Re-encryption device, method and computer readable medium to change the access range for ciphertext
A cryptographic system comprising an encryption device to generate a ciphertext; a master re-encryption key generation device to generate a master re-encryption key that cannot decrypt a ciphertext generated by the encryption device, but can generate a re-encryption key for changing an access range for a ciphertext generated by the encryption device; re-encryption device to generate a re-encryption key for re-encrypting a target ciphertext generated by the encryption device, using the master re-encryption key, and re-encrypts the target ciphertext to generate a re-encrypted ciphertext, using the generated re-encryption key; and a decryption device to decrypt at least one of the ciphertext generated by the encryption device and the re-encrypted ciphertext generated by the re-encryption device.
1. A re-encryption device for changing an access range for ciphertexts comprising:
processing circuitry to:
generate a re-encryption key for re-encrypting a target ciphertext generated by an encryption device, using a master re-encryption key that cannot decrypt the target ciphertext generated by the encryption device, but can generate the re-encryption key for changing an access range for the target ciphertext generated by the encryption device while the target ciphertext remains encrypted, and re-encrypt the target ciphertext to generate a re-encrypted ciphertext, using the generated re-encryption key,
wherein the master re-encryption key includes a key element k* r in which a parameter w{right arrow over ( )} is set, the parameter w{right arrow over ( )} corresponding to a parameter y{right arrow over ( )} set in a cipher element c 1 included in the target ciphertext generated by the encryption device,
wherein the re-encryption key for re-encrypting the target ciphertext includes: (i) a key element k{tilde over ( )}*r in which a random number r{tilde over ( )} is embedded in the key element k{tilde over ( )}*r, (ii) a cipher element c{tilde over ( )}r in which a parameter x{right arrow over ( )}′ indicating a changed access range is set, and (iii) an element D{tilde over ( )} in which the random number r{tilde over ( )} is encrypted, and
wherein the re-encrypted ciphertext includes: (i) element K in which the cipher element c 1 is decrypted with the key element k{tilde over ( )}*r, (ii) the cipher element c{tilde over ( )}r, and (iii) an element E in which the element D{tilde over ( )} is set.
2. The re-encryption device according to claim 1 , wherein the processing circuitry generates the element K in which the cipher element c 1 is decrypted with the key element k{tilde over ( )}*r and a random number r′ is embedded, and generates the element E in which the random number r′ is embedded in the element D{tilde over ( )}.
3. The re-encryption device according to claim 2 , wherein the processing circuitry generates the cipher element c{tilde over ( )}r in which a random number ζ{tilde over ( )} r is embedded, and generates the element D{tilde over ( )} in which the random number ζ{tilde over ( )} r is embedded.
4. The re-encryption device according to claim 3 , wherein the processing circuitry generates the re-encryption key including the key element k{tilde over ( )}*r, the cipher element c{tilde over ( )} r , and the element D{tilde over ( )} indicated in Formula 2,
using the master re-encryption key indicated in Formula 1, and
generates the re-encrypted ciphertext including the element K and the element E indicated in Formula 3 and including the cipher element c{tilde over ( )} r
k
r
*
:=
(
r
,
δ
r
w
→
,
0
n
,
η
→
r
,
0
)
𝔹
1
*
,
c
r
:=
(
ζ
r
,
0
n
,
0
n
,
0
n
,
φ
r
)
𝔹
0
,
D
:=
G
(
g
T
ζ
r
)
·
r
ϵ
𝔽
q
,
Where
η
→
r
←
U
𝔽
q
n
,
r
,
ζ
r
,
φ
r
,
δ
r
←
U
𝔽
q
,
G
:
Encode
function
𝔾
T
→
𝔽
q
,
g
T
∈
𝔾
T
,
𝔹
0
,
𝔹
1
*
:
Base
[
Formula
1
]
k
r
~
*
:=
r
~
k
r
*
+
(
0
,
0
n
,
0
n
,
η
→
′
,
0
)
𝔹
1
*
,
c
r
~
:=
(
c
r
.0
~
,
c
r
.1
~
)
,
c
r
.0
~
:=
(
0
,
w
~
r
.0
x
→
′
,
0
n
,
0
n
,
φ
~
r
.0
)
𝔹
0
,
c
r
.1
~
:=
(
ζ
~
r
,
w
~
r
.1
x
→
′
,
0
n
,
0
n
,
φ
~
r
.1
)
𝔹
0
,
D
~
=
D
·
G
(
g
T
ζ
~
r
)
·
r
~
,
Where
η
→
r
′
←
U
𝔽
q
n
,
r
′
,
r
~
,
ζ
~
r
,
φ
~
r
.0
,
φ
~
r
.1
,
w
~
r
.0
,
w
~
r
.1
←
U
𝔽
q
,
[
Formula
2
]
K
:=
e
(
c
1
,
k
r
~
*
)
r
′
,
E
:=
D
~
·
r
′
Where
c
1
=
ζ
b
1.
