Universal quantum obfuscation for quantum non-linear functions

Research on quantum cryptography has burgeoned in the recent decades and combined quantum mechanics and cryptography theory. Among the existing quantum cryptographic primitives, quantum obfuscation is an emergent force to be reckoned with. Quantum obfuscation means obfuscating a circuit by quantum mechanics to improve security. It is used to hide functionality and prevent the reverse engineering of quantum circuits. However, research studies on the construction of quantum obfuscation are relatively immature due to its difficulty in implementation and application. Also, the obfuscation for quantum non-linear functions has not been suggested yet, although quantum non-linear functions cover a wide range of quantum functions that can be obfuscated. In this paper, we initiate a universal definition of quantum obfuscation which utilizes quantum teleportation to construct an obfuscator and interpreter for quantum non-linear functions. Furthermore, we demonstrate the validity of applying the obfuscation to the quantum asymmetric encryption scheme and rigorously prove that the encryption realized by quantum obfuscation satisfies IND (indistinguishability)-security. This work provides a positive possibility of quantum obfuscation for quantum non-linear functions and will complement the theory of both quantum obfuscation and quantum asymmetric encryption.