JPH11161166A - Cipher communication equipment and method therefor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To permit high-speed processing for ciphering and deciphering without lowering the security of cipher communication by making the number of finite bodies less than that of elements of a Jacobi polymorphism. SOLUTION: A parameter selection part 4 selects an algebraic curve C, a finite body F(q) having (q) elements, and an element D of the Jacobi polymorphism J, and outputs the element of the Jacobi polymorphism J to a data reception device 3 and a data transmission device 2. To increase the safety of cipher communication, such a Jacobi polymorphism J that elements of Jacobi polymorphism J are as large as possible and the number of its elements can be divided by a large prime number is selected. The algebraic curve C and finite body (q) are so selected that the Jacobi polymorphism J is not mapped to a small multiplication group Z((g<n> )<k> )* by mapping called a Tate pair. To make it difficult to solve a discrete logarithmic problem on the Jacobi polymorphism, the algebraic curve C and finite body F(g) are so selected that the genus (g) of the algebraic curve C and the number (q) of the elements of the finite body F(q) have a relation 3g+1<=log (q).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a cryptographic communication device and a cryptographic communication method for encrypting digital information and securely performing secret communication.

[0002]

2. Description of the Related Art FIGS. 5, 6, and 7 are flowcharts showing a conventional cryptographic communication method. In the drawing, ST1 denotes an elliptic curve y ² = x ³ + ax + b and a finite field F (q) having q elements. q) and a step of selecting a point P on the elliptic curve, ST2 selects an integer x and uses the integer x as a secret key, ST3 calculates Y = xP on a finite field F (q), Y is a public key, ST4 is a step of selecting data (hereinafter, referred to as “plaintext”) m and an integer r to be encrypted, and ST5 is a first element of the ciphertext C ₁ = on the finite field F (q). calculating a second element C ₂ = rY + m of rP and ciphertext, the step of first element C ₁ and the second element C ₂ set the ciphertext (C _1, C ₂₎ ST6, ciphertext ST7 the (C _1, C ₂₎ and m = C ₂ -xC ₁ on the finite field F (q) from the secret key x Calculation steps, ST8 is a step of the plaintext m.

Next, the operation will be described. In the case of encrypting digital information and performing secret communication, first, a user of the encryption communication requires a finite field F (q) having q elements and parameters a and b of y ² = x ³ + ax + b indicating an elliptic curve C. Is selected, and a point P on the elliptic curve C is selected (step ST
1). However, it is necessary to select the elliptic curve C and the finite field F (q) so that the number N of points on the elliptic curve C is divisible by a large prime number. The reason is to make it difficult to decipher the public key cryptography using the elliptic curve C. Note that the number N of points on the elliptic curve C is q + 1-2 {q <N <q + 1 + 2}
is known to be q.

When a point P on the elliptic curve C is selected, an integer x is selected as a secret key (step ST2).
The secret key x is kept secret so that it cannot be known to others. Thus, when the secret key x is selected,
Y = xP is calculated on the finite field F (q), and Y is set as a public key (step ST3).

[0005] Next, the user of the encrypted communication selects data to be encrypted, that is, a plaintext m and an arbitrary integer r (step ST4), and places the first element of the ciphertext on the finite field F (q). C ₁
And the second element C ₂ of the ciphertext is calculated (step ST
5) C ₁ = rP C ₂ = rY + m

Then, when the first element C ₁ of the cipher text and the second element C ₂ of the cipher text are calculated, the set of the first element C ₁ and the second element C ₂ is converted to the cipher text (C ₁ , C ₂ ). (Step ST
6), and transmits the ciphertext (C ₁ , C ₂ ) to the other party.

[0007] Then, a user of the cipher communication sends a cipher text (C
₁ , C ₂ ), the other party sends the ciphertext (C
₁ , C ₂ ) and secret key x, on a finite field F (q), m = C
The ₂ -xc ₁ calculated (step ST7), to the m the plaintext (step ST8).

[0008] In this way, the encrypted data is decrypted. In the encryption communication method using the elliptic curve C,
In order to improve the confidentiality of the encrypted data, as described above, the number N of points on the elliptic curve C must be divisible by a large prime number, and the number N of points also becomes a large value.
Also, since the value of the number N of points is proportional to the number q of elements of the finite field F (q), increasing the value of q is also important for improving the security of cryptographic communication.

