Collaborative Research: CT-ISG: Efficient Cryptography Based on Lattices

合作研究：CT-ISG：基于格的高效密码学

• 批准号: 1042585
• 负责人: Chris Peikert
• 金额: $ 8.21万
• 依托单位: Georgia Tech Research Corporation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-02-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1042585&HistoricalAwards=false
• 关键词: Collaborative; Research; CT; ISG; Efficient

Only two number-theoretic assumptions --- hardness of factoring and ofcomputing discrete logarithms --- underlie essentially all public-keycryptosystems in widespread use today. For lower-level primitivessuch as hash functions, random number generators, and stream ciphers,the situation is even worse: existing provably-secure constructionsare too inefficient to compete with practical alternatives such asSHA-1 or AES, and so the primitives in use today have no rigorousjustification for their security. This research will investigate new classes of computationalassumptions based on lattices. Based on these assumptions, theinvestigators will seek to design cryptographic primitives that areboth provably secure and comparably efficient to existing, deployedschemes. The research will explore the use of lattices to constructbasic cryptographic primitives, including hash functions, pseudorandomgenerators, shared-key authentication protocols, public-key encryptionschemes (including those secure against chosen-ciphertext attacks),and digital signatures. The educational component of this work willfocus on educating graduate students as well as developing introductory-level surveys of lattice-based cryptography.

只有两个数论假设——因式分解的难度和计算离散对数的难度——基本上构成了当今广泛使用的所有公钥密码系统的基础。 对于哈希函数、随机数生成器和流密码等较低级别的原语，情况甚至更糟：现有的可证明安全的结构效率太低，无法与 SHA-1 或 AES 等实际替代方案竞争，因此当今使用的原语已经没有严格的理由来保证它们的安全。这项研究将研究基于格的新型计算假设。 基于这些假设，研究人员将寻求设计既可证明安全又与现有部署方案相当有效的加密原语。 该研究将探索使用格来构建基本的密码原语，包括散列函数、伪随机生成器、共享密钥身份验证协议、公钥加密方案（包括针对选择密文攻击的安全方案）和数字签名。 这项工作的教育部分将侧重于教育研究生以及开发基于格的密码学的入门级调查。