KR100679627B1 - Ciphering and Deciphering Method - Google Patents

Abstract

The present invention relates to an encryption / decryption method, wherein an elliptic curve on a F ₂ ^m finite body, a non-reducible polynomial used for modular operation of the elliptic curve, a transmission initial point on the elliptic curve and a transmission initial point on the elliptic curve Sharing information on the reception origin on the elliptic curve having a sender side and a receiver side; Sharing information about a super elliptic curve on a F ₂ ^m finite body and a non-reducible polynomial used for a modular operation of the super elliptic curve at a sender side and a receiver side; Selecting a first transmission secret key at the sender side; Generating a first transmission public key by repeatedly adding a transmission initial point on the elliptic curve by the number of times of the first transmission secret key on a sender side; Transmitting the first transmission public key to a receiver side; Selecting a first receiving secret key at the receiver side; Generating a first receiving public key by repeatedly adding a reception initial point on the elliptic curve by the number of times of the first receiving secret key on a receiver side; Transmitting the first receiving public key to a sender side; Generating an elliptic curve shared secret key by repeating adding the first received public key by the number of times of the first transmitted secret key at a sender side; Generating a super elliptic curve shared secret key based on the elliptic curve shared secret key at a sender side; Generating a second transmission public key by repeatedly adding a transmission initial point on the super elliptic curve as many times as the number of the super elliptic curve sharing secret keys on the sender side; Transmitting the second transmission public key to a receiver side; Generating the elliptic curve shared secret key by repeatedly adding the first transmit public key as many times as the number of the first received secret keys on a receiver side; Generating the super elliptic curve shared secret key based on the elliptic curve shared secret key at a receiver side; Generating a second receiving public key by repeatedly adding a reception initial point on the super elliptic curve by the number of times of the super elliptic curve sharing secret key at a receiver side; Transmitting the second receiving public key to a sender side; Generating an encryption / decryption shared secret key by adding a transmission origin of the super elliptic curve and the second receiving public key on a sender side; Encrypting plain text using the encryption / decryption shared secret key at a sender side; Transmitting the encrypted plain text to a receiver side; Generating the encryption / decryption shared secret key by adding a reception origin of the super elliptic curve and the second transmission public key at a receiver side; And decrypting the encrypted plain text transmitted from the sender side using the encryption / decryption shared secret key at the receiver side. As a result, the encryption strength can be improved.

Elliptic Curve, Encryption, Shared Secret, Plain Text, Initial Point

Description

Ciphering and Deciphering Method

1 is a flowchart of an encryption / decryption method according to an embodiment of the present invention;

Figure 2 is a table showing the vector value of the non-reduced polynomial for the elliptic curve in the darkening method according to an embodiment of the present invention,

Figure 3 is a table showing the vector value of the non-reduced polynomial for the super-elliptic curve in the darkening method according to an embodiment of the present invention,

4 is a flowchart of an encryption / decryption method according to another embodiment of the present invention;

5 is a flowchart of a conventional encryption / decryption method;

6 is a flowchart of a conventional double signature method.

The present invention relates to an encryption / decryption method, and more particularly, to a method for performing encryption and decryption by sharing a secret key in the form of a session key based on secret information generated by a sender and a receiver. will be.

Recently, with the rapid development of computer communication networks, techniques for encrypting important information such as personal privacy and e-commerce history have been devised and used.

Encryption methods can be classified into a secret key encryption method for performing encryption and decryption using the same key (secret key) and a public key encryption method for encrypting using a public key and decrypting using a private key.

In the case of public key cryptography, the basic functions are based on a difficult mathematical problem. Therefore, the operation speed of encryption and decryption is much slower than that of the secret key cryptography and requires a lot of system resources.

On the other hand, in the case of secret key encryption method, in order to secure confidentiality according to encryption, it is necessary to be careful not to expose the secret key to a third party other than a communication party, and in the case where the party exchanging information is N, one additional person joins N Since additional private keys are needed (in the case of public key cryptography, only a pair of public and private keys are added), it becomes difficult to manage the private key.

Considering the characteristics of the public key encryption method and the secret key encryption method, instead of encrypting the entire information according to the public key encryption method, the secret key encryption method encrypts the information and the secret key used for the encryption of the information is used as the public key encryption method. The sharing method in the sender side and the receiver side is widely used.

As described above, when the secret key used in the secret key encryption method is shared by the public key encryption method, it is unreliable to set the secret key in the form of a session key on the sender side unilaterally. Based on this, a method of sharing a secret key in the form of a session key is proposed.

Algorithms for sharing secret keys in the form of session keys are mostly based on the Diffie-Hellman algorithm.

5 is a flowchart of a conventional encryption / decryption method.