[0009]

Since the conventional cryptographic communication method is configured as described above, it is necessary to increase the number q of elements of the finite field F (q) in order to enhance the security of the cryptographic communication. (The number q of elements in the finite field F (q) needs to be as large as the number N of points on the finite field F (q), which is the number of elements in the group forming the discrete logarithm problem. ), Since the encryption and decryption operations of the encrypted communication are performed on the finite field F (q), the encryption is performed in proportion to the square of the number of bits q of the number q of elements of the finite field F (q). In addition, there is a problem that the processing speed of decoding becomes slow, and the circuit scale becomes large when implemented in hardware.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-described problems, and reduces the number of elements of a finite field without deteriorating the security of cryptographic communication, and increases the processing speed of encryption and decryption. It is an object of the present invention to provide a cryptographic communication device and a cryptographic communication method capable of reducing the circuit scale even when implemented in hardware, as well as speeding up.

[0011]

SUMMARY OF THE INVENTION A cryptographic communication apparatus according to the present invention generates a first element of a ciphertext by multiplying an element of a Jacobian manifold by an arbitrary integer on the Jacobian manifold, and generates a public key. Ciphertext generation for multiplying the public key generated by the generation means by an arbitrary integer on the Jacobi manifold and adding the multiplication result to the Jacobi manifold on the Jacobi manifold to generate a second element of the ciphertext Means for multiplying the first element of the ciphertext transmitted by the transmitting means with the secret key on the Jacobi manifold, and subtracting the multiplication result from the second element of the ciphertext on the Jacobi manifold, Decoding means for decoding a sentence.

The cryptographic communication apparatus according to the present invention selects a Jacobian variety such that the maximum prime factor of the number of elements of the Jacobian manifold is 40 or more decimal digits.

An encryption communication device according to the present invention selects an algebraic curve and a finite field so that a Jacobi variety is not mapped to a multiplicative group smaller than a predetermined multiplicative group.

In the cryptographic communication apparatus according to the present invention, the relation between the genus g of the algebraic curve and the number q of the elements of the finite field is 2g + 1 ≦ l
An algebraic curve and a finite field are selected so that og (q) is obtained.

The cryptographic communication apparatus according to the present invention selects an algebraic curve and a finite field so that the form of an equation representing an algebraic curve is V ² + V = U ^{2g +1} .

In the cryptographic communication apparatus according to the present invention, the genus g of the algebraic curve is set to 3 and the number q of the elements of the finite field is set to 2
¹¹³ .

The cryptographic communication system according to the invention, as well as in 11 the genus g of algebraic curves, in which the number q of elements of a finite field into 2 ^47.

The cryptographic communication method according to the present invention multiplies an element of the Jacobian manifold by an arbitrary integer on the Jacobian manifold,
The first element of the ciphertext is generated, the public key is multiplied by an arbitrary integer on the Jacobi manifold, and the multiplication result is added with the data to be encrypted on the Jacobi manifold to obtain the second element of the ciphertext. , While multiplying the first element of the ciphertext by the secret key on the Jacobi manifold, then multiplying the second element of the ciphertext by
The multiplication result is subtracted from the element on the Jacobi variety to decrypt the ciphertext.

In the cryptographic communication method according to the present invention, the Jacobi variety is selected such that the maximum prime factor of the number of elements of the Jacobi variety is 40 or more decimal digits.

The cryptographic communication method according to the present invention selects an algebraic curve and a finite field so that a Jacobi variety is not mapped to a multiplicative group smaller than a predetermined multiplicative group.

In the cryptographic communication method according to the present invention, the relation between the genus g of the algebraic curve and the number q of the elements of the finite field is 2g + 1 ≦ l
An algebraic curve and a finite field are selected so that og (q) is obtained.

In the cryptographic communication method according to the present invention, an algebraic curve and a finite field are selected such that the form of an equation representing an algebraic curve is V ² + V = U ^{2g +1} .

In the cryptographic communication method according to the present invention, the genus g of the algebraic curve is set to 3 and the number q of the elements of the finite field is set to 2
¹¹³ .

The encryption communication method according to the invention, as well as in 11 the genus g of algebraic curves, in which the number q of elements of a finite field into 2 ^47.

