A quantum cryptosystem based on algebraic codes, which uses single photons as quantum message carriers, is given. The cryptosystem is equipped with authentication, data integrity, and non-repudiation. There is no need for a parallel classical channel since public conversation is omitted. Indeed by using a suitable algebraic error-correcting code, Alice and Bob do not need to share a string of common bases. Therefore, they already share only one secret key for encryption. The secret key can be reused many times also in a noisy environment. The encryption and the decryption are similar, so the cryptosystem can be thought symmetric. Analysis shows that the cryptosystem is secure, low cost, and more practical compared with the previous ones.