The conventional encryption / decryption method is as follows. For the sake of convenience, it is assumed that the sender and receiver share p, a prime number greater than 2, and a generator g (1 <g <p) of Z (p) ^*, an integer less than p. . Here, the information about the prime number p and the generator g can be shared by exchanging them in the form of a session key when setting up a communication line for plain text transmission or by placing them on a public list accessible from the sender side and the receiver side. have.

First, the sender side and the receiver side arbitrarily select integers a and b smaller than p-1 as secret keys, respectively (S101). Where a and b are chosen to belong to a set of integers (1, 2, ..., p-2).

Next, the sender calculates the public key A = (g ^a ) mod p using the secret key a and transmits it to the receiver (S102).

Next, the receiver calculates the public key B = (g ^b ) mod p using the secret key b, and transmits it to the sender (S103).

Next, the sender side applies the secret key a to the public key from the receiver side to generate a shared secret key S _a = (B) ^a mod p = (g ^b ) ^a mod p = g ^ab mod p (S104).

The sender side then encrypts the plain text with the shared secret key and sends it to the receiver side (S105).

The receiver side then applies the secret key b to the public key from the sender side to generate a shared secret key S _b = (A) ^b mod p = (g ^a ) ^b mod p = g ^ab mod p (S106).

Finally, the receiver decrypts the cipher text from the sender using the shared secret generated by the receiver (S107). Since S _a = S _b , the sender side can decrypt the information transmitted to the receiver by using the public key from the sender.

On the other hand, authentication issues verify the identity of the sender, integrity issues to ensure that the information has not been compromised during the delivery, and non-repudiation to prevent the provider from denying the information. In order to solve the reputation problem, a digital signature method is proposed that encrypts the message digest with the sender's private key.

And if one wants to transmit information that is known only to specific recipients such as e-commerce and requires confidentiality to other recipients, the dual signature is used to collect the information delivered to both recipients and encrypt it with the sender's secret key at once. have.

6 is a flowchart of a conventional double signature method.

The conventional double signature method is described as follows.

First, the purchaser generates a message digest M1 by applying a hash function to the purchase information OI (S121).

Next, the buyer generates a message digest M2 by applying a hash function to the payment information PI (S122).

Next, the purchaser concatenates two message digests M1 and M2 to generate a concatenated result M1M2 (S123).

Next, a message digest M is generated by applying a hash function to the concatenated result M1M2 (S124).

Next, the purchaser generates an electronic signature (double signature) using the message digest M as the purchaser's own private key (S125).

Next, the buyer encrypts the payment information to be sent to the payment institution with the secret key (S126).

Next, the electronic key is generated by encrypting its private key with the public key of the payment institution (S127).

Next, the buyer transmits the purchase information, encrypted payment information, concatenated result M1M2, double signature, and electronic envelope to the seller (S128).

Meanwhile, the seller generates the message digest M1 'by applying the same hash function as the buyer to the received purchase information (S129).

Next, the seller replaces the received M1 M2 with the newly generated M1 'and then applies the same hash function to the replaced M1'M2 to generate the message digest M' (S130).

The seller then decrypts the received dual signature with the buyer's public key to generate the message M (S131).

Next, the seller compares the message digest M 'generated by applying the hash function with the message digest M decrypted with the buyer's public key, and determines that the purchase is a legitimate purchase request (S132).

Next, the seller transmits the encrypted payment information, the electronic envelope, the double signature, and the concatenated result M1M2 to the payment institution (S133).

Next, the payment institution decrypts the received electronic envelope with its private key (S134).

Next, the payment institution generates the payment information, the concatenated result M1M2, and the buyer's signature using the secret key obtained from the electronic envelope (S135).

Next, the payer generates a message digest M2 'by applying the same hash function as the buyer to the decrypted payment information (S136).

Next, the payment institution replaces the received M1M2 with the newly generated M2 ', and then applies the same hash function to the replaced M1M2' to generate the message digest M "(S137).

Next, the payer decrypts the received dual signature with the buyer's public key to generate a message digest M (S138).

Next, the seller compares the message digest M " generated by applying the hash function to the message digest M &quot; decrypted with the buyer's public key and determines that the payment is a legitimate payment request (S139).

However, according to the conventional encryption and decryption method, since encryption and decryption is performed by using the difficulty of prime factorization once, there is a problem in that the encryption strength is relatively weak when compared based on the same key size.

In addition, according to the conventional electronic signature method, there is a problem that the processing speed is lowered and the security of the information due to the eavesdropping of the electronic bag is reduced because the electronic envelope must be used.

Accordingly, it is an object of the present invention to provide an encryption / decryption method in which encryption strength is improved.