[0025]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below. Embodiment 1 FIG. FIG. 1 is a block diagram showing an encryption communication device according to a first embodiment of the present invention. In the figure, reference numeral 1 denotes a management device for managing a public key or the like, 2 denotes a data transmission device for encrypting and transmitting data, and 3 denotes A data receiving apparatus 4 for receiving and decrypting the encrypted data is composed of parameters of the entire system (algebraic curve C, finite field F (q) having coefficients of algebraic curve C as elements, algebraic curve C and finite field F (Q), a parameter selection unit (public key generation means) for selecting an element D of the Jacobi variety J defined from (q), 5 is an x selection unit (public key generation means) for selecting an integer x, and 6 is x selection. A secret key storage unit that stores the integer x selected by the unit 5 as a secret key. The multiplication unit 7 multiplies the element D of the Jacobi variety J selected by the parameter selection unit 4 with the secret key x on the Jacobi variety J. A public key generation unit (public) for generating a public key Y Generating means), 8 public key output unit for outputting the public key Y generated by the public key generation unit 7, the public key Y outputted from the public key output unit 8 9
Is a public key storage unit.

Reference numeral 10 denotes a data input unit (ciphertext generating means) for inputting data m to be encrypted, and 11 denotes a public key input unit for inputting a public key Y stored in a public key storage unit 9.
2 is an r selection unit (ciphertext generating means) for selecting an arbitrary integer r, 13 is a multiplication of the element D of the Jacobi variety J by the integer r on the Jacobi variety J, and a first element C ₁ of the ciphertext , And multiply the public key Y by an integer r on the Jacobi variety J, and add the data m to be added to the multiplication result on the Jacobi variety J to obtain the second element C ₂ of the ciphertext. An element calculation unit (ciphertext generating means) for calculating, 14 is the element calculation unit 1
The first element C ₁ and the second element C of the ciphertext calculated by
Ciphertext generator for the _second set the ciphertext (C _1, C ₂₎ (ciphertext generating means), 15 encryption sending each element C _1, C ₂ ciphertext calculated by element calculation unit 13 It is a sentence output unit (transmission means).

Further, reference numeral 16 denotes a ciphertext input unit for receiving the respective elements C ₁ and C ₂ of the ciphertext transmitted from the ciphertext output unit 15, and 17 denotes a first element of the ciphertext received by the ciphertext input unit 16. with multiplying the private key x on Jacobian variety J to C _1, the multiplication result from the second element C ₂ of the ciphertext xC ₁
Is subtracted on the Jacobi variety J to decrypt the ciphertext. FIGS. 2, 3 and 4 are flowcharts showing the cryptographic communication method according to the first embodiment of the present invention.

Next, the operation will be described. First, the parameter selection unit 4 of the management device 1 determines that the algebraic curve C (for example, V ²
+ V = U ^{2g + 1} , where g is one of the parameters characterizing the properties of the algebraic curve C, called the genus) and a finite field F (q) with q elements , When the element D of the Jacobi variety J is selected (step ST1)
1), the element D of the Jacobi variety J
And outputs the data to the data transmission device 2.

However, when the parameter selection unit 4 selects a parameter, the element of the Jacobi variety J is selected as large as possible to increase the security of the cryptographic communication. Is selected so that the maximum prime factor of the number is greater than or equal to 40 decimal digits), and a Jacobi variety J whose number of elements is divisible by a large prime number is selected. Also, even if the discrete logarithm problem on the Jacobi variety J is difficult, a small multiplicative group Z ((q ⁿ ) ^k ) ^*
, The cipher can be easily decrypted by solving the discrete logarithm problem on the multiplicative group. Therefore, the Jacobian variety J is transformed into a small multiplicative group Z ((q ⁿ ) ^k ) by a mapping called a Tate pair. Algebraic curve C so that it is not mapped to ^*
And a finite field F (q). Furthermore, in order to make it difficult to solve the discrete logarithm problem on the Jacobi variety J, the relation between the genus g of the algebraic curve C and the number q of elements of the finite field F (q) is 2g + 1 ≦ log (q). An algebraic curve C and a finite field F (q) are selected so that

When the element D of the Jacobi variety J is output from the parameter selection unit 4, x
When the selection unit 5 selects the integer x (step ST12) and outputs the integer x as a secret key to the secret key storage unit 6 and the public key generation unit 7, the public key generation unit 7 sets the element D of the Jacobi variety J Multiply the secret key x on the Jacobi variety J and get the public key Y
Is generated (step ST13).

