基于格的公钥加密方案的综述
关键词 公钥加密 后量子 格 GGH NTRU IBE
Title Summarize Public Key Cryptosystems Based on Lattices
Abstract
Publie key cryptosystems is the main teehniques for secret communications
network information security.The most common publie key cryptosystems used
at present are based on Integer Factoring Problem（IFP）and Diserete
Logarithm Problem（DLP）,which involve complex computing and not so
efficient.In addition,it has been proved that IFP and DLP can not resist
the attacks of quantum algorithms.So more effieient and more secure
cryptosystems are needed. In 1996，the seminal work of M.Ajtai presented,it
turned out to be a breakthrough in cryptographic construetions.As a
post-quantum cryptography,lattice-based publie key cryptosystems are
believed to be secure against quantum computers.Lattice-based publie key
cryptosystems have been found based on worst-case hardness,and have very
strong security proofs.What is more,Lattice-based publie key
cryptosystems are relatively more efficiently implemented, and more
simplicity.Here we describe and summarize some of the recent progress on
lattice-based cryptography,e.g.,GGH,NTRU,Lattice-Based IBE.
Keywords PKG lattice-based post-quantum GGH NTRU IBE
目录
１ 引言 1
２ 信息安全和密码学 2
2.1 信息安全及其意义 2
2.2 信息安全与密码学的联系 .. 2
2.3 密码学发展的简介 .. 3
2.4 密码体制 . 4
３ 密码学的基础数学知识.. 4
3.1 群、环、域 .. 4
3.2 最大公约数和模运算 .. 6
3.3 快速取模指数算法 . 7
4 公钥密码学. 8
4.1 对称密码体制的缺陷 8
4.2 公钥密码体制 8
4.3 RSA 公钥加密方案. 10
4.3.1 RSA 的算法描述 10
4.3.2 RSA 的安全性 .. 10
4.3.3 RSA 的可行性 .. 10
4.3.4 已知对 RSA的攻击及提高RSA 安全性的主意事项.. 11
5 格.. 11
5.1 格的基础知识 . 12
5.2 LLL格基规约.. 13
5.2.1 Gram-Schmidt正交化 .. 13
5.2.2 δ − LLL规约基 .. 15
5.2.3 LLL 格规约算法 16
5.3 最近平面算法 . 17
6 GGH公钥加密方案 18
6.1 GGH 加密方案的思想.. 18
6.2 GGH 加密方案算法的具体描述 19