格密码技术近期研究进展

发布时间：2018-05-05 06:04

本文选题：格密码 + 基于格的零知识证明　；参考：《计算机研究与发展》2017年10期

【摘要】：格理论最初是作为一种密码分析工具被引入到密码学中的,用于分析背包密码体制、RSA密码体制等.在1997年,Ajtai和Dwork第一次构造了一个基于格的密码体制Ajtai-Dwork,随后在1998年出现了NTRU密码体制.当时基于整数分解及离散对数的公钥密码体制是主流,格密码一直没有得到足够的重视.直到2009年,Gentry基于格密码构造了首个全同态密码方案,格密码才得到了广泛的发展.2015年,Peikert在"格密码十年"一文中,对之前格密码的发展做了一个很好的总结.同在2015年,美国国家标准和技术研究院(National Institute of Standards and Technology,NIST)发布了"后量子密码报告",报告指出:由于量子计算技术的飞速发展,现有的公钥密码标准在量子计算下将不再安全.同时NIST在全球范围内展开了后量子密码算法标准的征集工作.格密码作为一类经典的抗量子密码,公认是后量子密码算法标准最有力的竞争者,近2年得到了飞速的发展,出现了许多优秀的研究成果.从基于格的零知识证明、格加密、格签名以及格密钥交换4个方面,对近2年格密码研究进行了总结,并对格密码的发展趋势进行了展望.
[Abstract]:Lattice theory was first introduced into cryptography as a cryptographic analysis tool, which is used to analyze the knapsack cryptosystem and RSA cryptosystem. In 1997, Ajtai and Dwork first constructed a lattice-based cryptosystem, Ajtai-Dwork. then NTRU cryptosystem appeared in 1998. At that time, the public key cryptosystem based on integer decomposition and discrete logarithm was the mainstream. It was not until 2009 that Gentry constructed the first fully homomorphic cryptosystem based on lattice cipher that lattice cryptography was widely developed. In 2015, Peikert made a good summary of the development of previous lattice ciphers in "Trellis Cipher decade". Also in 2015, the National Institute of Standards and Technology Institute of National Standards and Technology released the Post-Quantum Cryptography report, which points out that due to the rapid development of quantum computing technology, existing public key cryptography standards will no longer be secure under quantum computing. At the same time, NIST has launched the collection of the post-quantum cryptographic algorithm standards around the world. Lattice cryptography, as a kind of classical anti-quantum cryptography, is recognized as the most powerful competitor to the standard of post-quantum cryptography. It has been rapidly developed in recent two years, and many excellent research results have emerged. This paper summarizes the research on lattice cryptography in the last two years from the following four aspects: lattice encryption, lattice encryption, lattice signature and lattice key exchange. The development trend of lattice cryptography is also prospected.
【作者单位】：山东大学软件学院;山东大学数学学院;山东师范大学信息科学与工程学院;
【基金】：国家自然科学基金项目(61572294);国家自然科学基金重点项目(61632020) 山东大学基本科研业务费专项资金项目(2017JC019)~~
【分类号】：TN918.1

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