Optimization of Binary Randomized Response Based on Lanke Privacy and Utility Analysis  

作　　者：Yihui Zhou Wenli Wang Jun Yan Zhenqiang Wu Laifeng Lu 

机构地区：[1]School of Computer Science,Shaanxi Normal University,Xi’an 710119,China [2]School of Mathematics and Statistics,Shaanxi Normal University,Xi’an 710119,China [3]School of Mathematics and Computer Applications,Shangluo College,Shangluo 726000,China

出　　处：《Chinese Journal of Electronics》2025年第1期242-256,共15页电子学报(英文版)

基　　金：supported by the Shaanxi Provincial Natural Science Foundation(Grant No.2020JM-288);the Fundamental Research Funds for the Central Universities(Grant Nos.GK201903091 and GK201903011);the Scientific and Technological Project of Shangluo(Grant No.2021-C-0004);the Research Project of Shangluo University(Grant No.21SKY126)。

摘　　要：Currently,it has become a consensus to enhance privacy protection.Randomized response(RR)technique,as the mainstream perturbation mechanism for local differential privacy,has been widely studied.However,most of the research in literature managed to modify existing RR schemes and propose new mechanisms with better privacy protection and utility,which are illustrated only by numerical experiments.We study the properties of generalized binary randomized response mechanisms from the perspectives of Lanke privacy and utility.The mathematical expressions of privacy and utility for the binary RR mechanism are given respectively.Moreover,the comparison principle for privacy and utility of any two mechanisms is proved.Finally,the optimization problem of the binary RR mechanism is discussed.Our work is based on a rigorous mathematical proof of privacy and utility for the general binary RR mechanism,and numerical verification illustrates the correctness of the conclusions.It can provide theoretical support for the design of binary RR mechanism and can be applied in data collection,analysis and publishing.

关 键 词：Randomized response Lanke privacy Utility optimization 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]