator in a geometric way and the relational operator which geometric shape can be converted into a shape. It is represented by a (relation) to represent a presentation.

First, when the i-th string and the i + 1 string are twisted in a predetermined direction, i.e., when the i + 1 string passes over the i-th string, this encounter is defined as the group's creator, σ _i , Also known as the Atin constructor, to distinguish it from the constructors in other group expressions. In addition, if the twisted direction is reversed, this is defined as σ _i ^-1 . Suppose any braid is represented by an atin expression, and each braid is represented by an atin constructor, reading a given braid from top to bottom. In this way, any complex braid can be expressed in words. To multiply the words of any two braids, attach the two braids from top to bottom. When each of the first two braids is expressed in words, the words in succession are the product of the two braids. If you define multiplication in this way, this set is grouped.

As shown in Figure 1, each of the two braids can be converted from one to the other by moving the strings properly in a fixed state of the top and bottom. By using this property, we can define the equivalence of two braids. If we express this as a relational operator, we can get the group expression as shown in Equation 2 below.

Equation 2 σ12n-1ii + 1ii + 1ii + 1ijji

Where | i-j | ≥2.

The conjugacy problem is called whether there exists a W that satisfies U = WVW ⁻¹ for a given word U, V for the group obtained in this way. In order to solve this problem, it is impossible to solve the conjugation problem in this way because all W must be investigated. Thus, an effective solution to this problem is not yet known, and many mathematicians have shown that it is a very difficult problem. It is not yet known whether this problem becomes a non-deterministic polynominal (NP), and it has been studied to be more difficult than NP. Based on this fact, an encryption / decryption system similar to the E1Gamal encryption / decryption system can be constructed.

2 is an exemplary view illustrating a transmission and reception structure of an encryption / decryption system using a braid operation according to the present invention.

The basic configuration of the present invention is a key generation unit (not shown in the figure) of the decryption system 12. Public key (a, bab) by performing an initialization process by a method as shown in FIG.^-One) And the private key b, then the public key (a, bab^-One) Is registered in the authentication system (CA) 21 (11), the authentication system 21 is a public key (a, bab to the encryption system 22)^-One(12). At this time, the authentication system 21 performs an authentication process for confirming whether the encryption system 22 and the decryption system 23 are legitimate users.

Then, the encryption system 22 to encrypt and transmit the message to the decryption system 23 uses the public key (a, bab- ¹ ) received from the authentication system 21 to describe the message in the method of FIG. 4 described below. The data is encrypted (13) and transmitted to the decryption system 23 (14).

Then, the decryption system 23 receiving the encrypted message decrypts the message by the method of FIG. 5 described later to restore the original message (15).

Next, referring to FIG. 3, a method for generating a public key and a secret key used in an encryption / decryption method using a braid operation will be described in detail.

3 is a flowchart illustrating a method for generating a key for encryption / decryption using a braid operation according to the present invention.

First, in the decryption system 23, one random braid a is obtained from 2n strings, and the braid b is obtained by twisting only the right n strings of the 2n strings (31).

Thereafter, in the decoding system 23, the conjugate bab ⁻¹ is calculated using the arbitrary braid a and the right braid b. The secret key is b, and a and bab ^-1 are public keys (32). Subsequently, as described above with reference to FIG. 1, when the public key (a, bab- ¹ ) is registered in the authentication system (CA) 21 (11), the authentication system 21 uses the public key ( a, bab ^-1 ) (12).

Next, the encryption process and the decryption process will be described in detail with reference to FIGS. 4 and 5.

4 is a flowchart illustrating an encryption method using a braid operation according to the present invention, and FIG. 5 is a flowchart illustrating a decryption method using a braid operation according to the present invention.

First, the process of encrypting the message, in the encryption system 22 converts the message M to braid m (41), and selects a random braid c with only n strings left of 2n strings (42). C is conjugated to public keys a and bab ^-1 to obtain cac ^-1 and cbab ^-1 c ^-1 , and multiplies braid m with conjugated public key cbab ^-1 c ^-1 to calculate mcbab ^-1 c ^-1 (43) The cipher text mcbab ^-1 c ^-1 and cac ^-1 are transmitted to the decryption system 23 (44).

