新的格上基于身份的全同态加密方案

汤永利; 胡明星; 刘琨; 叶青; 闫玺玺

doi:10.11959/j.issn.1000-436x.2017098

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新的格上基于身份的全同态加密方案

学术论文 | 更新时间：2024-06-05

- 新的格上基于身份的全同态加密方案
- Novel identity-based fully homomorphic encryption scheme from lattice
- 通信学报 2017年38卷第5期页码：39-47
- 作者机构：
  
  河南理工大学计算机科学与技术学院，河南焦作 454000
- 作者简介：
  
  [ "汤永利（1972-），男，河南孟州人，博士后，河南理工大学教授、硕士生导师，主要研究方向为信息安全、密码学。" ]
  [ "胡明星（1994-），男，河南鹿邑人，河南理工大学硕士生，主要研究方向为密码学。" ]
  [ "刘琨（1978-），女，河南焦作人，河南理工大学副教授、硕士生导师，主要研究方向为信息安全、密码学。" ]
  [ "叶青（1981-），女，辽宁营口人，博士，河南理工大学讲师、硕士生导师，主要研究方向为密码学。" ]
  [ "闫玺玺（1985-），女，河南灵宝人，河南理工大学讲师、硕士生导师，主要研究方向为密码学。" ]
- 基金信息：
  
  国家自然科学基金资助项目;The National Natural Science Foundation of China(61300216);河南省科技厅基金资助项目;The Project of Science and Technology Department of Henan Province(142300410147);河南省教育厅科研项目;Foundation of Henan Educational Committee(12A520021);河南省教育厅科研项目;Foundation of Henan Educational Committee(16A520013);河南理工大学博士基金资助项目;Doctoral Fund of Henan Polytechnic University(B2014-044);河南理工大学博士基金资助项目;Research Fund for the Doctoral Program of Henan Polytechnic University(B2013-043)
- DOI：10.11959/j.issn.1000-436x.2017098
  中图分类号： TP309
- 网络出版日期：2017-05，
  
  纸质出版日期：2017-05-25
- 稿件说明：
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汤永利, 胡明星, 刘琨, 等. 新的格上基于身份的全同态加密方案[J]. 通信学报, 2017,38(5):39-47.

Yong-li TANG, Ming-xing HU, Kun LIU, et al. Novel identity-based fully homomorphic encryption scheme from lattice[J]. Journal on communications, 2017, 38(5): 39-47.
汤永利, 胡明星, 刘琨, 等. 新的格上基于身份的全同态加密方案[J]. 通信学报, 2017,38(5):39-47. DOI： 10.11959/j.issn.1000-436x.2017098.

Yong-li TANG, Ming-xing HU, Kun LIU, et al. Novel identity-based fully homomorphic encryption scheme from lattice[J]. Journal on communications, 2017, 38(5): 39-47. DOI： 10.11959/j.issn.1000-436x.2017098.

摘要

分析以往格上基于身份的全同态加密方案，指出方案效率低的根本原因在于陷门生成和原像采样过程的复杂度过高，为此提出一种新的解决方案。先将新型陷门函数与对偶容错学习（LWE，learning with errors）算法有机结合，构造一种新的格上基于身份的加密方案；再利用特征向量方法转化为格上基于身份的全同态加密方案。对比分析表明，所提方案的陷门生成复杂度显著降低，原像采样复杂度约降低为以往方案的

，SIVP 近似因子缩小为以往方案的

。在标准模型下，方案安全性归约至判定性LWE的难解性，并包含严格的安全性证明。

Abstract

The previous identity-based homomorphic encryption schemes from lattice was analyzed.That the high complexity in previous schemes was mainly caused by trapdoor generation and preimage sampling was pointed out.A new solution was proposed.A novel identity-based encryption scheme from lattice by combining new trapdoor function and dual-LWE algorithm organically was constructed

and it was transformed to an identity-based fully homomorphic encryption scheme from lattice by employing the idea of eigenvector.Comparative analysis shows that the scheme’s complexity of trapdoor generation has a significant reduction

the complexity of preimage sampling has a nearly three-fold reduction

and the SIVP approximation factor has a

times reduction.The security of the proposed scheme strictly reduces to the hardness of decisional learning with errors problem in the standard model.

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Keywords

references

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