  We present a quantum probabilistic encryption algorithm for a private-key
encryption scheme based on conjugate coding of the qubit string. A
probabilistic encryption algorithm is generally adopted in public-key
encryption protocols. Here we consider the way it increases the unicity
distance of both classical and quantum private-key encryption schemes. The
security of quantum probabilistic private-key encryption schemes against two
kinds of attacks is analyzed. By using the no-signalling postulate, we show
that the scheme can resist attack to the key. The scheme's security against
plaintext attack is also investigated by considering the information-theoretic
indistinguishability of the encryption scheme. Finally, we make a conjecture
regarding Breidbart's attack.
