Quantum anonymous ranking and selection with verifiability

Anonymous ranking allows each user to perfectly know the position of his/her private datum in the ascending or descending sequence of all ranking data, while anonymous selection focuses on particular items. Both of them disclose each user's input and hide the accurate link between users and ranking data. Mature solutions of anonymous ranking and selection are usually crucial components of solving complex problems and are also extensively applied to many fields in daily life, such as auctions and commercial enterprises. In this paper, we propose two protocols of quantum anonymous ranking and selection with verifiability, in which each user can verify whether his/her ranking datum has been modified in a manner without detection and obtain the corresponding output with the property of anonymity. Furthermore, we demonstrate in detail that our protocols achieve security against outside eavesdroppers and inside malicious users under ideal or practical environment assumptions.