量子计算环境下的格公钥密码体制

项目名称： 量子计算环境下的格公钥密码体制

项目编号： No.61472309

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 胡予濮

作者单位： 西安电子科技大学

项目金额： 84万元

中文摘要： 格公钥密码的普适价值早已被认识。本项目将研究格公钥密码的两个紧迫的硬课题：（1）格上STFS（simpler, tighter, faster, and smaller）陷门；（2）格公钥密码在量子计算环境下的安全性。 我们将进一步发掘基于格的陷门机理，探索更巧妙的密码原型，研究在可证明安全前提下显著降低陷门的空间尺寸和简单的陷门生成方法。我们将研究格上STFS陷门在传统计算环境下的安全性，包括安全归约和安全证明，并研究陷门的隐藏弱点，发掘新型攻击。我们将探讨格上STFS陷门应用于分级/广播/同态/群组的可能性、安全性和时空性能，并研究标准模型下的各种应用方案。我们将研究格上交互式密码协议的量子安全性证明，以及量子随机预言机模型下的格公钥密码安全性分析。我们将致力于寻找新的基于格的量子安全密码应用。希望借助本课题能在格公钥密码理论与关键技术上做出我们突破性的工作。

中文关键词： 格公钥密码；量子计算；格基陷门

英文摘要： It has been realized for a long time that lattice-based cryptography is of great value.This project is devoted to studying two critical problems in lattice-based cryptography. (1) Trapdoors for lattices: simpler, tighter, faster, and smaller (STFS-trapdoors for short). (2) Security of lattice-based system in quantum computation setting. The mechanism of generating trapdoors and more ingenious cryptographic primitives for lattices will be explored so that we would have simpler ways for generating trapdoors with smaller size while keeping schemes provable secure. The security of STFS-trapdoors for lattices in conventional computation setting is also our focus, which includes security reduction, security proof, potential weakness of trapdoors, and novel attack methods. We will discuss the probability, security and space-time performance of using STFS-trapdoors to develop hierarchical/ broadcast/ homomorphic/ group lattice-based constructions while studying practical application schemes mentioned above in the standard model. We will focus on the secure proof of interactive lattice-based cryptographic protocol in quantum computation setting and the cryptoanalysis on lattice-based system available in the quantum-accessible random oracle model. Finding novel lattice-based cryptographic applications with the provable security in quantum computation setting is another aim. We are quite confident that, with the help of the Nation Science Foundation Project, we would do some outstanding work or make breakthroughs on cryptographic theory and key technology for lattice-based cryptography.

英文关键词： Lattice-based Cryptography;Quantum Computation;Trapdoors for Lattices