+
ω
1
c
+
φ
1
b
1.3
n
+
2
,
c
:=
(
0
,
w
y
→
,
0
n
,
0
n
,
φ
)
𝔹
1
ζ
,
w
,
w
1
,
φ
,
φ
1
←
U
𝔽
q
,
b
1.
,
b
1.3
n
+
2
:
basis
vector
.
[
Formula
3
]
{right arrow over (η)} r , r, ζ r , φ r , δ r correspond to random numbers, η corresponds to a number of elements,
c r correspond to a cipher element,
G: Encode function T → q ,
g T ∈ T ,
0 , * 1 : Base
q corresponds to a vector representation to a finite field,
k
r
~
*
:=
r
˜
k
r
*
+
(
0
,
0
n
,
0
n
,
η
→
′
,
0
)
𝔹
1
*
,
[
Formula
2
]
c
r
~
:=
(
c
r
.0
~
,
c
r
.1
~
)
,
[
c
r
.0
~
:=
c
r
+
(
0
,
w
~
r
.0
x
′
→
,
0
n
,
0
n
,
φ
˜
r
.0
)
𝔹
0
]
,
c
r
.1
~
:=
(
ζ
r
~
,
w
~
r
.1
x
′
→
,
0
n
,
0
n
,
φ
˜
r
.1
)
𝔹
0
D
~
:=
D
·
G
(
g
T
)
·
r
˜
,
Where
η
′
→
r
←
𝔽
q
n
,
r
′
,
r
˜
,
ζ
r
~
,
φ
~
r
.0
,
φ
~
r
.1
,
w
~
r
.0
,
w
~
r
.1
←
U
𝔽
q
,
n
′
→
r
,
r
′
,
r
~
,
ζ
r
~
,
φ
~
r
.0
,
φ
~
r
.1
,
w
¯
r
.0
,
w
¯
r
.1
correspond
to
random
numbers
,
K
:=
e
(
c
1
,
k
r
~
*
)
r
′
,
E
:=
D
~
·
r
′
[
Formula
3
]
Where
c
1
:=
ζ
b
1
.
0
+
w
1
c
+
φ
1
b
1
.
3
n
+
2
,
c
:=
(
(
0
,
w
y
→
,
0
n
,
0
n
,
φ
)
)
𝔹
1
ζ
,
w
,
w
1
,
φ
,
φ
1
←
U
𝔽
q
,
ζ
,
w
,
w
1
,
φ
,
φ
1
correspond
to
random
numbers
,
b
1
.
0
,
b
1
.
3
n
+
2
:
basis
vector
.