On the other hand, the braids of the right n strings among the 2n strings may be c, and the braids of the left n strings of the 2n strings may be b.

Next, the process of converting the message M into braid m will be described in more detail.

First, we need to convert the message (number) M to braided. In general, there are many other words which are equivalent to braid, but there is no shear history function in which the relationship between the general word and the message is maintained in a 1: 1 relationship. Therefore, the braid must be converted in some special way. If any two braids in any braid do not meet twice, and all braids are double braids, then this braid is called a canonical factor. At this point, when the starting point of each string is examined at which point, the permutation group can be created based on this, and the shear yarn function can be simply configured. Thus, the standard element and the permutation group are equivalent.

Next, let's take a look at how a message can be expressed in permutations and how a permutation is represented by braids.

First, let's look at how to express an arbitrary permutation as a number. There are various ways to indicate permutation, but one of them is a method represented by (π (1), π (2), ..., π (n)). In other words, similar to the standard element of braid, it is written how the end of the first string moved and how many times the end of the second string went. Find the inversion of this expression. In this case, the inversion column refers to a column in which the number of π (j) smaller than i is smaller than π (i) in the i th term. In this way, the following Equation 3 is obtained.

[Equation 3]

Α _k is the k-th term of the inversion string.

Conversely, an inverted sequence can be obtained by any number, and a permutation can also be obtained from any inverted sequence. There is completed the permutation, starting from the front column inversion, if the k-th column is inverted if α _k d is added to the k (k + 1) th permutation. When we're done with n like this, the columns from this are the permutations we want. In this way, a random permutation of n and n! Is a one-to-one correspondence, corresponding to the message and the standard element of the braid.

However, if the message M is expressed as a standard element, the braid itself is viewed from the attacker's point of view from the point of view of the permutations. The attacker can then figure out the message because the permutation problem is easily solved. Therefore, in the present invention, the message is encrypted by multiplying one standard element with another standard element. Here, there are many ways to select other standard elements, but in the present invention, after obtaining the inverse of the first braid, the braid is changed from the negative power of the inverse to the positive power. The product of the two braids is m.

Next, referring to FIG. 5, when the encrypted message is decrypted, the decryption system 23 receives the ciphertext cac ^-1 and mcbab ^-1 c ^-1 from the encryption system 22 (51). bcac ^-1 b ^-1 can be obtained by conjugating the secret key b to cac ^-1 . At this time, since b and c are selected as right braid and left braid, respectively, even if the order of the products is changed, the two products are equivalent, and the following equation (4) is established.

Equation 4 cbab-1-1-1-1

And, by multiplying the received encrypted message mcbab ^-1 c ^-1 by the inverse of bcac ^-1 b ^-1, the following Equation 5 is established.

[Equation 5] m = m (cbab-1-1-1-1-1

At this time, by substituting Equation 4 into Equation 5, m can be obtained (52). The braid m can then be decoded into the original message M in a simple manner (53). The method of the present invention as described above can be implemented as a program in a computer-readable form in a recording medium (CD-ROM, RAM, ROM, Floppy disk, hard disk, magneto-optical disk, etc.).

The present invention described above is not limited to the above-described embodiments and the accompanying drawings, and various substitutions, modifications, and changes are possible in the art without departing from the technical spirit of the present invention. It will be apparent to those of ordinary knowledge.

The present invention as described above, as a public key encryption / decryption system using a conjugated problem of braiding, it is possible to provide a completely new encryption / decryption system that has not been proposed even worldwide.

Furthermore, the present invention, unlike the conventional encryption / decryption system, which mainly takes a numerical approach, because the geometric structure is used as the basic skeleton, the message having an arbitrary length as well as the encryption of a message of a predetermined length or a simple text message. It can also be used to encrypt other forms of messages.