When the public key Y is generated in this manner, the public key Y is sent from the public key output unit 8 to the public key storage unit 9.
Is output to the public key input unit 1 of the data transmission device 2.
Input from 1. At this time, the data transmitting device 2
The data m to be encrypted is input from the data input unit 10 of the
Is selected (step ST14).

Then, when data m or the like to be encrypted is input, the element calculation unit 13 multiplies the element D of the Jacobi variety J by an integer r on the Jacobi variety J as shown below.
The first element C ₁ of the ciphertext is calculated, the public key Y is multiplied by an integer r on the Jacobi variety J, and the multiplication result is added to the data m to be encrypted on the Jacobi variety J to encrypt the result. calculating a second element C ₂ of the sentence (step ST1
5). C ₁ = rD C ₂ = rY + m

[0033] When the elements C _1, C ₂ of the ciphertext is calculated, the first element C ₁ and the ciphertext second element C ₂ set of ciphertext generating unit 14 is the ciphertext (C _1, C ₂ ) (step ST16), and the ciphertext output unit 15 outputs the first element C
₁ and the second element C ₂ are transmitted to the data receiving device 3.

[0034] Then, the ciphertext output unit 15 and the first element C ₁ ciphertext when the second element C ₂ is transmitted, the first element C ₁ and the second element C of the ciphertext input unit 16 is encrypted ₂ and the decryption unit 17 multiplies the first element C ₁ of the ciphertext by the secret key x on the Jacobi variety J as shown below.
The multiplication result xC ₁ is subtracted from the second element C ₂ of the cipher text on the Jacobi variety J (step ST17). m = C ₂ −xC ₁ Then, m, which is the result of the subtraction, is set as a decrypted plain text (step ST 18), and a series of processing ends.

As is clear from the above, the first embodiment
According to the group that constitutes the discrete logarithm problem is Jacobi variety J
So that Jacobi variety J (C, F
(Q)) The number of elements of the finite field F (q) can be made smaller than the number of elements of (F), and as a result, the processing speed of encryption and decryption can be achieved without deteriorating the security of encrypted communication. And the circuit scale can be reduced even when implemented in hardware.

Embodiment 2 In the first embodiment, the case where the data receiving device 3 transmits the public key Y to the data transmitting device 2 via the management device 1 has been described, but the data receiving device 3 transmits the public key Y directly to the data transmitting device 2. The transmission may be performed, and the same effect as in the first embodiment can be obtained.

Embodiment 3 In the first embodiment described above, an equation of the form V ² + V = U ^{2g + 1} is selected as the algebraic curve C. However, in the third embodiment, specifically, 3 is set as the genus g. Select (V ² + V = U ⁷ ),
A case where the number q of elements of the finite field F (q) is set to 2 ¹¹³ will be described. In this case, the number #J of elements of the Jacobi variety J
Is calculated as follows. That is, assuming that the zeta function associated with the algebraic curve C is Z (T), the number #J of elements of the Jacobi variety J is as follows.

[0038]

(Equation 1)

# J = 111987237108902
1052778721402842212390608
2274861733244728663941184
54217607997880341836646686
079373803521 Then, when the number #J of elements of the Jacobi variety J is factorized, #J becomes as follows. # J = 7 × 1583 × 75937 × 133087154
45125858503904350593436988
8884232635351754060420763
26739667429564557129519523
8138050393

Therefore, in this case, the number of elements #J (C, F (2 ¹¹³ )) of the Jacobi variety J is 339 bits, the maximum prime factor of which is 310 bits, and the Jacobi variety J
This is a sufficiently large value from the viewpoint of making it difficult to solve the discrete logarithm problem on (C, F (2 ¹¹³ )) (Jacobi variety J
Element number #J is 40 digits or more in decimal). Therefore, if encrypted communication is performed using this Jacobi variety J (C, F (2 ¹¹³ )), secure secret communication can be performed.

