A cryptographic processing system that performs a predicate encryption process using dual modules of a space V and a space V * paired through a pairing operation shown in Formula 1, the cryptographic processing system comprising: an encryption device that, using a processing device, generates as a cipher vector c 1 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 b i (i = 1,..., n) and a basis vector d n+1 which is a sum of two or more basis vectors b i (i = n+1,..., m) out of the basis vectors b i (i = n+1,..., N), the cipher vector c 1 being the vector in which attribute information is embedded as coefficients of one or more basis vectors out of the basis vector b i (i = 1,..., n), and predetermined information is embedded as a coefficient of the basis vector d n+1; and a decryption device that, using the processing device, performs the pairing operation e (c 1, k * L,dec) shown in Formula 1 on the cipher vector c 1 generated by the encryption device and a key vector k * L,dec to decrypt the cipher vector c 1 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. 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. an encryption device that, using a processing device, generates as a cipher vector c 1 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 b i (i = 1,..., n) and a basis vector d n+1 which is a sum of two or more basis vectors b i (i = n+1,..., m) out of the basis vectors b i (i = n+1,..., N), the cipher vector c 1 being the vector in which attribute information is embedded as coefficients of one or more basis vectors out of the basis vector b i (i = 1,..., n), and predetermined information is embedded as a coefficient of the basis vector d n+1; and a decryption device that, using the processing device, performs the pairing operation e (c 1, k * L,dec) shown in Formula 1 on the cipher vector c 1 generated by the encryption device and a key vector k * L,dec to decrypt the cipher vector c 1 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.