The object is, according to the present invention, an elliptic curve on the F ₂ ^m finite body, a non-reduced polynomial used for the modular operation of the elliptic curve, a transmission initial point on the elliptic curve and a transmission initial point on the elliptic curve. Sharing information on the reception origin on the elliptic curve having a sender side and a receiver side; Sharing information about a super elliptic curve on a F ₂ ^m finite body and a non-reducible polynomial used for a modular operation of the super elliptic curve at a sender side and a receiver side; Selecting a first transmission secret key at the sender side; Generating a first transmission public key by repeatedly adding a transmission initial point on the elliptic curve by the number of times of the first transmission secret key on a sender side; Transmitting the first transmission public key to a receiver side; Selecting a first receiving secret key at the receiver side; Generating a first received public key by repeatedly adding a reception initial point on the elliptic curve by the number of times of the first received secret key on a receiver side; Transmitting the first receiving public key to a sender side; Generating an elliptic curve shared secret key by repeating adding the first received public key by the number of times of the first transmitted secret key at a sender side; Generating a super elliptic curve shared secret key based on the elliptic curve shared secret key at a sender side; Generating a second transmission public key by repeatedly adding a transmission initial point on the super elliptic curve as many times as the number of the super elliptic curve sharing secret keys on the sender side; Transmitting the second transmission public key to a receiver side; Generating the elliptic curve shared secret key by repeatedly adding the first transmit public key as many times as the number of the first received secret keys on a receiver side; Generating the super elliptic curve shared secret key based on the elliptic curve shared secret key at a receiver side; Generating a second receiving public key by repeatedly adding a reception initial point on the super elliptic curve by the number of times of the super elliptic curve sharing secret key at a receiver side; Transmitting the second receiving public key to a sender side; Generating an encryption / decryption shared secret key by adding a transmission origin of the super elliptic curve and the second receiving public key on a sender side; Encrypting plain text using the encryption / decryption shared secret key at a sender side; Transmitting the encrypted plain text to a receiver side; Generating the encryption / decryption shared secret key by adding a reception origin of the super elliptic curve and the second transmission public key at a receiver side; And decrypting an encrypted plaintext transmitted from the sender side using the encryption / decryption shared secret key at a receiver side.

The generating of the super elliptic curve shared secret key may include selecting either one of an x value and a y value of the elliptic curve shared secret key, converting the selected elliptic curve shared secret key value into a binary number; And converting the elliptic curve shared secret key value converted to binary to decimal.

And the super-elliptic curve sharing secret key is independently generated between the sender side and the receiver 1 side and between the sender side and the receiver 2 side to remove the electronic envelope and improve processing speed and security; Generating a message digest M1 by applying a hash function to the receiver 1 side information at a sender side, generating a message digest M2 by applying the hash function to the receiver 2 side information at the sender side; Generating a concatenated result M1M2 by concatenating the message digests M1 and M2 at the sender side, generating a message digest M by applying the hash function to the concatenated result M1M2 at the sender side, and at the sender side Generating the digital signature DS ₁ by using the decryption shared secret key for the receiver 1 on the message digest M; and encrypting the decryption shared secret key for the receiver 2 on the message digest M on the sender side. Applying the digital signature to generate a DS ₂ ; Encrypting the receiver 2 side information with an encryption / decryption shared secret key for the receiver 2 side at the sender side, the receiver 1 side information, the encrypted receiver 2 side information, the concatenated result M1M2, and at the sender side; Transmitting the digital signatures DS ₁ and DS ₂ to the recipient 1 side, generating the message digest M1 'by applying the hash function to the receiver 1 side information at the receiver 1 side, and at the receiver side. Replacing M1 in the concatenated result M1M2 with the message digest M1 ', generating a message digest M' by applying the hash function to the replaced M1'M2, and receiving the digital signature DS ₁ at the receiver 1 side; Decrypting with the encryption / decryption shared secret key for the sender side to generate a message digest M, and receiving the message digest M 'at the receiver 1 side; Comparing the message digest M decrypted with the encryption / decryption shared secret key to the sender side and determining that the message is a legitimate purchase request, and at the receiver 1 side, the encrypted receiver 2 side information, the concatenated result M1M2 and the electronic device; Transmitting a signature DS ₂ to the recipient 2 side, decrypting the encrypted recipient 2 side information with an encryption / decryption shared secret key for the sender side, and decrypting the decrypted recipient 2 side information; Generating a message digest M2 'by applying the hash function, replacing M2 of the concatenated result M1M2 with the message digest M2', and then applying the hash function to the replaced concatenation result M1M2 '. &Quot;, and converts the digital signature DS ₂ to the encryption / decryption shared secret for the sender side at the receiver 2 side. Decrypting and generating a message digest M, and comparing the message digest M " and the message digest M decrypted with the encryption / decryption shared secret key for the sender side and determining that the request is a legitimate purchase request. It is preferable to configure to include.

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

1 is a flowchart of an encryption / decryption method according to an embodiment of the present invention, and FIG. 2 is a table showing a vector value of an inflexible polynomial with respect to an elliptic curve in an encryption / decoding method according to an embodiment of the present invention. 3 is a table showing the vector value of the non-reduced polynomial with respect to the super-elliptic curve in the darkening method according to an embodiment of the present invention.

