A security system using an RSA algorithm that includes a key input section for receiving a secret key and a public key used in one of encryption and decryption of a message, a random coefficient generating section for generating a random coefficient r having a bit of a predetermined size, a first calculation section for dividing the secret key into a first secret key and a second secret key by using the value of r, and performing an exponentiation of RSA algorithm by using the respective secret keys and the public key, and a second calculation section for performing one of the encryption and the decryption by combining results of exponentiation calculated respectively by using the first and the second secret keys.