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

只有两个数论假设——分解的困难和计算离散对数的困难——是当今广泛使用的所有公钥密码系统的基础。对于较低级别的原语（如哈希函数、随机数生成器和流密码），情况甚至更糟：现有的可证明安全的构造效率太低，无法与asSHA-1或AES等实际替代方案竞争，因此目前使用的原语没有严格的安全性理由。本研究将探讨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加密原语，包括哈希函数、伪随机生成器、共享密钥认证协议、公钥加密方案（包括那些防止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。

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.