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

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

1999-09-16

2004-08-31

Morse, Gregory (Department: 2134)

Cryptography

Particular algorithmic function encoding

C380S030000

Reexamination Certificate

active

06785388

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to an encryption method for converting a plaintext into a ciphertext, and a decryption method for converting a ciphertext into an original plaintext, and more particularly to product-sum cryptosystem.
2. Description of the Related Art
In today's so-called advanced information society, text and image data important from the standpoint of business are transmitted/communicated and processed in the form of electronic data via an infrastructure of computer networks. Such electronic data can be readily reproduced, and it is impossible to distinguish the reproduction from the original, thus placing great importance on the issue of data protection. The realization of computer networks, which satisfy the requisites of “computer resource sharing,” “multiple access,” and “wide area networking,” are essential to the establishment of an advanced information society, but such networks incorporate elements that are inconsistent with the goal of data protection between concerned parties. As an effective technique for eliminating these inconsistencies, attention is focusing on cryptography techniques, which historically have been utilized principally in the military and diplomatic fields.
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 an original text (plaintext), which is understandable by anyone, to a text, the meaning of which is not understood by a third party (ciphertext), is encryption, the changing of ciphertext back into plaintext is decryption, and the overall process of this encryption and decryption is called a cryptosystem. In the encryption process and decryption process, secret data called an encryption key and a decryption key are utilized. Since a secret decryption key is required for decryption, only a person who knows this decryption key can decrypt a ciphertext, enabling the confidentiality of information to be maintained in accordance with encryption.
Encryption schemes can be broadly categorized into two types: common-key encryption schemes, and public-key encryption schemes. In a common-key encryption scheme, the encryption key and decryption key are identical, and encrypted communication is carried out in accordance with the sender and the receiver having the same key. A sender encrypts a plaintext on the basis of a secret common-key, and sends it to a receiver, and the receiver uses this common-key to decrypt the ciphertext into its original plaintext.
By contrast, in a public-key encryption scheme, the encryption key and decryption key are different, and encrypted, communication is performed such that a sender encrypts a plaintext with a receiver's public key, and the receiver decrypts this ciphertext using his own secret key. The public key is used for encryption, 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.
With regard to product-sum cryptosystem, which is a public-key encryption scheme, new schemes and attack methods are being proposed one after another, and the development of an encryption/decryption technique, which is capable of highspeed decryption so as to enable lots of data to be processed in a short period of time, is especially desirable.
SUMMARY OF THE INVENTION
An object of the present invention is to provide a novel encryption method and decryption method, which are applicable to the product-sum cryptosystem and capable of highspeed decryption processing in accordance with multi-adic numbers.
According to the first aspect of the present invention, there is provided an encryption method which produces a ciphertext C=m
0
B
0
+m
1
B
1
+ . . . +m
K−1
B
K−1
using a plaintext vector m=(m
0
, m
1
, . . . , m
K−1
), which divides a plaintext into K parts, and a base vector B=(B
0
, B
1
, . . . , B
K−1
), and is characterized in that the plaintext vector B
i
(0≦i≦K−1) is set to B
i
=b
0
b
1
, . . . b
i
using an integer b
i
.
K may be a power of 2.
A random number vector v=(v
0
, v
1
, . . . , v
K−1
) may further be used to produce a ciphertext C=m
0
v
0
B
0
+m
1
v
1
B
1
+ . . . +m
K−1
v
K−1
B
K−1
.
A plurality of groups of K terms of b
i
(i=0, 1, . . . , K−1) may be provided, and a ciphertext may be produced for each of the groups.
According to the second aspect of the present invention, there is provided a decryption method for decrypting a ciphertext C, which has been encrypted by the above described encryption method, characterized in that plaintext vector m=(m
0
, m
1
, . . . , m
K−1
) is determined from ciphertext C according to the algorithm below.
Step 0
C
0
=C/b
0
m
0
≡C
0
(mod
b
1
)
Step i (i=1, 2, . . . , K−2)
C
i
=(
C
i−1
−m
i−1
)/
b
i
m
i
≡C
i
(mod
b
i+1
)
Step K−1
m
K−1
=(
C
K−2
−m
K−2
)/
b
K−1
According to the third aspect of the present invention, there is provided an encryption method for producing ciphertext C=m
0
B
0
+m
1
B
1
+ . . . +m
K−1
B
K−1
using plaintext vector m=(m
0
, m
1
, . . . , m
K−1
), which divides a plaintext into K parts, and base vector B=(B
0
, B
1
, . . . , B
K−1
), characterized in that the above-mentioned B
i
(0≦i≦K−1) is set to B
i
=v
i
b
0
b
1
. . . b
i
using integer b
i
, and random number v
i
.
A plurality of groups of K terms of b
i
(i=0, 1, . . . , K−1) may be provided, and a ciphertext may be produced for each of these groups.
According to the fourth aspect of the present invention, there is provided an encryption/decryption method which uses plaintext vector m=(m
0
, m
1
, . . . , m
K−1
) obtained by dividing a plaintext into K parts, and base vector B=(B
0
, B
1
, . . . , B
K−1
) to convert the plaintext to a ciphertext, and which further converts this ciphertext to the original plaintext, characterized in that this encryption/decryption method includes the step of setting the base vector B
i
(0≦i≦K−1) to B
i
=b
0
b
1
. . . b
i
using integer b
i
; the step of selecting w, which satisfies w<P (P: prime number), and determining public-key vector c=(c
0
, c
1
, . . . , c
K−1
) according to Formula (a);
c
i
≡wB
i
(mod
P
)  (a)
the step of preparing ciphertext C shown in Formula (b) according to the scalar product of plaintext vector m and public-key vector c;
C=m
0
c
0
+m
1
c
1
+ . . . +m
K−1
c
K−1
  (b)
The step of determining an interim decrypted text M for ciphertext C as described in Formula (c);
M≡w
−1
C
(mod
P
)  (c)
and the step of determining plaintext vector m=(m
0
, m
1
, . . . , m
K−1
) by decrypting this interim decrypted text M according to the algorithm below:
Step 0
M
0
=M/b
0
m
0
≡M
0
(mod
b
1
)
Step i (i=1, 2, . . . , K−2)
M
i
=(
M
i−1
−m
i−1
)/
b
i
m
i
≡M
i
(mod
b
i+1
)
Step K−1
m
K−1
=(
M
K−2
−m
K−2
)/
b
K−1
According to the fifth aspect of the present invention, there is provided an encryption/decryption method which uses plaintext vector m=(m
0
, m
1
, . . . , m
K−1
) obtained by dividing a plaintext into K (K is a power of 2) parts, and base vector B=(B
0
, B
1
, . . . , B
K−1
) to convert the plaintext to a ciphertext, and which further converts the ciphertext to the original plaintext, characterized in that the method includes the step of setting the base vector B
i
(0≦i≦K−1) to B
i
=b
0
b
1
. . . b
i
using integer b
i
; the step of selecting w, which satisf

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