JPH03195229A - Cryptographic communication system - Google Patents

Abstract

PURPOSE:To efficiently execute cryptographic processing of two-dimensional information by generating a secret key and a public key in each station, preserving the secret key respectively, informing the public key to other station, using the public key of an opposite reception station in a transmission station in the stage of cryptographic processing state and using the secret key of its own station in a reception station in the stage of decoding. CONSTITUTION:The cryptographic device 10 of stations 1, 2 in the stage of key generation uses an arithmetic circuit 13 to calculate the public key and the secret key, informs the public key to other station from a data output circuit 16 and stores the secret key to the data storage memory 14 of its own station. In the case of cryptographic processing, the cryptographic device 10 of a transmission station (station A) 1 reads a plain sentence (M1, M2) and uses a specific public key of a reception station (station B) 2 stored in a data storage memory 14, generates a cryptographic sentence (C1, C2) according to equation I and sends the result to the reception station (station B) 2 from the data output circuit 16. In the case of decoding, the cryptographic device 10 of the reception station (station B) 2 uses the secret key specific to its own station (station B) 2 stored in the data storage memory 14 to calculate the plain sentence (M1, M2) from the received cryptographic sentence (C1, C2) and outputs the result from the data output circuit 16.

Description

[Detailed Description of the Invention] [Field of Industrial Application] The present invention relates to a cryptographic communication method using a public key, and in particular,
It relates to a method for efficiently encrypting and decoding two-dimensional information.

[Conventional technology]

Conventionally, the Rabin cipher is known as a public key cryptosystem capable of high-speed encryption (M, RaI)j41;
“Digitalized signatures a
nd publ, ic keycryptosystem
s”, MIT/LC8/TR-212°Technic
al Report MIT (1979))
, the Rabin cipher is secure as long as it cannot be decomposed into prime factors, but it cannot be encrypted by taking advantage of the characteristics of two-dimensional information.

As a two-dimensional public key cryptosystem, there is a cryptographic method by Kobayashi et al.
A, N (15, pp, 850-851° (1989)
). This is an extension of the Rabin cipher described above to two-dimensional information.

[Problem to be solved by the invention]

In the prior art, the Rabin cipher cannot encrypt by taking advantage of the characteristics of two-dimensional information, and it is impossible to improve the efficiency of passing ciphertext. On the other hand, Kobayashi et al.'s two-dimensional modified Rabin cipher is only a special example, and the problem is that the encryption speed cannot be increased.

An object of the present invention is to generalize the cipher proposed by Kobayashi et al. and to realize an encrypted communication system with a faster encryption speed.

[Means to solve the problem]

- In order to achieve the above objectives, the present invention provides key generation.

In an information communication system consisting of multiple stations with encryption and decryption functions, in the key generation stage, each station generates a private key and a public key, stores the private key at that station, and transfers the public key to other stations. In the encryption stage, the transmitting station uses the public key of the receiving station to transmit a set of plaintexts (Ml, M
2), one set of ciphertexts (C1, C2) is written as (J:, □=2M□M7 modn C2=M2"+λM1" modn (λ≠-2
) is generated and sent to the receiving station, and at the decoding stage,
At the receiving station, the private key of the receiving station is used to extract J-set of plaintexts (M, , M2) from one set of ciphertexts (C1, C2).
It is characterized by restoring.

[For production]

The cryptographic communication method according to the present invention is performed in three stages: key generation stage, encryption stage, and decryption stage. −
Once the first stage of key generation is performed, the second and third stages of encryption and decryption are repeated. The procedure for each step is shown below.

Each station in Fuhong performs the following calculations to generate its own private key and public key. In order to easily calculate the square root in mod p and mod q, let p and q be prime numbers that satisfy p=4α+3(1) q=4β+3(2). Here, α and β are non-negative integers.

Let n be the product of p and q.

Define n''pq - λ to be the square remainder mod p and mod q.

P +2-”' P 2” = λ (modp)qt
' = qz'' = PILI that satisfies λ (modq)
P21 q□l q2 can be easily calculated as α+1 pgo=λmodp P2=−p, mod p β+1 q□=λ mod q q2= qlmod q. Furthermore, n= (Pl, T)2) mod pV” (
q1'12) Find the multiplicative cousin u g' V HX g '/ -mod q x=p'-1 mod q 'j=q-' mod q.

The public keys are n and λ, and the private keys are p, q, pl, p2 .
ql.

qz+unV+X'+'J.

Each station performs the following operations when transmitting (encrypting) secret communications. Plaintext (M t□M2) is O≦M□
(n is a set of integers in the range of (i=1.2).

Using the variable Z Z2−λmod n, the plaintext polynomial M
, Z + M, is defined. mod n of plaintext polynomial
Let the square of be the ciphertext. That is, f (Z) = (M1Z + M2) 2, f (Z)' mod n =2M1M2Z+ (M2"+λMt") mod
It is encrypted as n=C1Z+C7mod n. Therefore, the set of ciphertexts (C□.

C2) is C1=2M1. Mz mod n
(3) C2=M2” ++λM12 mod n
(4) becomes.

[Reply] Each station performs the following operations when receiving (decoding) secret communications.