In addition, the present invention is excellent in safety because it has to solve a problem more difficult than NP, unlike the conventional encryption / decryption system whose security is suspected by a new calculation method, a quantum computer, or the like.

In addition, the present invention provides a speed that can be used in terms of speed, and can be said to be a system that can be actually applied.

Claims (23)

In the encryption / decryption system using a braid operation, The registering the public key to generate a first predetermined braids (a) a second predetermined braids, (b) the ball liquefied (bab ^-1) by the private key (b) and public keys (a, bab ^-1) for Key generation means for; Authentication means for receiving a public key (a, bab ^-1 ) from the key generation means and transferring it to an encryption means; Converts a predetermined message (M) into a braid (m), and conjugates a third predetermined braid (c) to the public key (a, bab ^-1 ) (cac ^-1 , cbab ^-1 c ^-1 ) The encryption means for encrypting the braid (m) (cac ^-1 , mcbab ^-1 c ^-1 ); And Conjugating the secret key (b) to a part of the cipher text (cac ^-1 ) received from the encryption means (bcac ^-1 b ^-1 ) to another part of the cipher text (mcbab ^-1 c ^-1 ) received from the encryption means Decoding means for obtaining and decoding the braid (m) by performing operation (m = m (cbab ^-1 c ^-1 ) (bcac ^-1 b ^-1 ) ^-1 ) Encryption / decryption system comprising a. The method of claim 1, The key generating means, Obtaining the first predetermined braid (a) and obtaining the second predetermined braid (b) which is equivalent to the product of the third predetermined braid (c), and obtaining the second predetermined braid (b) to the first predetermined braid (a). ball predetermined braids, (b) liquefaction (bab ^-1) by the private key (b) and public key encryption / decryption, characterized in that to generate the (a, bab ^-1) for registering the public key to the authentication means system. The method of claim 2, The encryption means, The predetermined message M is converted into a braid m, the third predetermined braid c is selected, and the third predetermined braid is applied to the public keys a and bab ⁻¹ received from the authentication means. (c) a ball multiplied by the liquefied ^{(cac -1, cbab -1 c -1} ), braids (m) and the ball liquefied public key (cbab ^-1 c ^-1) the message is converted after (mcbab ^{- 1} c ^-1 ) to generate a ciphertext (cac ^-1 , mcbab ^-1 c ^-1 ) and transmit it to the decryption means. The method of claim 3, wherein The decoding means, After the secret key b is conjugated (bcac ^-1 b ^-1 ) to a part of the ciphertext (cac ^-1 ) received from the encryption means, the order of the products of the second and third predetermined braids is changed. The inverse of the value is multiplied by another portion (mcbab- ¹ c ^-1 ) of the cipher text received from the encryption means to obtain the braid (m) to decrypt the predetermined message (M), characterized in that . The method according to any one of claims 1 to 4, The process of converting the predetermined message (M) into braid (m) in the encryption means, And the predetermined message (M) is expressed as a product of canonical factors. The method of claim 5, The third predetermined braid (c) is any left braid where only n strings (n is a factor of braid group) on the left of 2n strings are twisted. The second predetermined braid (b) is an encryption / decryption system, characterized in that the right braid twisted only n strings out of 2n strings. The method of claim 5, The third predetermined braid (c) is any right braid, in which only n strings on the right side of the 2n strings are twisted. The second predetermined braid (b) is an encryption / decryption system, characterized in that the left braid is twisted only the left n of the 2n string. In the encryption / decryption method applied to an encryption / decryption system using a braid operation, First predetermined by braids (a) a second predetermined braids, (b) the ball liquefied (bab ^-1) to generate a private key (b) and public keys (a, bab ^-1) for registering the public key First step; Converts a predetermined message (M) into a braid (m), and conjugates a third predetermined braid (c) to the public key (a, bab ^-1 ) (cac ^-1 , cbab ^-1 c ^-1 ) A second step of