The Jacobi variety J (C, F)
(2 ¹¹³ )) does not map to a small multiplicative group
The maximum prime factor of J (C, F (2 ¹¹³ )) is (2 ¹¹³ ) ^k
This can be confirmed by not dividing -1. Here, k <log (q ¹¹³ ) ² .

In the conventional cryptographic communication using an elliptic curve, in order to set the maximum prime factor of #J to 310 bits, the size of the finite field F (q) must be approximately the same. However, in the third embodiment, #J
Even if the size of the maximum prime factor is 310 bits, the size of the finite field F (q) needs to be 113 bits (#
J) (approximately one third of the largest prime factor of J), so that the encryption and decryption processing can be performed at high speed, and
When implemented in hardware, there is an effect that the circuit scale can be reduced.

Embodiment 4 FIG. In the first embodiment described above, an equation of the form of V ² + V = U ^{2g + 1} is selected as the algebraic curve C. However, in the fourth embodiment, specifically, 11 is used as the genus g. Select (V ² + V =
U ²³ ), a case where the number q of elements of the finite field F (q) is set to 2 ⁴⁷ will be described. In this case, the number #J of elements of the Jacobi variety J becomes the following value (for the calculation method of #J, see the third embodiment).

# J = 42949853757581631
071863687994258870707933
9702585896588801539966199
096448936253546934828988915
8336706306156363334692253070
375930069599399234436005731
Then, when the number #J of elements of the Jacobi variety J is factorized, #J becomes as follows. # J = 3 × 23 × 29 × 34687 × 254741 × 3
81077 × 836413 × 4370719 × 1228
03256446193 × 10157840605219
16029 × 1396360023741601228
72280490593436436404443801
77105909466009612010801386
78351892941224093667687457

Accordingly, in this case, the number of elements #J (C, F (2 ⁴⁷ )) of the Jacobi variety J is 518 bits, the maximum prime factor of which is 310 bits, and the Jacobi variety J
This is a sufficiently large value from the viewpoint of making it difficult to solve the discrete logarithm problem on (C, F (2 ⁴⁷ )) (the number #J of elements of the Jacobi variety J is 40 decimal digits or more). Therefore, if encrypted communication is performed using this Jacobi variety J (C, F (2 ⁴⁷ )), secure secret communication can be performed.

The Jacobi variety J (C, F (2 ⁴⁷ ))
Is not mapped to a small multiplicative group is that #J (C, F
Maximum prime factor of (2 ⁴⁷⁾⁾ can be confirmed by not Warikira a (2 ^{47) k} -1. However, k <log
(Q ⁴⁷⁾ is ^2.

In the conventional cryptographic communication using an elliptic curve, in order to set the maximum prime factor of #J to 310 bits, the size of the finite field F (q) must be the same. However, in the fourth embodiment, #J
Even if the size of the largest prime factor of is 310 bits, the size of the finite field F (q) can be 47 bits (#J
(Approximately one-seventh of the largest prime factor), the encryption and decryption processes can be performed at a high speed, and the circuit scale can be reduced when implemented in hardware. .

[0048]

As described above, according to the present invention, the first element of the ciphertext is generated by multiplying the element of the Jacobi variety by an arbitrary integer on the Jacobi variety, and the public key generation means is provided. Ciphertext generating means for multiplying the public key generated by the above with an arbitrary integer on the Jacobi manifold, adding the result of the multiplication to the Jacobi manifold on the Jacobi manifold, and generating the second element of the ciphertext; and , The first of the ciphertexts transmitted by the transmitting means
Decryption means for multiplying the element by a secret key on the Jacobi manifold, subtracting the result of the multiplication from the second element of the ciphertext on the Jacobi manifold, and decrypting the ciphertext. As a result, the number of elements in the finite field can be made smaller than the number of elements in the Jacobi variety, and as a result, the processing speed of encryption and decryption can be increased without deteriorating the security of cryptographic communication. Be able to
Even when implemented in hardware, there is an effect that the circuit scale can be reduced.

According to the present invention, since the Jacobi variety is selected so that the maximum prime factor of the number of elements of the Jacobi variety is 40 or more decimal digits, the security of cryptographic communication can be improved. There is an effect that can be done.

According to the present invention, the algebraic curve and the finite field are selected so that the Jacobi variety is not mapped to a multiplicative group smaller than the predetermined multiplicative group. Therefore, the discrete logarithm problem on the multiplicative group can be solved. This makes it difficult to secure the encrypted communication.

