Cryptographic processing system, key generation device, key delegation device, encryption device, decryption device, cryptographic processing method, and cryptographic processing program

A cryptographic processing method, implemented on a cryptographic processing system, of performing a predicate encryption process using dual vector spaces of a space V and a space V* paired through a pairing operation, the cryptographic processing method comprising:

• generating, by a hardware processor, as a cipher vector c1 a vector of a basis B^, the basis B^ having, out of basis vectors bi (i=1, . . . , n, . . . , N) (N being an integer of 3 or greater and n being an integer from 1 to N−2) that constitute a predetermined basis B of the space V, basis vectors bi (i=1, . . . , n) and a basis vector dn+1 which is a sum of two or more basis vectors bi (i=n+1, . . . , m) out of the basis vectors bi (i=n+1, . . . , N), the cipher vector c1 being the vector in which attribute information is embedded as coefficients of one or more basis vectors out of the basis vector bi (i=1, . . . , n), and predetermined information is embedded as a coefficient of the basis vector dn+1;
• and
• performing the pairing operation e(c1, k*L,dec) shown in Formula 1 on the cipher vector c1 generated and a key vector k*L,dec as follows,
• e
• ⁡
• (
• p
• ,
• q
• )
• :=
• ∏
• i
• =
• 1
• N
• ⁢
• ⁢
• e
• ⁡
• (
• χ
• i
• ⁢
• b
• i
• ,
• η
• i
• ⁢
• b
• i
• *
• )
• ⁢
• ⁢
• where
• ⁢
• ⁢
• p
• :=
• ∑
• i
• =
• 1
• N
• ⁢
• χ
• i
• ⁢
• b
• i
• ,
• ⁢
• q
• :=
• ∑
• i
• =
• 1
• N
• ⁢
• η
• i
• ⁢
• b
• i
• *
• ,
• ⁢
• χ
• i
• ,
• η
• i
• :
• predetermined
• ⁢
• ⁢
• values
• ,
• [
• Formula
• ⁢
• ⁢
• 1
• ]
• to decrypt the cipher vector c1 and to extract a value concerning the predetermined information, the key vector k*L,dec being a vector of a basis B* of the space V* and constructed such that predicate information is embedded as coefficients of one or more basis vectors of basis vectors b*i (i=1, . . . , n) out of basis vectors b*i (i=1, . . . , n, . . . , N) that constitute the basis B*, and coefficients of basis vectors b*i (i=n+1, . . . , m) of the basis B* are embedded such that a sum of the coefficients of the basis vectors b*i (i=n+1, . . . , m) is 1.

A non-transitory computer readable medium storing a cryptographic processing program that performs a predicate encryption process using dual vector spaces of a space V and a space V* paired through a pairing operation, the cryptographic processing program causing a computer to execute:

• an encryption process that generates as a cipher vector c1 a vector of a basis B^, the basis B^ having, out of basis vectors bi (i=1, . . . , n, . . . , N) (N being an integer of 3 or greater and n being an integer from 1 to N−2) that constitute a predetermined basis B of the space V, basis vectors bi (i=1, . . . , n) and a basis vector d n+1 which is a sum of two or more basis vectors bi (i=n+1, . . . , m) out of basis vectors bi (i=n+1, . . . , N), the cipher vector c1 being the vector in which attribute information is embedded as coefficients of one or more basis vectors out of the basis vector bi (i=1, . . . , n), and predetermined information is embedded as a coefficient of the basis vector dn+1;
• and
• a decryption process that performs the pairing operation e(c1, k*L,dec) shown in Formula 1 on the cipher vector c1 generated by the encryption device and a key vector k*L,dec as follows,
• e
• ⁡
• (
• p
• ,
• q
• )
• :=
• ∏
• i
• =
• 1
• N
• ⁢
• ⁢
• e
• ⁡
• (
• χ
• i
• ⁢
• b
• i
• ,
• η
• i
• ⁢
• b
• i
• *
• )
• ⁢
• ⁢
• where
• ⁢
• ⁢
• p
• :=
• ∑
• i
• =
• 1
• N
• ⁢
• χ
• i
• ⁢
• b
• i
• ,
• ⁢
• q
• :=
• ∑
• i
• =
• 1
• N
• ⁢
• η
• i
• ⁢
• b
• i
• *
• ,
• ⁢
• χ
• i
• ,
• η
• i
• :
• predetermined
• ⁢
• ⁢
• values
• ,
• [
• Formula
• ⁢
• ⁢
• 1
• ]
• to decrypt the cipher vector c1 and to extract a value concerning the predetermined information, the key vector k*L,dec being a vector of a basis B* of the space V* and constructed such that predicate information is embedded as coefficients of one or more basis vectors of basis vectors b*i (i=1, . . . , n) out of basis vectors b*i (i=1, . . . , n, . . . , N) that constitute the basis B*, and coefficients of basis vectors b*i (i=n+1, . . . , m) of the basis B* are embedded such that a sum of the coefficients of the basis vectors b*i (i=n+1, . . . , m) is 1.