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同态密码理论与应用进展

杨亚涛 赵阳 张卷美 黄洁润 高原

杨亚涛, 赵阳, 张卷美, 黄洁润, 高原. 同态密码理论与应用进展[J]. 电子与信息学报. doi: 10.11999/JEIT191019
引用本文: 杨亚涛, 赵阳, 张卷美, 黄洁润, 高原. 同态密码理论与应用进展[J]. 电子与信息学报. doi: 10.11999/JEIT191019
Yatao YANG, Yang ZHAO, Juanmei ZHANG, Jierun HUANG, Yuan GAO. Recent Development of Theory and Application on Homomorphic Encryption[J]. Journal of Electronics and Information Technology. doi: 10.11999/JEIT191019
Citation: Yatao YANG, Yang ZHAO, Juanmei ZHANG, Jierun HUANG, Yuan GAO. Recent Development of Theory and Application on Homomorphic Encryption[J]. Journal of Electronics and Information Technology. doi: 10.11999/JEIT191019

同态密码理论与应用进展

doi: 10.11999/JEIT191019
基金项目: “十三五”国家密码发展基金(MMJJ20170110)
详细信息
    作者简介:

    杨亚涛:男,1978年生,副教授,研究方向为信息安全、同态密码系统、密码协议和算法设计

    赵阳:男,1995年生,硕士生,研究方向为同态加密与信息安全

    张卷美:女,1963年生,副教授,研究方向为密码计算方法,同态密码

    黄洁润:女,1995年生,硕士生,研究方向为格密码与信息安全

    高原:女,1979年生,讲师,主要研究方向为信息安全与算法

    通讯作者:

    杨亚涛 yy2008@163.com

  • 中图分类号: TP309.7

Recent Development of Theory and Application on Homomorphic Encryption

Funds: The State Cryptography Development Fund of Thirteen Five-year(MMJJ20170110)
  • 摘要: 随着云计算、云存储等各类云服务的普及应用,云环境下的隐私保护问题逐渐成为业界关注的焦点,同态密码成为解决该问题的关键手段,其中,如何构造高效的全同态加密方案是近年来同态加密研究的热点之一。首先,该文介绍了同态密码的发展情况,从不同角度对同态加密方案进行了分类分析,着重描述了可验证全同态加密方案的研究进展。通过分析近年来公开的同态加密领域知识产权文献,对同态加密在理论研究和实际应用中所取得的进展进行了归纳总结。其次,对比分析了目前主流全同态加密库Helib, SEAL以及TFHE的性能。最后,梳理了同态加密技术的典型应用场景,指出了未来可能的研究与发展方向。
  • 图  1  Bootstrapping原理

    表  1  提高全同态加密效率的解决方案

    方式解决方案
    优化BootstrappingGentry09[2]:首次提出Bootstrapping
    Ducas15[12]:运行时间从6 min缩短至1 s以内
    Chillotti16[13]:运行时间从1 s以内缩短至0.1 s以内,密钥大小从1 GB减小至24 MB
    Chen18[14]:自举深度从${\log _{\rm{2}}}h + 2{\log _{\rm{2}}}t$降至${\log _{\rm{2}}}h + {\log _{\rm{2}}}t$
    BatchingSmart14[15]:构造可支持SIMD操作的FHE方案
    Castryck18[16]:提高了明文封装容量和参数优化灵活性
    无噪声FHEKipnis12[18]:基于矩阵和多项式的无噪声FHE方案MORE和PORE
    Gentry14[20]:基于完备群概念的无噪声FHE框架
    FPGA设计Shi18[24]:16×24 bits有限域FFT算法的FPGA设计
    Xie19[25]:768 kbits大整数乘法器FPGA设计
    下载: 导出CSV

    表  2  全同态加密在整数域和实数域上的研究进展

    类型解决方案
    明文空间为整数的FHEGentry10[27]:第1个基于整数的FHE方案DGHV方案
    Cheon13[28]:将批处理技术引入DGHV方案
    Nuida15[29]:将DGHV方案的明文空间从${Z_2}$扩展至${Z_Q}$
    Cheon15[31]:将LWE问题归约为AGCD问题的一个变体
    明文空间为实数的FHEJaschke16[33]:通过与2的幂迭代相乘近似将有理数表示为整数
    Dowlin17[34]:将定点小数编码为整系数多项式,但明文模随电路深度的增加呈指数增大
    Cheon17[35]:可进行浮点数近似计算的CKKS方案,但仅为层次型FHE方案
    Cheon18[36]:将文献[35]中的层次型同态加密方案扩展为全同态加密方案
    下载: 导出CSV

    表  3  可验证同态加密研究进展

    解决方案研究进展存在问题
    Johnson02[41]首次提出同态签名的概念
    Boneh11[42]首个可执行确定阶数多项式运算的同态签名方案
    Rosario13[43]形式化定义了同态消息认证的概念
    Catalano13[44]支持低次多项式运算的同态MAC方案不能同时满足简洁性和复合性
    Catalano14[46]引入了一个新的密码学原语LAEPuV
    Joo14[48]首次给出在HAE中IND-CPA和IND-CCA的定义
    Bai18[45]基于默克尔哈希树的同态认证方案复合度上有所不足
    Fiore16[50]提出多密钥同态认证(M-HS)方案可能存在不可信签名者
    Lai18[51]基于零知识证明提出了一种M-HS通用结构没有分析其认证安全性和实用性
    Alagic17[52]可验证的量子全同态加密方案
    下载: 导出CSV

    表  4  同态加密相关的知识产权聚焦的不同应用领域

    文献应用领域
    文献[59,60]硬件系统
    文献[61-64]密文检索
    文献[65-67]密文机器学习
    文献[68]安全多方计算
    文献[69,70]安全协议
    文献[71-76]其他应用
    下载: 导出CSV

    表  5  Test_Timing效率测试结果(us)

    m密钥生成加密解密同态加同态乘
    4051317037678640399726701
    4369571082804151739831477
    485966413810497755419341354
    下载: 导出CSV

    表  6  SEAL中BFV方案效率测试

    PolyCoeffPlain加密(us)解密(us)同态加(us)同态乘(us)重线性化(us)
    4096109786433934643230631439019263711
    819221878643326772711289810741510281319876
    16384438786433884862439232434161461311846517
    下载: 导出CSV

    表  7  SEAL中CKKS方案效率测试

    PolyCoeff加密(us)解密(us)同态加(us)同态乘(us)重线性化(us)
    40961098755733593091247663459
    819221827421512748107147599314501
    163844389648215146543172002481850888
    下载: 导出CSV
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    • 收稿日期:  2019-12-23
    • 修回日期:  2020-06-09
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