Referring to the encryption and decryption method according to an embodiment of the present invention as follows.

Step 1: Sharing Information on Elliptic Curves (S1)

x² + 1이라고 하고, 감축불가 다항식 f(x) = x⁴ + x + 1이라고 한다.The elliptic curve is chosen to be a non-supersingular elliptic curve on the F ₂ ⁴ finite body, where the finite body is set such that ^m of F ₂ ^m is a positive integer greater than one. Elliptic curve selected for convenience of explanation E: y ² + xy = x ³ +

It is called x ² + 1 and the non-reducible polynomial f (x) = x ⁴ + x + 1.

즉, 16개가 존재한다. 여기서 벡터 값은

로서 4bit로 구성되어 있다는 점을 고려하여 각 bit의 위치 값을 나타내는

의 멱승(power)으로 벡터 값과 위치값(

⁰,

¹,

²,

³) 표현을 나타내면 도2와 같다. 도2에서 표시된 g는 감축불가다항식을 벡터 값으로 변환할 때 기준이 되는 생성자(generator)를 의미한다.A vector value that can be composed of α-unreducible polynomial f (x) = x ⁴ + x + 1

That is, there are 16. Where the vector value is

The position value of each bit

The power of the vector value and the position value (

⁰ ,

¹ ,

² ,

³ ) Expression is as shown in FIG. In FIG. 2, g denotes a generator that is a reference when converting an irreducible polynomial to a vector value.

³,

³), (

³,

⁰), (

⁵,

¹²), (

⁵,

¹⁴), (

⁶,

¹⁰), (

¹⁵,

⁷), (

¹⁵,

⁹), (

⁶,

⁷), (

⁹,

²), (

⁹,

¹¹), (

¹⁰,

²), (

¹⁰,

⁴), (

¹²,

²), (

¹²,

⁷), (

⁰,

¹⁵)을 얻을 수 있다. 여기서

⁰ = 1로서 감축불가다항식의 마지막 벡터 값을 나타낸다.When a finite point satisfying an elliptic curve is calculated based on the non-reduced polynomial vector value of FIG. 2, (0, 1), (

³ ,

³ ), (

³ ,

⁰ ), (

⁵ ,

¹² ), (

⁵ ,

¹⁴ ), (

⁶ ,

¹⁰ ), (

¹⁵ ,

⁷ ), (

¹⁵ ,

⁹ ), (

⁶ ,

⁷ ), (

⁹ ,

² ), (

⁹ ,

¹¹ ), (

¹⁰ ,

² ), (

¹⁰ ,

⁴ ), (

¹² ,

² ), (

¹² ,

⁷ ), (

⁰ ,

¹⁵ ). here

⁰ = 1, which represents the last vector value of the non-reducible polynomial.

⁹,

²)이라고 한다.And the sender side selects an initial point (P _er) either a finite point on the elliptic curve selected as the initial point (P _es), and the receiver side so as to have a value equal to the transmission zero point (P _es). For convenience of explanation, P _es = _Per =

⁹ ,

² ).

The information on the elliptic curve can be shared by exchanging it in the form of a session key when setting up a communication line for plain text transmission or by placing it on a public list accessible from the sender side and the receiver side.

Step 2: share information about the super-elliptic curve (S2)

The hyper elliptic curve is selected on the F ₂ ⁵ finite body (where the finite body is set such that ^m of F ₂ ^m is a positive integer greater than 1). The elliptic curve is HE: v ² + (u ² + u) v = u ⁵ + u ³ + 1, and the non-reduced polynomial used for the modular operation of the super elliptic curve is p (x) = x ⁵ + x ² + 1 It is called. Here, the non-reduced polynomial used in the modular operation of the super elliptic curve may be selected in the same way as the elliptic curve.

⁵,

¹⁵), (

⁵,

²⁷), (

⁷,

⁴), (

⁷,

²⁵), (

⁹,

²⁷), (

⁹,

³⁰), (

¹⁰,

²³), (

¹⁰,

³⁰), (

¹⁴,

⁸), (

¹⁴,

¹⁹), (

¹⁵,

⁰), (

¹⁵,

⁸), (

¹⁸,

²³), (

¹⁸,

²⁹), (

¹⁹,

²), (

¹⁹,

²⁸), (

²⁰,

¹⁵), (

²⁰,

²⁹), (

²³, 0), (

²³,

⁴), (

²⁵,

), (

²⁵,

¹⁴), (

²⁷,0), (

²⁷,

²), (

²⁸,

⁷), (

²⁹, o), (

²⁹,

), (

³⁰,0), (

³⁰,

¹⁶)을 얻을 수 있다.The vector value of the non-reduced polynomial of the super-elliptic curve described above is calculated as shown in FIG. 3, and when a finite point satisfying the super-elliptic curve is calculated based on the non-reduced polynomial vector of FIG. ,One), (

