A cryptographic system (10) performs a cryptographic process using a basis. B and a basis B*. An encryption device (200) generates a ciphertext including a transmission-side vector being a vector in the basis B and being generated using one vector of a first vector consisting of coefficients yj of a polynomial having xi as roots and a second vector consisting of v1i being a power of v1. A decryption device (300) decrypts the ciphertext generated by the encryption device (200) with a decryption key including a reception-side vector being a vector in the basis B* and being generated using the other vector of the first vector and the second vector.