encoding the braid (m) (cac ^-1 , mcbab ^-1 c ^-1 ); And The part of the encrypted cipher text (cac ^-1) to another part of the encrypted cipher text to the ball liquefied (bcac ^-1 b ^-1) the secret key ^{(b) (mcbab -1 c -1} ) and calculation (m = The third step of obtaining and decoding the braid (m) by m (cbab ^-1 c ^-1 ) (bcac ^-1 b ^-1 ) ^-1 Encryption / decryption method comprising a. The method of claim 8, The first step is, A fourth step of obtaining the first predetermined braid (a) and obtaining the second predetermined braid (b) which is a product of the third predetermined braid (c); And The first predetermined braids (a) the second predetermined braids, (b) the ball liquefied (bab ^-1) and a private key (b) the public key to generate (a, bab ^-1) on the public key 5th step to register Encryption / decryption method comprising a. The method of claim 9, The second step, A sixth step of converting the predetermined message M into braids m; Selecting the third predetermined braid (c) to conjugate (cac ^-1 , cbab ^-1 c ^-1 ) the third predetermined braid (c) to the registered public key (a, bab ^-1 ) Seventh step; And The ciphertext (cac ^-1 , mcbab ^-1 c ^-1 ) is generated by multiplying the braid (m) to which the message is converted and the conjugated public key (cbab ^-1 c ^-1 ) (mcbab ^-1 c ^-1 ) 8th step to transmit by Encryption / decryption method comprising a. The method of claim 10, The third step, A ninth step of receiving the encrypted cipher text (cac ^-1 , mcbab ^-1 c ^-1 ); A tenth to conjugate (bcac ^-1 b ^-1 ) the secret key (b) to a portion (cac ^-1 ) of the received ciphertext and change the order of the product of the second and third predetermined braids in its value; step; And An eleventh step of deciphering the predetermined message (M) by obtaining the braid (m) by multiplying the inverse of the multiplication order of the product by another portion of the encrypted cipher text (mcbab- ¹ c ^-1 ) Encryption / decryption method comprising a. The method according to any one of claims 8 to 11, The process of converting the predetermined message (M) into braid (m), And the predetermined message (M) is expressed as a product of canonical factors. The method of claim 12, The third predetermined braid (c) is any left braid where only n strings (n is a factor of braid group) on the left of 2n strings are twisted. The second predetermined braid (b) is an encryption / decryption method, characterized in that the right braid twisted only n strings out of 2n strings. The method of claim 12, The third predetermined braid (c) is any right braid, in which only n strings on the right side of the 2n strings are twisted. The second predetermined braid (b) is an encryption / decryption method, characterized in that the left braid twisted only the left n string of the 2n string. In the key generation method applied to the key generation device of the encryption / decryption system using the braiding operation, A first step of obtaining a first predetermined braid (a) and a second predetermined braid (b) which is equivalent to a product with the third predetermined braid (c); And The first predetermined braids (a) the second predetermined braids, (b) the ball liquefied (bab ^-1) and a private key (b) the public key to generate (a, bab ^-1) on the public key 2nd step to register Key generation method comprising a. In the encryption method applied to the encryption system using a braid operation, A first step of obtaining a first predetermined braid (a) and a second predetermined braid (b) which is equivalent to a product with the third predetermined braid (c); The first predetermined braids (a) the second predetermined braids, (b) the ball liquefied (bab ^-1) and a private key (b) the public key to generate (a, bab ^-1) on the public key A second step of registering; A third step of converting the predetermined message M into braids m; The fourth predetermined braid (c) to conjugate (cac ^-1 , cbab ^-1 c ^-1 ) the third predetermined braid (c) to the public key (a, bab- ¹ ) step; And The ciphertext (cac ^-1 , mcbab ^-1 c ^-1 ) is generated by multiplying the braid (m) to which the message is converted and the conjugated public key (cbab ^-1 c ^-1 ) (mcbab ^-1 c ^-1 ) The fifth step Encryption method using a braid operation comprising a. The method of claim 16, The first step is, And the