⁵ ,

¹⁵ ), (

⁵ ,

²⁷ ), (

⁷ ,

⁴ ), (

⁷ ,

²⁵ ), (

⁹ ,

²⁷ ), (

⁹ ,

³⁰ ), (

¹⁰ ,

²³ ), (

¹⁰ ,

³⁰ ), (

¹⁴ ,

⁸ ), (

¹⁴ ,

¹⁹ ), (

¹⁵ ,

⁰ ), (

¹⁵ ,

⁸ ), (

¹⁸ ,

²³ ), (

¹⁸ ,

²⁹ ), (

¹⁹ ,

² ), (

¹⁹ ,

²⁸ ), (

²⁰ ,

¹⁵ ), (

²⁰ ,

²⁹ ), (

²³ , 0), (

²³ ,

⁴ ), (

²⁵ ,

), (

²⁵ ,

¹⁴ ), (

²⁷ , 0), (

²⁷ ,

² ), (

²⁸ ,

⁷ ), (

²⁹ , o), (

²⁹ ,

), (

³⁰ , 0), (

³⁰ ,

¹⁶ ).

On the other hand, the sender side selects any one of the finite points on the super elliptic curve as the initial point P _hes , and the receiver side selects any one of the finite points on the super elliptic curve as the initial point P _her .

³⁰, 0), P_her은 (

²⁹,0)이라고 한다.For convenience of description below, P _hes is (

³⁰ , 0), P _her is (

^29,0 ).

The information about the super elliptic curves other than the sender side initial point P _hes on the super elliptic curve and the receiver side initial point P _{her on} the super elliptic curve can be shared in the same way as the information on the elliptic curve.

Step 3: selection of the first transmission secret key (S3)

The sender side arbitrarily selects the first transmission secret key SK _s1 . For convenience of explanation, the first transmission secret key SK _s1 is referred to as 15.

Fourth step: generation and transmission of the first transmission public key (S4)

The sender side generates the first sender public key by repeatedly adding the initial transmission point on the elliptic curve as many times as the first sender secret key in the following manner, and transmits it to the receiver side.

⁹,

¹¹)라는 제1송신공개키를 얻을 수 있다. 이하 설명의 편의를 위해 타원곡선상의 송신초기점 P_es = P라고 가정하기로 한다.If the first transmission secret key SK _s1 is 15, then OK _s1 = P _es SK _s1 is calculated as follows:

⁹ ,

¹¹ ), the first transmission public key can be obtained. For convenience of explanation, it will be assumed that the transmission origin P _es = P on the elliptic curve.

To reduce the computation time of adding P 15 times, convert SK _s1 = 15 to binary (1111) ₂ and simply calculate 15P = P + 2P + 4P + 8P.

① First, 2P is calculated by applying addition law on elliptic curve when two points coincide.

이다.Because of

to be.

       (2) Calculate 4P = 2P + 2P by applying the addition rule on the elliptic curve when two points coincide next.

이다.Because of,

to be.

       (3) Calculate 8P = 4P + 4P by applying the addition rule on the elliptic curve when the two points coincide.

이다.Because of,

to be.

       ④ Next, if we apply the addition rule on the elliptic curve when two points are different, calculate 1P + 2P,

이다.= 1P + 2P

to be.

       ⑤ Calculate (1P + 2P) + 4P by applying the addition rule on the elliptic curve when two points are different.

이다.(1P + 2P) + 4P =

to be.

       ⑥ Calculate (1P + 2P + 4P) + 8P by applying the addition rule on the elliptic curve when two points are different.

이다.(1P + 2P + 4P) + 8P =

to be.

Step 5: selecting the first receiving secret key (S5)

The receiver side arbitrarily selects the first reception secret key SK _r1 . For convenience of explanation, it is assumed that the first receiving secret key SK _r1 is 13.

Step 6: generation and transmission of the first public key (S6)

Receiver side transmits by creating a first number of first receiving a secret key by repeatedly adding the received initial points on the elliptic curve first received public key OK _r1 = P _er SK _r1, the side of the sender.

¹²,

²)를 얻을 수 있다.By calculation, where the first public key received in the same way as in the case of the first transmitted public key P _{er r1} = SK (

¹² ,

² ) can be obtained.

Step 7: generation of the sender side elliptic curve sharing secret key (S7)

The sender side generates the elliptic curve shared secret key SK _te = SK _s1 ( _Per OK _r1 ) by repeatedly adding the first receiving public key as many times as the first transmitting secret key.

¹²,

²)이고 제1송신비밀키 SK_s1는 15이므로 SK_s1(P_erOK_r1)=13(P_erOK_r1)=(P_erOK_r1)+4(P_erOK_r1)+8(P_erOK_r1)을 제1송신공개키의 경우와 동일한 방법으로 계산하면 (

¹²,

⁷)라는 타원곡선공유비밀키를 얻을 수 있다.Where the first public key OK _r1 is (

¹² ,

²⁾ a first secret key SK transmission _s1 is a _{15-SK s1 (P er OK r1)} = 13 (P er OK r1) = (P er OK r1) +4 (P er OK r1) +8 (P er OK _{If r1} ) is calculated in the same way as for the first transmission public key,

¹² ,

⁷ ), an elliptic curve shared secret can be obtained.

