基于量子非线性函数的量子混淆方法

Quantum Obfuscation Based on Quantum Nonlinear Function

混淆是一种通过对函数功能加密来保证通信安全性的新型加密方法.量子混淆衍生于经典混淆,利用量子比特加密线路或函数的功能从而保护线路信息.在对量子混淆所加密的函数方面,非线性混淆理论仍需要深入研究.本文结合量子非线性函数和混淆理论,明确定义了量子幂函数,根据量子隐形传态基本原理和所混淆函数的功能,提出基于量子非线性函数的量子混淆方法,设计量子混淆器和量子解释器线路,证明其在随机预言模型下的可混淆性.提出了量子非线性函数混淆在同态加密中的密码学应用,证明其满足不可区分安全性.

Obfuscation is a new form of encryption method which ensures the security of commu-nication by encrypting functionality.Derived from classical obfuscation,quantum obfuscation utilizes qubits to protect circuit information by encrypting the functionality of circuits or functions.In terms of obfuscating specific functions,researches on quantum nonlinear obfuscation theory are still at the infant stage.This paper combines quantum nonlinear function and its obfuscation theory to initiate a clear definition of quantum power function.According to quantum teleportation theory and the func-tionality of quantum nonlinear function to be obfuscated,this paper proposes quantum obfuscation method of quantum nonlinear function,designs specific circuits of quantum obfuscator and quantum interpreter,and proves the obfuscatability of quantum nonlinear function under random oracle model.This paper also constructs a homomorphic encryption scheme based on quantum nonlinear function obfuscation which is proved to satisfy indistinguishability security.