  It is well known that Shor's quantum algorithm for integer factorization can
break down the RSA public-key cryptosystem, which is widely used in many
cryptographic applications. Thus, public-key cryptosystems in the quantum
computational setting are longed for cryptology. In order to define the
security notions of public-key cryptosystems, we have to model the power of the
sender, receiver, adversary and channel. While we may consider a setting where
quantum computers are available only to adversaries, we generally discuss what
are the right security notions for (quantum) public-key cryptosystems in the
quantum computational setting. Moreover, we consider the security of quantum
public-key cryptosystems known so far.
