A homomorphic operation system according to an embodiment includes a homomorphic encryption device configured to output a first ciphertext data generated based on a first base, a homomorphic encryption server including a storage device storing base conversion table configured to convert ciphertext data based on the first base into a second ciphertext data based on a second base and the first ciphertext data received from the homomorphic encryption device, and a homomorphic encryption operation device configured to perform a predetermined operation using the base conversion table on the first ciphertext data to convert the first ciphertext data into the second ciphertext data based on the second base.