According to the present invention, the algebraic curve and the finite field are selected so that the relation between the genus g of the algebraic curve and the number q of the elements of the finite field is 2g + 1 ≦ log (q). It becomes difficult to solve the discrete logarithm problem on the Jacobi variety, and as a result, there is an effect that the security of cryptographic communication can be enhanced.

According to the present invention, the algebraic curve and the finite field are selected so that the form of the equation representing the algebraic curve is V ² + V = U ^{2g + 1} , so that the security of the cryptographic communication is improved. There is an effect that can be.

According to the present invention, the genus g of the algebraic curve is set to 3
In addition, since the number q of the elements of the finite field is configured to be 2 ¹¹³ , the size of the finite field can be reduced to about one third as compared with the conventional one, and The encryption and decryption processes can be performed at high speed, and when implemented in hardware, there is an effect that the circuit scale can be reduced.

According to the present invention, the genus g of the algebraic curve is 1
Since the number of elements of the finite field is set to 2 ⁴⁷ , the size of the finite field can be reduced to about 1/7 of that of the conventional one. In addition, the encryption and decryption processes can be performed at a high speed, and when implemented in hardware, the circuit scale can be reduced.

According to the present invention, the element of the Jacobi variety is multiplied by an arbitrary integer on the Jacobi variety to obtain the first ciphertext.
Generate a second element of the ciphertext by multiplying the public key by an arbitrary integer on the Jacobi manifold and adding the multiplication result to the encrypted data on the Jacobi manifold, A first element of the ciphertext is multiplied by a secret key on a Jacobi manifold, and a result of the multiplication is subtracted from a second element of the ciphertext on the Jacobi manifold to decrypt the ciphertext. As a result, the number of elements in the finite field can be made smaller than the number of elements in the Jacobi variety, and as a result, the processing speed of encryption and decryption can be increased without deteriorating the security of cryptographic communication. In addition to the above, there is an effect that the circuit scale can be reduced even when implemented in hardware.

According to the present invention, since the Jacobi variety is selected so that the maximum prime factor of the number of elements of the Jacobi variety is 40 digits or more in decimal, the security of cryptographic communication can be improved. There is an effect that can be done.

According to the present invention, the algebraic curve and the finite field are selected so that the Jacobi variety is not mapped to a multiplicative group smaller than the predetermined multiplicative group. Therefore, the discrete logarithm problem on the multiplicative group can be solved. This makes it difficult to secure the encrypted communication.

According to the present invention, the algebraic curve and the finite field are selected such that the relationship between the genus g of the algebraic curve and the number q of the elements of the finite field satisfies 2g + 1 ≦ log (q). It becomes difficult to solve the discrete logarithm problem on the Jacobi variety, and as a result, there is an effect that the security of cryptographic communication can be enhanced.

According to the present invention, the algebraic curve and the finite field are selected so that the form of the equation representing the algebraic curve is V ² + V = U ^{2g + 1} , so that the security of cryptographic communication can be improved. There is an effect that can be.

According to the present invention, the genus g of the algebraic curve is set to 3
In addition, since the number q of the elements of the finite field is configured to be 2 ¹¹³ , the size of the finite field can be reduced to about one third as compared with the conventional one, and The encryption and decryption processes can be performed at high speed, and when implemented in hardware, there is an effect that the circuit scale can be reduced.

According to the present invention, the genus g of the algebraic curve is 1
Since the number of elements of the finite field is set to 2 ⁴⁷ , the size of the finite field can be reduced to about 1/7 of that of the conventional one. In addition, the encryption and decryption processes can be performed at a high speed, and when implemented in hardware, the circuit scale can be reduced.

[Brief description of the drawings]

FIG. 1 is a configuration diagram illustrating an encryption communication device according to a first embodiment of the present invention.

FIG. 2 is a flowchart showing an encrypted communication method according to the first embodiment of the present invention.

FIG. 3 is a flowchart showing an encrypted communication method according to the first embodiment of the present invention.

FIG. 4 is a flowchart showing an encrypted communication method according to the first embodiment of the present invention.

FIG. 5 is a flowchart showing a conventional encryption communication method.

FIG. 6 is a flowchart showing a conventional encryption communication method.