Step 8: Generation of the Super Elliptic Curve Sharing Secret Key on the Sender Side (S8)

First, the sender selects either the x or y value of the elliptic curve sharing secret key. For convenience of explanation, it is assumed that an x value is selected (S8-1).

¹²를 도2를 참조하여 이진수로 변환하면 (1111)₂가 된다(S8-2).The x value of the elliptic curve shared secret

Converting ¹² to binary with reference to FIG. 2 results in (1111) ₂ (S8-2).

Subsequently, converting the elliptic curve shared secret key value (1111) ₂ converted to binary number into decimal number (15) _10, that is, the super elliptic curve shared secret key SK _the can be obtained (S8-3).

Step 9: generation and transmission of the second transmission public key (S9)

The sender side adds the transmission initial point on the super elliptic curve by the number of times the super elliptic curve shared secret key is generated, generates a second transmission public key OK _s2 = SK _the P _hes, and transmits it to the receiver side.

³⁰,0)라고 할 경우 다음과 같은 방법으로 계산하면 (

²⁹, 0)라는 제2송신공개키를 얻을 수 있다. 이하 설명의 편의를 위해 초타원곡선상의 송신초기점 P_hes = P라고 가정하기로 한다.Transmit start point P _hes on the super elliptic curve (

³⁰ , 0) If you calculate in the following way (

²⁹ , 0) to obtain a second public key. For convenience of explanation, it is assumed that the transmission initial point P _hes = P on the super elliptic curve.

   (1) First, convert P to divisor type.

을 계산한다.div

Calculate

,

,

...(i)

... (i)

이므로, 양변에 +1을 한다.If d = 1 in (i)

Therefore, we add +1 to both sides.

... 양변에

의 곱셈의 역원인

을 곱한다.

... on both sides

Inverse of multiplication of

Multiply by

therefore,

, div

를 이용해 덧셈을 계산한다.(2) div

, div

Calculate addition using.

①

②

를 약분하면,

On both sides

In short,

therefore,

③

를 계산한다.first,

Calculate

이므로

가 된다.

Because of

Becomes

④

Loosen the parentheses and tie the same terms together,

양변에

의 곱셈의 역원인

을 곱하면,

따라서,

On both sides

Inverse of multiplication of

Multiply by

therefore,

⑤

⑥

로 소인수 분해를 한다.⑦ Next

Perform prime factorization with.

양변에

의 곱셈의 역원인

을 양변에 곱한 후,

On both sides

Inverse of multiplication of

Multiply by both sides,

⑧

First divide the numerator easily.

...(i)

... (i)

...(ii)

... (ii)

The results of (i) + (ii)

...(iii)

... (iii)

로 나눈 결과는 (iii) d =

Divided by

...(iv)

... (iv)

한 결과는

(iv) mod a = mod

One result is

을 좌표로 변환시키면,

,

이 되고 2P한 결과는

이다.therefore

Converting to coordinates,

,

And the result of 2P

to be.

Step 10: generation of the receiver side elliptic curve sharing secret key (S10)

¹²,

⁷)을 갖게 된다.The receiver side adds the first transmission public key as many times as the number of the first reception secret keys to generate an elliptic curve sharing secret key SK _te = SK _r1 (P _es SK _s1 ). The elliptic curve shared secret generated by the receiver is the same value as the elliptic curve shared secret generated by the sender.

¹² ,

⁷ )

Step 11: generation of the receiver side super elliptic curve sharing secret key (S11)

The receiver side selects the x value of the elliptic curve shared secret key like the sender side, and then generates a super elliptic curve shared secret key through binary and decimal conversion. The super elliptic curve shared secret generated by the receiver has the same value as the super elliptic curve shared secret generated by the sender.

Step 12: generating and transmitting a second receiving public key (S12)

The receiver side adds the reception initial point on the super elliptic curve as many times as the number of the super elliptic curve sharing secret keys, generates a second receiving public key OK _r2 , and transmits it to the sender side.

²⁹, 0)를 이용하여 제1송신공개키의 경우와 동일한 방법으로 계산하면 P_herSK_the = (

⁷,

⁴)라는 제2수신공개키를 얻을 수 있다.Here, the super elliptic curve sharing secret key SK _the 15, the receiving initial point P _her on the super elliptic curve (

²⁹ , 0) using the same method as for the first transmission public key, P _her SK _the = (

⁷ ,

⁴ ) a second receiving public key can be obtained.

