基于密文转换的高效通用同态加密框架

doi:10.3969/j.issn.1671-1122.2023.04.006

信息网络安全 ›› 2023, Vol. 23 ›› Issue (4): 51-60.doi: 10.3969/j.issn.1671-1122.2023.04.006

基于密文转换的高效通用同态加密框架

杜卫东¹^,², 李敏¹(), 韩益亮², 王绪安²

1.火箭军工程大学作战保障学院，西安 710025
2.武警工程大学密码工程学院，西安 710086

收稿日期:2022-12-16 出版日期:2023-04-10 发布日期:2023-04-18
通讯作者: 李敏 E-mail:proflimin@163.com
作者简介:杜卫东（1988—），男，河北，博士研究生，主要研究方向为深度学习隐私保护|李敏（1971—），女，陕西，教授，博士，主要研究方向为深度学习隐私保护、深度学习目标检测和对抗生成网络|韩益亮（1977—），男，甘肃，教授，博士，主要研究方向为公钥密码学、网络安全和深度学习隐私保护|王绪安（1981—），男，湖北，教授，博士，主要研究方向为可验证公钥加密、安全多方计算协议和网络安全。
基金资助:
国防科技创新计划自主科研项目(ZZKY20222201)

An Efficient Versatile Homomorphic Encryption Framework Based on Ciphertext Conversion Technique

DU Weidong¹^,², LI Min¹(), HAN Yiliang², WANG Xu’an²

1. College of War Support, Rocket Force University of Engineering, Xi’an 710025, China
2. College of Cryptography, Engineering University of PAP, Xi’an 710086, China

Received:2022-12-16 Online:2023-04-10 Published:2023-04-18
Contact: LI Min E-mail:proflimin@163.com

摘要/Abstract

摘要：

针对不同应用算法的具体特点设计与之匹配的同态加密方案是设计高效的具有隐私保护功能算法的关键途径。文章首先针对深度学习预测中多项式运算只需要密文-密文加法和常数-密文乘法的特点，以多项式向量空间为明文空间，设计了一个基于系数编码的RLWE同态加密方案；然后基于该方案构造了一个同时支持多项式运算和非多项式运算的通用同态加密框架，该框架可以在RLWE密文上进行多项式运算，从RLWE密文中提取出LWE密文，通过查表方法进行非多项式运算；最后利用密文转换方法将LWE密文重新打包成RLWE密文，方便后续进行多项式运算。实验结果表明，相比于通用同态加密框架PEGASUS，文章所提框架的RLWE密文消息容量提高了1倍，并且多项式运算效率也提高了1倍。而在非多项式运算中，文章所提框架不需要转换密文中消息的编码方式，重新打包过程只需要自同构运算，因此，该框架具有更高的通信效率和运算效率。

关键词: 多项式运算, 非多项式运算, 同态加密框架, 隐私保护

Abstract:

Designing homomorphic encryption schemes to match the specific characteristics of different application algorithms is a key way to design efficient algorithms with privacy-preserving features. Firstly, the article designed a coefficient encoding-based RLWE homomorphic encryption scheme for deep learning prediction in which polynomial operations require only ciphertext-ciphertext addition and constant-ciphertext multiplication, using the polynomial vector space as the plaintext space Then a general homomorphic encryption framework supporting both polynomial and non-polynomial operations was constructed based on this scheme, which can perform polynomial operations on the RLWE ciphertext, extract the LWE ciphertext from the RLWE ciphertext, and perform non-polynomial operations by the looking up method. Finally, the LWE ciphertext was repackaged into RLWE ciphertext using the ciphertext conversion method to facilitate subsequent polynomial operations. The verification experimental results show that the RLWE ciphertext message capacity of the proposed framework is increased by a factor of 1 and the polynomial operation efficiency is increased by a factor of 1 compared with the newly proposed general homomorphic encryption framework PEGASUS. Besides, it does not need to convert the encodings in the ciphertext in non-polynomial evaluations, and it can repack LWE ciphertexts by only performing automorphism operations. Thus, our framework is more efficient in communication and computation.

Key words: polynomial operations, non-polynomial operations, homomorphic encryption framework, privacy protection

中图分类号:

TP309

杜卫东, 李敏, 韩益亮, 王绪安. 基于密文转换的高效通用同态加密框架[J]. 信息网络安全, 2023, 23(4): 51-60.

DU Weidong, LI Min, HAN Yiliang, WANG Xu’an. An Efficient Versatile Homomorphic Encryption Framework Based on Ciphertext Conversion Technique[J]. Netinfo Security, 2023, 23(4): 51-60.

图/表 6

图1

表1

表2

非多项式函数计算复杂度比较

类别	消耗模数/个	旋转/次	明文-密文乘法/次	外积/次
PEGASUS	$O({{\log }_{r}}(n))$	$O(\sqrt{r}{{\log }_{r}}(n))$	$O(r{{\log }_{r}}(n))$	$O(n)$
本文框架	$0$	$0$	$0$	$O(n)$

表2

表3

重新打包过程计算复杂度比较

类别	消耗模数/个	旋转/次	明文-密文乘法/次	消息容量/个
PEGASUS	$O(1)$	$O(\sqrt{l})$	$O(l)$	$n/2$
本文框架	$0$	$O(l)$	$0$	$n$

表3

图2

图3

参考文献 21

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方法	多项式运算是否支持SIMD	非多项式运算类型	效率
本文框架	是	丰富	高
文献[10,11]方案	是	有限	高
文献[9,12]方案	否	丰富	高
文献[13]方案	是	丰富	低

基于密文转换的高效通用同态加密框架

An Efficient Versatile Homomorphic Encryption Framework Based on Ciphertext Conversion Technique

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