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

只有两个数论假设- 对于较低级别的可证明性，如散列函数、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SHA-1或AES等实际替代方案竞争，因此今天使用的原语没有严格的安全性证明。这项研究将调查新的类computationalassumptions基于格。 基于这些假设，研究人员将寻求设计既可证明安全又对现有部署方案有效的密码原语。 该研究将探索使用格来构造基本的密码原语，包括散列函数，伪随机数生成器，共享密钥认证协议，公钥加密方案（包括那些可以抵御选择密文攻击的方案）和数字签名。 这项工作的教育部分将集中在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.