Step 13: generation of sender-side encryption / decryption shared secret key (S13)

The sender side adds the initial point of the super-elliptic curve and the second receiving public key to generate the encryption / decryption shared secret key SK _cd = _Phes OK _r2 . Here, the sender-side encryption / decryption shared secret key may generate the encryption / decryption shared secret key in the same manner as the case of calculating the second transmission public key.

Step 14: transmission of encryption and cipher text (S14)

The sender side encrypts the plain text using the encryption / decryption shared secret key and transmits it to the receiver side.

Step 15: generation of a receiver side encryption / decryption shared secret key (S15)

In addition to repeating the received zero point and the second transmit the public key on the recipient's side second elliptic curve to generate the decryption shared secret key SK _cd = P _{s2 her} OK. Here, the receiver side encryption / decryption shared secret key can be calculated in the same manner as in the case of calculating the above-described second transmission public key.

Step 16: decrypt ciphertext (S16)

The receiver side decrypts the cipher text from the sender side using the encryption / decryption shared secret key generated by the receiver side. Here, the encryption / decryption shared secret generated by the receiver has the same value as the encryption / decryption shared secret generated by the sender (P _hes OK _r2 = P _hes P _her SK _the P _her = P _hes P _her SK _the = P _her OK _s2 ) The ciphertext from the sender side can be decrypted using the encryption / decryption shared secret key generated by the sender.

Meanwhile, in the above-described embodiment, a method of generating and decrypting an encryption / decryption shared secret key by a pair of the sender side and the receiver side has been described. However, as in e-commerce, the sender side includes one piece of related information. Of course, the present invention can also be applied to transmission to the receiver 2 and the receiver side.

4 is a flowchart of an encryption / decryption method according to another embodiment of the present invention.

Referring to the encryption and decryption method according to another embodiment of the present invention are as follows.

First, in one embodiment of the present invention described above between the sender side (hereinafter referred to as "buyer") and receiver 1 side (hereinafter referred to as "seller") and between the buyer and receiver 2 side (hereinafter referred to as "payment authority"). According to the encryption / decryption method described above, different encryption / decryption shared secrets are generated (S21).

Next, the purchaser generates a message digest M1 by applying a hash function to the purchase information OI (S22).

Next, the buyer generates a message digest M2 by applying a hash function to the payment information PI (S23).

Next, the buyer concatenates two message digests M1 and M2 and generates a concatenated result M1M2 (S24).

Next, the purchaser generates a message digest M by applying a hash function to the concatenated result M1M2 (S25).

Next, the purchaser generates the digital signature DS ₁ using the message digest M as the encryption / decryption shared secret for the seller (S26).

Next, the purchaser generates the digital signature DS ₂ with the message digest M as the encryption / decryption shared secret for the payment institution (S27).

Next, the buyer encrypts the payment information to be sent to the payment institution with the encryption / decryption shared secret for the payment institution (S28).

Next, the buyer transmits the purchase information, encrypted payment information, the concatenated result M1M2, the digital signatures DS ₁ and DS ₂ to the seller (S29).

Meanwhile, the seller generates the message digest M1 'by applying the same hash function as the buyer to the received purchase information (S30).

Next, the seller replaces the received M1 M2 with the newly generated M1 'and then applies the same hash function to the replaced M1'M2 to generate the message digest M' (S31).

Next, the seller decrypts the received digital signature DS ₁ with the encryption / decryption shared secret key for the seller to generate a message digest M (S32).

Next, the seller compares the message digest M 'generated by applying the hash function with the message digest M decrypted with the encryption / decryption shared secret for the seller, and determines that the purchase is a legitimate purchase request (S33).

Next, the seller transmits the encrypted payment information from the buyer, the digital signature DS ₂ , and the concatenated result M1M2 to the payment institution (S34).

Next, the payment institution decrypts the received payment information with the encryption / decryption shared secret for the buyer (S35).

Next, the payer generates a message digest M2 'by applying the same hash function as the buyer to the decrypted payment information (S36).

Next, the payer replaces M2 in the received concatenation product M1M2 with the newly generated M2 ', and then applies the same hash function to the replaced concatenation product M1M2' to generate a message digest M "(S37).

Next, the payment institution decrypts the received digital signature DS ₂ with the encryption / decryption shared secret key for the buyer to generate a message digest M (S38).

Next, the seller compares the message digest M " generated by applying the hash function with the message digest M decrypted with the encryption / decryption shared secret for the seller, and determines that the payment is a legitimate payment request (S39).

As described above, according to the exemplary embodiment of the present invention, the encryption strength can be improved by using the difficulty of two discrete algebra problems in encryption and decryption by reflecting the organic relationship between the elliptic curve and the super elliptic curve.

And by removing the electronic envelope using a shared secret key, it is possible to improve the processing speed and security of information.

Therefore, according to the present invention, the encryption strength can be improved by using the difficulty of two discrete algebra problems in encryption and decryption by reflecting the organic relationship between the elliptic curve and the super elliptic curve.

