基于格的身份基矩阵加密方案

doi:10.3969/j.issn.1671-1122.2019.01.005

信息网络安全 ›› 2019, Vol. 19 ›› Issue (1): 34-41.doi: 10.3969/j.issn.1671-1122.2019.01.005

基于格的身份基矩阵加密方案

李明祥¹(), 王洪涛²

1.河北金融学院金融研究所,河北保定 071051
2.华北电力大学控制与计算机工程学院,河北保定 071003

收稿日期:2018-09-20 出版日期:2019-01-20 发布日期:2020-05-11
作者简介:
作者简介：李明祥(1968—),男,山东,副教授,博士,主要研究方向为公钥密码学和区块链技术;王洪涛(1983—),男,山东,讲师,博士,主要研究方向为物联网安全、信息内容安全和人工智能安全。
基金资助:
国家自然科学基金[61802124];河北省重点研发计划[16210701];河北省高等学校科学技术研究项目[ZD2017228]

Identity-based Matrix Encryption Scheme Based on Lattices

Mingxiang LI¹(), Hongtao WANG²

1. Institute of Financial Research, Hebei Finance University, Baoding Hebei 071051, China
2. School of Control and Computer Engineering, North China Electric Power University, Baoding Hebei 071003, China

Received:2018-09-20 Online:2019-01-20 Published:2020-05-11

摘要/Abstract

摘要：

基于格的密码体制是一类抗量子计算攻击的公钥密码体制。量子计算机一旦问世,将对目前广泛使用的公钥密码体制,如基于大数分解的密码体制、基于离散对数的密码体制等,造成冲击。因此基于格的密码体制近年来成为网络安全领域的研究热点。身份基加密体制简化了用户公钥的管理过程,它可应用到资源受限的环境中。目前人们已提出了许多基于格的身份基加密方案,但这些方案都是单比特加密方案。鉴于此,文章利用Peikert、Vaikuntanathan和Waters的密文包装技术,设计了一个基于格的矩阵公钥加密方案,并基于LWE问题困难假设,证明了该公钥加密方案是IND-CPA安全的。文章进而以所提出的公钥加密方案为基础,依据Gentry、Peikert和Vaikuntanathan提出的对偶加密系统,构造了一个基于格的身份基矩阵加密方案,并基于LWE问题困难假设,证明了该身份基加密方案满足IND-sID-CPA安全。

关键词: 身份基加密, 格, LWE问题, 包装

Abstract:

The lattice-based cryptosystem is a public key cryptosystem that resists quantum computing attacks. Once the quantum computer is available, it will impact on the widely used public key cryptosystems, such as integer factorization-based cryptosystems and discrete logarithm-based cryptosystems. Hence, the lattice-based cryptosystem has become a research focus in the network security field in the recent years. Identity-based encryption scheme simplifies the management of the user’s public key, and can be applied to the resource-constrained situations. At present, many identity-based encryption schemes based on lattices have been proposed. But these schemes are all single-bit encryption schemes. Consequently, this paper designs a lattice-based matrix public key encryption scheme by using Peikert, Vaikuntanathan and Waters’ ciphertext packing technique. This paper proves that the proposed public key encryption scheme is IND-CPA secure based on the LWE hardness assumption. And then, based on the proposed public key encryption scheme, this paper constructs an identity-based matrix encryption scheme based on lattices in the light of the dual cryptosystem defined by Gentry, Peikert and Vaikuntanathan. This paper proves that the proposed identity-based encryption scheme satisfies the IND-sID-CPA security based on the LWE hardness assumption.

Key words: identity-based encryption, lattice, LWE problem, packing

中图分类号:

TP309

李明祥, 王洪涛. 基于格的身份基矩阵加密方案[J]. 信息网络安全, 2019, 19(1): 34-41.

Mingxiang LI, Hongtao WANG. Identity-based Matrix Encryption Scheme Based on Lattices[J]. Netinfo Security, 2019, 19(1): 34-41.

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基于格的身份基矩阵加密方案

Identity-based Matrix Encryption Scheme Based on Lattices

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