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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.

Quantum probabilistic encryption scheme based on conjugate coding