一种基于同态加密的密文符号函数计算优化方法  

An Optimized Computation Method for Cipher Symbol Functions Based on Homomorphic Encryption

作　　者：李晓东 周苏雅 赵炽野 李慧 袁文博 张健毅 Li Xiaodong;Zhou Suya;Zhao Chiye;Li Hui;Yuan Wenbo;Zhang Jianyi(Department of Cyberspace Security,Beijing Electronic Science and Technology Institute,Beijing 100070)

机构地区：[1]北京电子科技学院网络空间安全系,北京100070

出　　处：《信息安全研究》2025年第2期100-106,共7页Journal of Information Security Research

基　　金：上海市2023年度“科技创新行动计划”区块链关键技术攻关专项项目(23511101400);北京电子科技学院-北京隐算科技有限公司合作横向项目(20230008H0113);中央高校基本科研业务费资金项目(20230035Z0114)。

摘　　要：同态加密方案的比较运算是深度学习等多种应用中常见的操作之一.已有研究专注于同态比较运算,以有效评估同态加密方案.在仅支持加法和乘法运算的同态加密环境中,对数据执行比较操作一直是具有挑战性的非算术任务.对之前(2023 CNS)的动态多项式比较方法进行改进,即多项式波动范围能够落在(-2,2),找到全新的方程组求解动态多项式.同时利用有限3次和5次多项式构建新的复合多项式,以更加精确和高效地逼近符号函数.分析该近似方法的深度消耗和计算复杂性方面的最优性,在平摊运行时间内(对于ε=2^(-α),α=20)需要0.69 ms,相比之前(2023 CNS)最优方法减少了约32%的运行时间.Fully homomorphic encryption extends encryption to computations,allowing ciphertext processing without decryption.Comparative operations,crucial in applications like deep learning,pose a challenge in homomorphic encryption environments restricted to addition and multiplication.Feng et al.(CNS 2023)proposed a comparison method using dynamic polynomial combinations.This paper enhances dynamic polynomial,allowing polynomial fluctuations within(-2,2).It introduces a novel equation system for solving dynamic polynomials and utilizes finite third and fifth-degree polynomials to construct more precise composite polynomials for approximating the sign function.It analyzes the method’s optimality in depth consumption and computational complexity,achieving a 32%reduction in runtime compared to the optimal method in a previous study(CNS 2023).The homomorphic comparison algorithm in this paper,forε=2^(-20),α=20 requires only 0.69 ms in amortized runtime.

关 键 词：全同态加密 同态比较 符号函数 动态多项式 深度消耗 

分 类 号：TP309.2[自动化与计算机技术—计算机系统结构]