格密码的设计与分析

项目名称： 格密码的设计与分析

项目编号： No.61272040

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 王鲲鹏

作者单位： 中国科学院信息工程研究所

项目金额： 60万元

中文摘要： 由于量子计算理论和技术的发展，抗量子攻击的密码学研究已受到极大重视，成为新的研究热点。量子科技的发展必然对密码学产生重大影响。格密码以能抵抗量子攻击、平均安全性可以建立在格问题最坏情况复杂度、快速的加解密速度以及可以构建全同态加密体制等优点受到了广泛的关注。本课题即是对这个趋势和发展的一个反应。 本项目主要研究基于格的密码体制的设计与分析。包括研究基于格上困难问题的公钥密码体制和基于LWE问题的公钥体制；优化和设计新型的格基规约算法；优化现有的随机格和具有特殊代数结构格上的公钥密码方案；研究已提出的基于LWE的公钥体制：包括公钥加密方案、基于身份加密方案、密钥相关消息的加密方案、抗密钥泄露加密方案、全同态加密方案和数字签名等。

中文关键词： 量子计算；格；全同态加密体制；LWE问题；格上困难问题

英文摘要： Recently, cryptologists focus on the post-quantum cryptography which become a new hotspot because of advances in quantum computation theory and technology. The development of quantum science and technology has inevitably great influence on the cryptography. Cryptographer pay wide attention to the lattice-based cryptography because of resistance of quantum attack, average-case safety can be based on lattices worst-case complexity, fast speed of encryption and decryption, building fully homomorphic encryption and so on. This project is a reaction to the trend and development. The project mainly researches the design and analysis of lattice-based cryptography including research on public key cryptosystems based on the hard problems of lattice and LWE respectively. We will optimize or design new algorithms about the lattice reduction, and optimize the public key cryptosystems based on the existing random lattices and lattices with special algebraic structure. Also we will study LWE-based public key systems proposed: including public key encryption schemes(PKE), identity-based encryption schemes(IBE), key dependent messages encryption schemes (KDM), resistance key leak encryption schemes, fully homomorphic encryption schemes(FHE) and digital signature, etc.

英文关键词： post-quantum cryptography；lattice；FHE cryptosystem；LWE problem；hard problems of lattice