First, F s, ” f (p□) mod pF2=f (
p,) mod pF3=f (ql)
mod qF” 4 ==f (q,)
mod q Fl, F2. F,, F,
seek. The value of their square root is α→1 α+1±F1
mod p+ ±F2 mod p. Let the values of the plaintext M□1M, mod p and mod q, be M 1
PI M2pg M), q + M2q, then α+
1 Ml, pp1+M2p=±F”, modpα+1 M 1 p p , 10 M 2 F = ± 1”
2 mod pβ+1 M 1q q 1 + M, 2 q = ±F3mod
(1β+1 MH, q q 2 + M 2 q = ±F4mod
Since q holds true, α+1 α+1 M1F= [± Fl 壬 F2
u nod pα+1 α+1 M2p= [±P1. F2 + p2Fl ]
Find u mod p. Next, the plaintext M at nod n, 2M2 is expressed as M1=M1-pq, Y+M1qpx mod n using the Chinese remainder theorem.
(5) Mz: M2Pqy+M2qpX mod n
(6) Note that if both P and q are large numbers, 16 decrypted texts can be obtained for the − set of ciphertexts with a probability of almost 1. By including redundancy check pins 1 to 1 in the original plaintext, one correct palindrome is selected from among 16 decrypted texts.

There are an infinite number of specific examples of the general two-dimensional cryptography mentioned above. The two-dimensional cryptography of Kobayashi et al. can be regarded as a specific implementation example of a general two-dimensional cryptography. In Kobayashi et al.'s two-dimensional cryptography, λ=-2. Set a=2a, β-2b (a, b are non-negative integers)8 so that -2 becomes a square remainder with mod p and mod q, and p and q are p=8a+3 (=4-X2a+3).

It is a prime number that satisfies q=8b+3 (=4X2b+3). Therefore, the encryption function of Kobayashi et al.'s cipher is: Cx,=211C,M2mod n
(7) C2=M2”-2M12mod n
(8).

Here, we will take up the case of λ=1 as an example with the least number of calculations among the concrete implementation examples of general two-dimensional cryptography.

In the method of the present invention, the number of multiplications during encryption is one less than in the code of Kobayashi et al. Since mod p and nod q are square remainders, α and β can be arbitrary non-negative integers. Let P and q be p = 4. a + 3.

It is a prime number that satisfies q = 4- b +3. Therefore, the encryption function of the present invention is C□:2MIM2 mod n
(9) C,,=M2''+M1' mod n
(10).

〔Example〕

An embodiment of the present invention will be described below with reference to the drawings.

FIG. 1 shows the information flow of the encrypted communication system of the present invention. Here, 1 is the transmitting station (station A), 2 is the receiving station (station B).
). Each station 1, 2 is equipped with a cryptographic device that realizes key generation, encryption, and decryption. An embodiment of the cryptographic device is shown in FIG.

At the key generation stage, the cryptographic devices 10 of each station 1 and 2 use
is generated through the prime number generation circuit 12, and the public key (n) and private key (p + p21 qi + q21 u
, +V+x+y) are calculated by the arithmetic circuit 1-3 under the control of the key generation program stored in the program storage memory 15. Then, the public key n is sent to the data output circuit 16.
The secret IU (p + qr
F3. I P2+ 'Jxr q, t u+ V+
XI y) in the data storage memory 14 of its own station.

However, λ (=1) is a public key common to each station. The public key n notified from another station is inputted from the data input circuit and passed through the arithmetic circuit 13 as it is to the data storage memory 1.
Store in 4.

During encryption, the encryption device 10 of the transmitting station (station A) l:
The plaintext (M, , M2) is read from the data input circuit 11, and the encryption program in the program storage memory 15 is controlled using the unique public key nIl of the receiving station (station B) 2 stored in the data storage memory 14. Below is the formula (9L (1
0), the arithmetic circuit 13 generates the ciphertext (C1, C2)
Convert to Then, this ciphertext (c x , C2) is output from the data output circuit 16 and sent to the receiving station (station B) 2.

At the time of decryption, the encryption device 10 of the receiving station (station B) 2:
The received ciphertext (C1, C2) is read from the data input circuit J1, and using the private key unique to the own station (station B) stored in the data storage memory 14, it is decoded under the control of the decryption program in the program storage memory 15. F1+Fz+F:+? 1 Find F4, then M1p+ M2pI Miqg M2
Find q and finally calculate the plaintext (M, , M2).

Then, this plaintext (Ml, M2) is sent to the data output circuit 1.
Output from 6.

〔Effect of the invention〕

Below 1-. The encrypted communication method of the present invention described above has the following advantages.

■ Two-dimensional information can be encrypted efficiently.

In particular, applications that utilize the unique properties of two-dimensional cryptography, such as
Image data with a constant inner product or a constant distance can be efficiently encrypted.

■ It can be proven that the difficulty of deciphering the code is equivalent to the difficulty of decomposing the factors, making it highly secure.

■ It can be proven that the difficulty of obtaining information such as the value of the ratio of plaintext is equivalent to the difficulty of decomposing prime factors, so it is highly secure.

[Brief explanation of drawings]

FIG. 1 is a diagram showing the information flow of the encrypted communication method of the present invention,
FIG. 2 is a block diagram of an embodiment of a cryptographic device that realizes key generation, encryption, and decryption. 12-1...Data input circuit, ]2...Prime number generation circuit,
3... Arithmetic circuit, 14... Data storage memory, 5... Program storage memory, 6... Data output circuit.

Claims (1)

[Claims] (1) In an information communication system consisting of multiple stations with key generation, encryption, and decryption functions, at the key generation stage, each station generates a private key and a public key, stores the private key at that station, and The public key is notified to other stations, and in the encryption stage, the transmitting station converts a set of ciphertexts (C_1, C_2) from a set of plaintexts (M_1, M_2) to C_1 using the public key of the other receiving station. =2M_1M_2modn C_2=M_2^2+λM_1^2modn(λ≠-2
) and sends it to the receiving station, and in the decryption stage, the receiving station uses the private key of the receiving station to extract one set of plaintext (M_1, M_2) from one set of ciphertexts (C_1, C_2). An encrypted communication method characterized by restoring .