FIG. 7 is a flowchart showing a conventional encryption communication method.

[Explanation of symbols]

4 parameter selection unit (public key generation unit), 5x selection unit (public key generation unit), 7 public key generation unit (public key generation unit), 10 data input unit (ciphertext generation unit), 12
r selection unit (ciphertext generation unit), 13 element calculation unit (ciphertext generation unit), 14 ciphertext generation unit (ciphertext generation unit), 15 ciphertext output unit (transmission unit), 17 decryption unit (decryption) means).

Claims (14)

[Claims] 1. A public key generating means for generating a public key by multiplying an element of a Jacobi manifold defined by an algebraic curve and a finite field with a secret key on the Jacobi manifold; Is multiplied on the Jacobi variety to generate the first element of the ciphertext, and the public key generated by the public key generation means is multiplied by an arbitrary integer on the Jacobi variety. Ciphertext generating means for adding the data to be encrypted to the Jacobi manifold to generate a second element of the ciphertext; transmitting means for transmitting each element of the ciphertext generated by the ciphertext generating means; The first element of the ciphertext transmitted by the transmitting means is multiplied by the secret key on the Jacobi manifold, and the result of the multiplication is subtracted from the second element of the ciphertext on the Jacobi manifold to obtain the ciphertext. Decryption means for decrypting No. communication device. 2. The cryptographic communication apparatus according to claim 1, wherein the Jacobi variety is selected such that the maximum prime factor of the number of elements of the Jacobi variety is 40 or more decimal digits. 3. The cryptographic communication apparatus according to claim 1, wherein an algebraic curve and a finite field are selected such that the Jacobi variety is not mapped to a multiplicative group smaller than a predetermined multiplicative group. 4. The genus g of an algebraic curve and the number q of elements in a finite field
2. The cryptographic communication device according to claim 1, wherein an algebraic curve and a finite field are selected such that the relationship with satisfies 2g + 1 ≦ log (q). 5. The form of an equation showing an algebraic curve is V ² + V =
The cryptographic communication device according to claim 1, wherein an algebraic curve and a finite field are selected so as to be ^{U2g + 1} . 6. The genus g of an algebraic curve is set to 3;
5. The cryptographic communication device according to claim 4, wherein the number q of elements of the finite field is set to 2 ¹¹³ . 7. while a genus g of 11 algebraic curves, finite element cryptographic communication device according to claim 4, characterized in that the two ⁴⁷ the number q of. 8. A public key is generated by multiplying a Jacobi variety element defined by an algebraic curve and a finite field by a secret key on the Jacobi variety, and an arbitrary integer is assigned to the Jacobi variety element by the Jacobi variety element. Multiply on the manifold to generate the first element of the ciphertext, multiply the public key by an arbitrary integer on the Jacobi manifold, and add the data to be encrypted to the multiplication result on the Jacobi manifold. When the second element of the ciphertext is generated by the addition, each element of the ciphertext is transmitted. On the other hand, the first element of the transmitted ciphertext is multiplied by a secret key on a Jacobi manifold, and then the ciphertext is transmitted. A cryptographic communication method for subtracting a result of multiplication from a second element of a sentence on a Jacobi manifold and decoding a ciphertext. 9. The cryptographic communication method according to claim 8, wherein the Jacobi variety is selected such that the maximum prime factor of the number of elements of the Jacobi variety is 40 or more decimal digits. 10. The cryptographic communication method according to claim 8, wherein an algebraic curve and a finite field are selected such that the Jacobi variety is not mapped to a multiplicative group smaller than a predetermined multiplicative group. 11. The algebraic curve and the finite field are selected such that the relation between the genus g of the algebraic curve and the number q of elements of the finite field satisfies 2g + 1 ≦ log (q). Encryption communication method. 12. The form of an equation showing an algebraic curve is V ² + V
^9. The cryptographic communication method according to claim 8, wherein an algebraic curve and a finite field are selected such that = ^{U2g + 1} . 13. The cryptographic communication method according to claim 11, wherein the genus g of the algebraic curve is set to 3 and the number q of elements of the finite field is set to 2 ¹¹³ . 14. The cryptographic communication method according to claim 11, wherein the genus g of the algebraic curve is set to 11, and the number q of the elements of the finite field is set to 2 ⁴⁷ .