Encryption method, decryption method, encryption/decryption...

Details Encryption method, decryption method, encryption/decryption... Encryption method, decryption method, encryption/decryption...

1999-09-16

2004-09-28

Morse, Gregory (Department: 2134)

Cryptography

Particular algorithmic function encoding

C380S030000

Reexamination Certificate

active

06798884

ABSTRACT:

This application relates to two applications concurrently filed herewith entitled (1) “CRYPTOGRAPHIC COMMUNICATION METHOD, ENCRYPTION METHOD, AND CRYPTOGRAPHIC COMMUNICATION SYSTEM” that claims foreign priority based on Japanese patent applications 10-262035, filed Sep. 16, 1998 and 10-338190, filed Nov. 27, 1998 inventors: Masao Kasahara and Yasuyuki Murakami; Express Mail EL 446 156 915 US) and (2) “ENCRYPTION METHOD, DECRYPTION METHOD, ENCRYPTION/DECRYPTION METHOD, CRYPTOGRAPHIC COMMUNICATIONS SYSTEM, AND COMPUTER USABLE MEDIUM” that claims foreign priority based on Japanese patent applications 10-262036, filed Sep. 16, 1998 and 11-105815, filed Apr. 13, 1999 inventors: Masao Kasahara and Yasuyuki Murakami; Express Mail EL 446 156 827 US), which applications are hereby incorporated by reference in their entirety.
BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to an encryption method for converting plaintext into ciphertext, and to a decryption method for converting ciphertext into the original plaintext, and more particularly relates to product-sum type cryptosystem.
2. Description of the Related Art
In today's world, characterized by sophisticated information utilization, important business document and image information are transmitted and communicated in the form of electronic information over an infrastructure of computer networks. By its very nature, electronic information can be easily copied, making it extremely difficult to distinguish between the copy and the original, and information security has become a very serious problem. The realization of computer networks which support “computer resource sharing,” “multi-accessing,” and “wide-area implementation” is particularly indispensable to the establishment of a high-level information society. However, that very realization involves factors that are in conflict with the goal of information security between involved parties. An effective technique for eliminating those inconsistencies is encryption technology, whichup until now, in the course of human history, has been primarily used in the fields of military operations and foreign diplomacy.
Cryptography is the exchange of information in such a way that the meaning of that information cannot be understood by anyone other than the authorized parties. In cryptography, the conversion of the original text (plaintext), that is understandable by anyone, to a text (ciphertext), the meaning of which is not understood by a third party is called encryption, and the changing of ciphertext into plaintext is decryption. The overall process of this encryption and decryption is called a cryptosystem. In the encryption process and decryption process, respectively, secret data called an encryption key and a decryption keys are employed. Since a secret decryption key is necessary for decryption, only a party who knows that decryption key can decrypt the ciphertext, enabling the confidentiality of the information to be maintained in accordance with encryption.
Generally, there are two types of encryption schemes. Namely common key encryption scheme and public key encryption scheme. In a common key encryption scheme, the encryption key and the decryption key are identical, and cryptographic communication is conducted with the identical keys in the possession of both the sending party and the receiving party. The sending party encrypts plaintext based on the common key and sends it to the receiving party, whereupon the receiving party uses the common key to decrypt the ciphertext into the original plaintext.
By contrast, in a public key encryption scheme, the encryption key and decryption key are different. In conducting cryptographic communications in this system, the sending party encrypts the plaintext with the public key of a receiving party, and the receiving party decrypts that ciphertext with his or her own secret key. The public key is used for encryption, and the secret key is a key for decrypting the ciphertext encrypted by the public key. The ciphertext encrypted by the public key can only be decrypted using a secret key.
New methods for product-sum type cryptosystem, which is one public key encryption scheme, as well as attack methods (methods for breaking the codes), are being proposed one after another. A particularly urgent task is now that of developing cryptographic techniques capable of high-speed decryption so as to enable large volumes of information be processed in short times.
SUMMARY OF THE INVENTION
An object of the present invention, which was devised in view of the situation described in the foregoing, is to provide a new encryption method and decryption method for product-sum type cryptosystem wherewith high-speed decryption processing is possible.
Another object of the present invention is to provide an encryption method and decryption method wherewith vulnerability to attack by the LLL (Lenstra-Lenstra-Lovasz) method is minimized and security is enhanced.
According to the first aspect of the present invention, there is provided an encryption method comprising the step of preparing a plaintext vector m=(m
0
, m
1
, . . . , m
K−1
) that is obtained by dividing plaintext by K, the step of preparing base vectors D=(D
0
, D
1
, . . . , D
K−1
), with D
i
(0≦i≦K−1) being set to D
i
=d/d
i
(where d=d
0
d
1
. . . d
K−1
, and any two numbers d
i
and d
j
are prime relative to each other), and the step of yielding ciphertext C=m
0
D
0
+m
1
D
1
+ . . . +m
K−1
D
K−1
from the plaintext vector m and base vectors D.
Random number vectors v=(v
0
, v
1
, . . . , v
K−1
) may further be used to yield ciphertext C=m
0
v
0
D
0
+m
1
v
1
D
1
+ . . . +m
K−1
v
K−1
D
K−1
. A plurality of sets each containing K terms of d
i
(i=0, 1, 2, . . . , K−1) elements may be provided, and ciphertext is obtained for each of those sets, respectively.
According to the second aspect of the present invention, there is provided an encryption method comprising the step of preparing a plaintext vector m=(m
0
, m
1
, . . . , m
K−1
that K-divides plaintext, the step of preparing base vectors D=(D
0
, D
1
, . . . , D
K−1
), with D
i
(0≦i≦K−1) being set to D
i
=(d/d
i
)v
i
(where d=d
0
d
1
. . . d
K−1
, any two numbers d
i
and d
j
are prime relative to each other, and v
i
is a random number), and the step of yielding ciphertext C=m
0
D
0
+m
1
D
1
+ . . . +m
K−1
D
K−1
from the plaintext vector m and base vectors D.
A plurality of sets each containing K terms of d
i
(i=0, 1, 2, . . . , K−1) elements may be provided, and ciphertext is obtained for each of those sets, respectively.
According to the third aspect of the present invention, there is provided a decryption method for decrypting the ciphertext C encrypted by any of the above described encryption methods, wherein the plaintext vector m=(m
0
, m
1
, . . . , m
K−1
) is found by formula (a) below.
m
i
≡CD
i
−1
(mod
d
i
)  (a)
According to the fourth aspect of the present invention, there is provided an encryption/decryption method comprising the steps of:
providing a plaintext vector m=(m
0
, m
1
, . . . , m
K−1
) that K-divides plaintext;
providing base vectors D=(D
0
) D
1
, . . . , D
K−1
), with D
i
(0≦i≦K−1) being set to d/d
i
, using the integer d
i
, (where d=d
0
d
1
. . . d
K−1
, and any two numbers d
i
and d
j
are prime relative to each other);
selecting w to satisfy w<P (P=prime number), and finding a public key vector c=(c
0
, c
1
, . . . , c
K−1
) from formula (b),
c
i
≡wD
i
(mod
P
)  (b);
producing the ciphertext C indicated in formula (c) from the inner product of a plaintext vector m and public key vector c,
C=m
0
c
0
+m
1
c
1
+ . . . +m
K−1
c
K−1
  (c);
finding

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