predetermined message (M) is expressed as a product of canonical factors. In the decoding method applied to the decoding system using a braid operation, A first step of receiving an encrypted cipher text (cac ^-1 , mcbab ^-1 c ^-1 ) in the encryption process; A second step of conjugating (bcac ^-1 b ^-1 ) the secret key (b) to a portion (cac ^-1 ) of the received cipher text and changing the order of the products of the two braids that are equivalents of the products in the value; And A third step of decrypting a predetermined message (M) by obtaining a braid (m) by multiplying the inverse of the order of the product by another portion of the encrypted ciphertext (mcbab- ¹ c ^-1 ) Decoding method using a braid operation comprising a. The method of claim 18, One of the two braids equivalent to the product is any left braid where only the left n of the 2n strings (n is the argument of the braid group) are twisted, The other one of the two braids equivalent to the product is a decoding method using a braid operation, characterized in that the right braid twisted only n strings out of 2n strings. In an encryption / decryption system with a processor, to encrypt / decrypt a message using a braid operation, First predetermined by braids (a) a second predetermined braids, (b) the ball liquefied (bab ^-1) to generate a private key (b) and public keys (a, bab ^-1) for registering the public key First function; Converts a predetermined message (M) into a braid (m), and conjugates a third predetermined braid (c) to the public key (a, bab ^-1 ) (cac ^-1 , cbab ^-1 c ^-1 ) A second function of encoding the braid (m) (cac ^-1 , mcbab ^-1 c ^-1 ); And The part of the encrypted cipher text (cac ^-1) to another part of the encrypted cipher text to the ball liquefied (bcac ^-1 b ^-1) the secret key ^{(b) (mcbab -1 c -1} ) and calculation (m = Third function for obtaining and decoding the braid (m) by m (cbab ^-1 c ^-1 ) (bcac ^-1 b ^-1 ) ^-1 A computer-readable recording medium having recorded thereon a program for realizing this. In order to generate a key used for encryption / decryption using a braid operation, to a key generation device having a processor, A first function of obtaining a first predetermined braid (a) and a second predetermined braid (b) which is equivalent to the product of the third predetermined braid (c); And The first predetermined braids (a) the second predetermined braids, (b) the ball liquefied (bab ^-1) and a private key (b) the public key to generate (a, bab ^-1) on the public key 2nd function to register A computer-readable recording medium having recorded thereon a program for realizing this. In a key generation and encryption system with a processor to encrypt a message using a braid operation, A first function of obtaining a first predetermined braid (a) and a second predetermined braid (b) which is equivalent to the product of the third predetermined braid (c); The first predetermined braids (a) the second predetermined braids, (b) the ball liquefied (bab ^-1) and a private key (b) the public key to generate (a, bab ^-1) on the public key A second function to register; A third function of converting a predetermined message M into braids m; The fourth predetermined braid (c) to conjugate (cac ^-1 , cbab ^-1 c ^-1 ) the third predetermined braid (c) to the public key (a, bab- ¹ ) function; And The ciphertext (cac ^-1 , mcbab ^-1 c ^-1 ) is generated by multiplying the braid (m) to which the message is converted and the conjugated public key (cbab ^-1 c ^-1 ) (mcbab ^-1 c ^-1 ) 5th function to do A computer-readable recording medium having recorded thereon a program for realizing this. In a decryption system with a processor, to decrypt a message using a braid operation, A first function of receiving an encrypted cipher text cac ^-1 and mcbab ^-1 c ^-1 in an encryption process; A second function of conjugating a secret key (b) to a portion (cac ^-1 ) of the received ciphertext (bcac ^-1 b ^-1 ) to change the order of the products of two braids that are equivalents of the products in the value; And A third function of decrypting a predetermined message M by multiplying the inverse of the multiplication of the product by another portion of the encrypted ciphertext (mcbab- ¹ c ^-1 ) to obtain a braid (m) A computer-readable recording medium having recorded thereon a program for realizing this.