5. A re-encryption method for changing an access range for ciphertexts comprising:
generating a re-encryption key for re-encrypting a target ciphertext generated by an encryption device, using a master re-encryption key that cannot decrypt the target ciphertext generated by the encryption device, but can generate a re-encryption key for changing an access range for the target ciphertext generated by the encryption device while the target ciphertext remains encrypted; and
re-encrypting the target ciphertext to generate a re-encrypted ciphertext, using the re-encryption key,
wherein the master re-encryption key includes a key element k* r in which a parameter w{right arrow over ( )} is set, the parameter w{right arrow over ( )} corresponding to a parameter y{right arrow over ( )} set in a cipher element c 1 included in the target ciphertext generated by the encryption device,
wherein the re-encryption key for re-encrypting the target ciphertext includes: (i) a key element k{tilde over ( )}*r in which a random number r{tilde over ( )} is embedded in the key element k* r , (ii) a cipher element c{tilde over ( )}r in which a parameter x{right arrow over ( )}′ indicating a changed access range is set, and (iii) an element D{tilde over ( )} in which the random number r is encrypted, and
wherein the re-encrypted ciphertext includes: (i) an element K in which the cipher element c 1 is decrypted with the key element k{tilde over ( )}*r, (ii) the cipher element c{tilde over ( )}r, and (iii) an element E in which the element D{tilde over ( )} is set.
6. A non-transitory computer readable medium storing a re-encryption program for changing an access range for ciphertexts that causes a computer to function as a re-encryption device to perform:
a re-encryption key generation process of generating a re-encryption key for re-encrypting a target ciphertext generated by an encryption device, using a master re-encryption key that cannot decrypt the target ciphertext generated by the encryption device, but can generate a re-encryption key for changing an access range for the target ciphertext generated by the encryption device while the target ciphertext remains encrypted; and
a re-encryption process of re-encrypting the target ciphertext to generate a re-encrypted ciphertext, using the re-encryption key generated by the re-encryption key generation process,
wherein the master re-encryption key includes a key element k* r in which a parameter w{right arrow over ( )} is set, the parameter w{right arrow over ( )} corresponding to a parameter r set in a cipher element c 1 included in the target ciphertext generated by the encryption device,
wherein the re-encryption key for re-encrypting the target ciphertext includes: (i) a key element k{tilde over ( )}*r in which a random number r{tilde over ( )} is embedded in the key element k* r , (ii) a cipher element c{tilde over ( )}r in which a parameter x{right arrow over ( )}′ indicating a changed access range is set, and (iii) an element D{tilde over ( )} in which the random number r{tilde over ( )} is encrypted, and
wherein the re-encrypted ciphertext includes: (i) an element K in which the cipher element c 1 is decrypted with the key element k{tilde over ( )}*r, (ii) the cipher element c{tilde over ( )}r, and (iii)an element E in which the element D{tilde over ( )} is set.
7. A cryptographic system comprising:
an encryption device comprising a processing circuitry to generate a ciphertext;
a master re-encryption key generation device comprising a processing circuitry to generate a master re-encryption key that cannot decrypt the ciphertext generated by the encryption device, but can generate a re-encryption key for changing an access range for the ciphertext generated by the encryption device while the ciphertext remains encrypted,
the master re-encryption key including a key element k* r in which a parameter w{right arrow over ( )} is set, the parameter w{right arrow over ( )} corresponding to a parameter y{right arrow over ( )} set in a cipher element c 1 included in the ciphertext generated by the encryption device;
a re-encryption device comprising a processing circuitry to generate a re-encryption key for re-encrypting a target ciphertext generated by the encryption device, using the master re-encryption key generated by the master re-encryption key generation device, the re-encryption key including: (i) a key element k{tilde over ( )}*r in which a random number r{tilde over ( )} is embedded in the key element k*r, (ii) a cipher element c{tilde over ( )}r in which a parameter x{right arrow over ( )}′ indicating a changed access range is set, and (iii) an element D{tilde over ( )} in which the random number r{tilde over ( )} is encrypted, and
re-encrypt the target ciphertext, using the generated re-encryption key, so as to generate a re-encrypted ciphertext including: (i) an element K in which the cipher element ci is decrypted with the key element k{tilde over ( )}*r, (ii) the cipher element c{tilde over ( )}r, and (iii) an element E in which the element D{tilde over ( )} is set; and
a decryption device comprising a processing circuitry to decrypt at least one of the ciphertext generated by the encryption device and the re-encrypted ciphertext generated by the re-encryption device.