量子访问控制问题的可混淆性

Obfuscatability of Quantum Access Control Problem

混淆是在数据加密的基础之上衍生出的对功能加密的概念. 2001年Barak等人证明,最强大的经典混淆工具,即通用黑盒混淆器,是不存在的.近年来一些文献已经提出了满足比黑盒稍弱定义的混淆方案,并且可以对一些特殊功能进行混淆.与此同时,量子通信和量子计算在本世纪得到了长足的发展,但对于量子混淆理论的研究目前仍处于空白阶段.本文结合量子点函数和混淆理论,分析量子访问控制问题的可混淆性.首先,定义了量子点函数,并证明在随机预言模型下量子点函数的可混淆性.随后定义量子访问控制问题,通过辅助问题解决量子访问控制问题的指数规模困难,证明量子访问控制问题的可混淆性.最后提出量子混淆理论未来有价值的研究方向,包括量子黑盒混淆器的量子力学机制实现、对经典线路的量子混淆、不可重复使用的量子混淆、量子随机预言机的删除.

Obfuscation is a concept of functionality encryption conceived from the concept of data encryption.It is known that,the most strong obfuscation of classic program,the so-called general blackbox obfuscation,is proved to be nonexistent by Barak in 2001.It has shown in recent years that,some weaker obfuscations still work efficiently on some specific functions.Meanwhile,quantum communication and quantum computing have made great progress in this century.However,academic research on the theory of quantum obfuscation is still at a blank stage.This study combines the two leading disciplines of quantum theory and obfuscation theory and develops the theory of quantum obfuscation.We first define quantum point functions and prove that the quantum point functions are obfuscatable under quantum-accessible random oracle model.Subsequently,we define quantum access control problems and auxiliary problems to avoid exponential hardness.We prove the obfuscatability of quantum access control problems.Finally,we present the future valuable research directions of quantum obfuscation theory,including quantum black box obfuscator’s realization,quantum obfuscation for classical circuits,non-reusable quantum obfuscation,and removing quantum random oracles.