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
李晓东 1周苏雅 1赵炽野 1李慧 1袁文博 1张健毅1
作者信息
- 1. 北京电子科技学院网络空间安全系 北京 100070
- 折叠
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.
Abstract
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,for ε=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Key words
fully homomorphic encryption/homomorphic comparison/sign function/dynamic polynomial/depth consumption引用本文复制引用
出版年
2025
国家科技期刊平台
NSTL
万方数据