A Fully Homomorphic Encryption Scheme Based on NTRU

LI Zi-chen; ZHANG Juan-mei; YANG Ya-tao; ZHANG Feng-juan

doi:10.3969/j.issn.0372-2112.2018.04.023

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A Fully Homomorphic Encryption Scheme Based on NTRU

更新时间：2025-07-16

- A Fully Homomorphic Encryption Scheme Based on NTRU
- Acta Electronica Sinica Vol. 46, Issue 4, Pages: 938-944(2018)
- 作者机构：
  
  1. 北京印刷学院,北京,102600
  2. 北京电子科技学院,北京,100070
  3. 西安电子科技大学通信工程学院,陕西,西安,710071
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2018.04.023
  CLC： TP309.7
- Published Online：25 April 2018，
  
  Published：2018
- 稿件说明：
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LI Zi-chen, ZHANG Juan-mei, YANG Ya-tao, et al. A Fully Homomorphic Encryption Scheme Based on NTRU[J]. Acta Electronica Sinica, 2018, 46(4): 938-944.
DOI：

LI Zi-chen, ZHANG Juan-mei, YANG Ya-tao, et al. A Fully Homomorphic Encryption Scheme Based on NTRU[J]. Acta Electronica Sinica, 2018, 46(4): 938-944. DOI： 10.3969/j.issn.0372-2112.2018.04.023.

摘要

本文提出一种基于公钥密码体制（Number Theory Research Unit，NTRU）选择明文攻击（Chosen Plaintext Attack，CPA）可证明安全的全同态加密方案.首先，对NTRU的密钥生成算法进行改进，通过格上的高斯抽象算法生成密钥对，避免了有效的格攻击，同时，没有改变密钥的分布.然后，基于改进的NTRU加密算法，利用Flattening技术，构造了一个全同态加密体制，并在标准模型下证明方案是选择明文攻击不可区分性IND-CPA安全的.

Abstract

A fully homomorphic encrgption scheme was presented based on number theory research unit (NTRU)

which is provable security about indistinguishable chosen plaintext attack (IND-CPA). Firstly

to avoid the effective lattice attacks

we modified the key generation algorithm of NTRU by Gaussian abstraction algorithm of lattices

and the distribution of the key is not changed. Then

we proposed a new homomorphic encryption scheme based on the improved NTRU encryption algorithm by using the Flattening technique. Its IND-CPA security was proved strictly under the standard model.

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