Claims (3)

F ₂ ^m an elliptic curve on a finite body, a non-reducible polynomial used for the modular operation of the elliptic curve, a transmission initial point on the elliptic curve and a reception initial point on the elliptic curve having the same value as the transmission initial point on the elliptic curve. Sharing information on the sender side and the receiver side; Sharing information about a super elliptic curve on a F ₂ ^m finite body and a non-reducible polynomial used for a modular operation of the super elliptic curve at a sender side and a receiver side; Selecting a first transmission secret key at the sender side; Generating a first transmission public key by repeatedly adding a transmission initial point on the elliptic curve by the number of times of the first transmission secret key on a sender side;

Transmitting the first transmission public key to a receiver side; Selecting a first receiving secret key at the receiver side; Generating a first receiving public key by repeatedly adding a reception initial point on the elliptic curve by the number of times of the first receiving secret key on a receiver side; Transmitting the first receiving public key to a sender side; Generating an elliptic curve shared secret key by repeating adding the first received public key by the number of times of the first transmitted secret key at a sender side; Generating a super elliptic curve shared secret key based on the elliptic curve shared secret key at a sender side; Generating a second transmission public key by repeatedly adding a transmission initial point on the super elliptic curve as many times as the number of the super elliptic curve sharing secret keys on the sender side; Transmitting the second transmission public key to a receiver side; Generating the elliptic curve shared secret key by repeatedly adding the first transmit public key as many times as the number of the first received secret keys on a receiver side; Generating the super elliptic curve shared secret key based on the elliptic curve shared secret key at a receiver side; Generating a second receiving public key by repeatedly adding a reception initial point on the super elliptic curve by the number of times of the super elliptic curve sharing secret key at a receiver side; Transmitting the second receiving public key to a sender side; Generating an encryption / decryption shared secret key by adding a transmission origin of the super elliptic curve and the second receiving public key on a sender side; Encrypting plain text using the encryption / decryption shared secret key at a sender side; Transmitting the encrypted plain text to a receiver side; Generating the encryption / decryption shared secret key by adding a reception origin of the super elliptic curve and the second transmission public key at a receiver side; And decrypting an encrypted plaintext transmitted from the sender side using the encryption-decryption shared secret key at a receiver side. The method of claim 1, The generating of the super elliptic curve shared secret key may include selecting either one of an x value and a y value of the elliptic curve shared secret key, converting the selected elliptic curve shared secret key value into a binary number; And an elliptic curve shared secret key value converted into a binary number. The method according to claim 1 or 2, The super-elliptic curve sharing secret keys are generated independently between the sender side and the receiver 1 side and between the sender side and the receiver 2 side, respectively; Generating a message digest M1 by applying a hash function to the receiver 1 side information at a sender side, generating a message digest M2 by applying the hash function to the receiver 2 side information at the sender side; Generating a concatenated result M1M2 by concatenating the message digests M1 and M2 at the sender side, generating a message digest M by applying the hash function to the concatenated result M1M2 at the sender side, and at the sender side Generating the digital signature DS ₁ by using the decryption shared secret key for the receiver 1 on the message digest M; and encrypting the decryption shared secret key for the receiver 2 on the message digest M on the sender side. Generating a digital signature DS ₂ by applying a; Encrypting the receiver 2 side information with an encryption / decryption shared secret key for the receiver 2 side at the sender side, the receiver 1 side information, the encrypted receiver 2 side information, the concatenated result M1M2, and at the sender side; Transmitting the digital signatures DS ₁ and DS ₂ to the recipient 1 side, generating the message digest M1 'by applying the hash function to the receiver 1 side information at the receiver 1 side, and at the receiver side. Replacing M1 in the concatenated result M1M2 with the message digest M1 ', generating a message digest M' by applying the hash function to the replaced M1'M2, and receiving the digital signature DS ₁ at the receiver 1 side; Decrypting with the encryption / decryption shared secret key for the sender side to generate a message digest M, and receiving the message digest M 'at the receiver 1 side; Comparing the message digest M decrypted with the encryption / decryption shared secret key to the sender side and determining that the message is a legitimate purchase request, and at the receiver 1 side, the encrypted receiver 2 side information, the concatenated result M1M2 and the electronic device; Transmitting a signature DS ₂ to the recipient 2 side, decrypting the encrypted recipient 2 side information with an encryption / decryption shared secret key for the sender side, and decrypting the decrypted recipient 2 side information; Generating a message digest M2 'by applying the hash function, replacing M2 of the concatenated result M1M2 with the message digest M2', and then applying the hash function to the replaced concatenation result M1M2 '. &Quot;, and converts the digital signature DS ₂ to the encryption / decryption shared secret for the sender side at the receiver 2 side. Decrypting and generating a message digest M, and comparing the message digest M " and the message digest M decrypted with the encryption / decryption shared secret key for the sender side and determining that the request is a legitimate purchase request. Encryption and decryption method comprising a.

Images