支持同态算术运算的数据加密方案算法研究

杨攀; 桂小林; 姚婧; 林建财; 田丰; 张学军

doi:10.11959/j.issn.1000-436x.2015019

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支持同态算术运算的数据加密方案算法研究

学术论文 | 更新时间：2024-06-05

- 支持同态算术运算的数据加密方案算法研究
- Research on algorithms of data encryption scheme that supports homomorphic arithmetical operations
- 通信学报 2015年36卷第1期页码：167-178
- 作者机构：
  
  1. 西安交通大学电子与信息工程学院，陕西西安 710049
  2. 西安交通大学陕西省计算机网络重点实验室，陕西西安 710049
- 作者简介：
  
  [ "杨攀（1987-），男，陕西歧山人，西安交通大学博士生，主要研究方向为云计算的用户数据隐私保护及同态加密技术等。" ]
  [ "桂小林（1966-），男，江西新余人，博士，西安交通大学教授、博士生导师，主要研究方向为云计算、网络与信息安全、物联网与社会网络理论等。" ]
  [ "姚婧（1987-），女，陕西西安人，西安交通大学博士生，主要研究方向为云计算安全及网络信息安全。" ]
  [ "林建财（1988-），男，福建泉州人，西安交通大学硕士生，主要研究方向为云计算安全及同态加密技术。" ]
  [ "田丰（1987-），男，陕西紫阳人，西安交通大学博士生，主要研究方向为云计算安全、基于位置的服务及位置隐私保护问题。" ]
  [ "张学军（1977-），男，宁夏中宁人，西安交通大学博士生，主要研究方向为服务计算及隐私保护。" ]
- 基金信息：
  
  国家科技重大专项基金资助项目(2012ZX03002001);高等学校博士学科点专项科研基金资助项目(20120201110013);陕西省科技攻关基金资助项目(2012K06-30);国家自然科学基金资助项目(61172090);国家自然科学基金资助项目(61472316);陕西省科技统筹创新工程基金资助项目(2013SZS16-Z01/P01/K01)
- DOI：10.11959/j.issn.1000-436x.2015019
  中图分类号： TP309
- 网络首发：2015-01，
  
  纸质出版：2015-01-25
- 稿件说明：
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杨攀, 桂小林, 姚婧, 等. 支持同态算术运算的数据加密方案算法研究[J]. 通信学报, 2015,36(1):167-178.

ANGPan Y, UIXiao-lin G, AOJing Y, et al. Research on algorithms of data encryption scheme that supports homomorphic arithmetical operations[J]. Journal on Communications, 2015, 36(1): 167-178.
杨攀, 桂小林, 姚婧, 等. 支持同态算术运算的数据加密方案算法研究[J]. 通信学报, 2015,36(1):167-178. DOI： 10.11959/j.issn.1000-436x.2015019.

ANGPan Y, UIXiao-lin G, AOJing Y, et al. Research on algorithms of data encryption scheme that supports homomorphic arithmetical operations[J]. Journal on Communications, 2015, 36(1): 167-178. DOI： 10.11959/j.issn.1000-436x.2015019.

摘要

针对在计算服务中，对用户信息加密以保护隐私时，无法对密文进行计算的问题，提出一种高效的支持密文四则算术运算的同态加密方案CESIL，包括密钥生成、加密、解密及密文运算4个算法。该方案首先借助多项式环重新定义向量的加法和乘法运算，构建多项式系数向量环；然后利用理想格在向量环上划分剩余类，建立商环及其代表元集合；最后，将整数明文映射为代表元，并用代表元所在剩余类的其他元素替换该代表元，以对明文进行加密。商环的运算特性保证CESIL方案支持对密文的加法和乘法运算。在实现CESIL方案时，利用快速傅里叶变换(FFT)算法进一步提高运算效率、减少密钥长度。理论分析及实验结果表明，CESIL是语义安全的，且相比已有的一些同态加密方案，CESIL支持更多的运算类型，拥有较高的运行效率和较小的密钥及密文长度，能更好地满足实际应用需求。

Abstract

An efficient homomorphic encryption scheme called CESIL was proposed to meet the requirements of operating on encrypted data when protecting users' privacy in computing services.CESIL included key generation algorithm

encryption algorithm

decryption algorithm and calculation algorithm.In CESIL

a polynomial coefficient vector ring was established by defining addition and multiplication using polynomial ring; by using ideal lattice

the vector ring was partitioned into many residue classes to produce a quotient ring and its representative set; the plaintext was encrypted by mapping it to a representative and replacing the representative with another element in the same residue class.The features of operations in quotient ring ensured CESIL operate on encrypted data.Furthermore

the fast Fourier transform (FFT) algorithm was used to increase the efficiency and decrease the length of key.Theoretical analysis and experimental results show that CESIL is semantically secure

and can do addition and multiplication operations on encrypted data homomorphically in a specific scope.Comparing to some existing homomorphic encryption schemes

the CESIL runs efficiently

and has shorter length in key and ciphertext.Thus

the CESIL fits the practical applications better.

关键词

Keywords

references

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