n this paper we propose a quantum asymmetric-key cryptosystem, which does not rely on a computationally hard problem for security, 
but on uncertainty principles of quantum mechanics, thus obtaining security against a computationally unbounded adversary. 
We first propose a universally composable security criteria for quantum asymmetric-key cryptosystems by adapting the universally 
composable security of quantum key distribution by Mayers et al. to the context of quantum asymmetric-key encryption. 
We then give a specific implementation using this security notion, 
which improves the quantum asymmetric-key cryptosystem of Kawachi et al. in the sense of information-theoretic security. 
We prove that the information leak on the decryption key from the multiple copies of the encryption keys released 
in our scheme is exponentially smaller than that of Kawachi et al., which allows Alice to produce exponentially more encryption keys.