# Forum Romancedrive.com O Inurl:homemarket.asp Is 1 Romance Drive RE-ENCRYPTION KEY GENERATOR, RE-ENCRYPTION APPARATUS, AND PROGRAM - Toshiba Solutions Corporation

## Forum Romancedrive.com O Inurl:homemarket.asp Is 1 Romance Drive

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The decryption apparatus 50 verifies the ciphertext data Ci generated by the encryption apparatus 20 in the same manner as in step ST41. If the verification has succeeded, the decryption apparatus 50 decrypts the ciphertext data Ci using the private key ski to obtain a message m. This decryption is described by:

$m=C3/e(g1g2,C2X)1xi$

Whether or not the decryption result of the above equation is m can be verified by:

$m·e(g1g2,g)r/e(g1g2,C2X)1xi=m·e(g1g2,g)r/e(g1g2,gxir)1xi=m·e(g1g2,g)r/e(g1g2,g)r=m.$

[Modification 2]

In addition to modification 1, as will be described below, the first embodiment may be modified to a mode in which ciphertext data is decrypted without re-encryption. In this case as well, only the key setup processing, encryption processing, and decryption processing can be executed. The key setup processing and decryption processing of this modification are the same as those in the first embodiment. The encryption processing and decryption processing of this modification will be described below. Note that j refers to identification information of the decryption apparatus 50 in this modification.

The encryption parameter generation unit 23 of the encryption apparatus 20 generates (ssk, svk) (step ST21′) in the same manner as in step ST21 and sets the verification key svk in ciphertext data C1 (C1=svk).

Also, the encryption parameter generation unit 23 generates five random numbers; r, s, t, k, and θεZp* and outputs them to the ciphertext generation unit 24.

The ciphertext generation unit 24 generates encrypted data C2X′, C2X″, C2Y′, C2Y″, C2Z′, C2Z″, C2Z1′, C2Z1″, C2′″, C5X, C5Y, C5Z, C3, and C4 with respect to a message mεGT as plaintext data using these random numbers r, s, t, k, and θ, and the public key pkj of the decryption apparatus 50 (step ST22′). These encrypted data are respectively given by:

$C2X′=Y2js, C2X″=Y2jrs, C2Y′=Xjt, C2Y″=Xjrt, C2Z′=Y2jk, C2Z″=Y2jrk, C2Z1′=Xjk, C2Z1″=Xjrk, C3=e(g1g2,g)r·m, C4=(usvk·υ)r, C5X=(g1·gθ)1s, C5Y=gθ+1t, C5Z=(g1·gθ+1)1k$

After completion of step ST22′, the ciphertext generation unit 24 generates a one-time signature σ in the same manner as in step ST23.

After that, the ciphertext generation unit 24 generates ciphertext data Cj=(C1, C2X′, C2X″, C2Y′, C2Y″, C2Z′, C2Z″, C2Z1′, C2Z1″, C2′″, C5X, C5Y, C5Z, C3, C4, σ) including all the encrypted data C1 to C4 and the one-time signature σ, and writes the obtained ciphertext data in the temporary data storage unit 21.

The communication unit 22 transmits the ciphertext data Cj in the temporary data storage unit 21 to the decryption apparatus 50 under the control of the control unit 25.

The decryption apparatus 50 verifies the ciphertext data Cj generated by the encryption apparatus 20 in the same manner as in step ST51. If the verification has succeeded, the decryption apparatus 50 decrypts the ciphertext data Cj using the private key skj to obtain a message m. This decryption is described by:

$m=C3/{}$

Whether or not the decryption result of the above equation is m can be verified by:

$C3/{}=C3/{}=C3/{}=m·e(g1g2,g)r/(e(g,g)βr·e(g,g)αr)=m.$

Note that the above equation is described by rewriting g1=gα and g2=gβ.

[Modification 3]

In the example described in the first embodiment, the public parameters include the three members g, g1, and g2 of the system fixed values. However, the present invention is not limited to this. For example, the member g2 may not be generated, and the public parameters may not include the member g2. In this case, in the first embodiment, g2=g may be set to replace g2 by g. The same applies to the following embodiments and modifications.

[Modification 4]

In the example described in the first embodiment, the public parameters include the three members g, g1, and g2 of the system fixed values. However, the present invention is not limited to this. For example, the public parameters may include four or more members of the system fixed values. For example, when the public parameters include four members g, g1, g2, and g3, g2=g2g3 may be set to replace g2 by g2g3 in the first embodiment. Also, for example, when the public parameters include five members g, g1, g2, g3, and g4, g1=g1g3 and g2=g2g4 may be set to respectively replace g1 by g1g3 and g2 by g2g4 in the first embodiment. The same applies to the following embodiments and modifications.

# Second Embodiment

This embodiment will explain an example in which a re-encryption key is updated every certain period. As a parameter which expresses a period, a time parameter L is used. Of the key setup processing, encryption processing, re-encryption key generation processing, re-encryption processing, and decryption processing, the encryption processing, re-encryption key generation processing, and re-encryption processing use the time parameter. The time parameter is used as follows. For example, when the encryption processing is executed in a certain period t1, the encryption processing to be described later is executed to have L=t1; when the encryption processing is executed in the next period t2, the encryption processing to be described later is executed to have L=t2. The key setup processing, encryption processing, re-encryption key generation processing, re-encryption processing, and decryption processing of this embodiment will be described below. Note that parts common to the first embodiment described above will be described using the same reference numerals and a description thereof will not be repeated.

(1) Key Setup Processing

Public parameters are the same as those in the first embodiment. Letting i be identification information of a re-encryption key generator 30, a public key/private key generation unit 14 generates a private key xi, yi, zi, w eForum Romancedrive.com O Inurl:homemarket.asp Is 1 Romance Drive RE-ENCRYPTION KEY GENERATOR, RE-ENCRYPTION APPARATUS, AND PROGRAM - Toshiba Solutions Corporationl v a Www88xoxo.com tForum Romancedrive.com O Inurl:homemarket.asp Is 1 Romance Drive RE-ENCRYPTION KEY GENERATOR, RE-ENCRYPTION APPARATUS, AND PROGRAM - Toshiba Solutions Corporationm h WWW.MMB33.COM