哈希证明系统及其在公钥加密中的应用

Provable Security is a theory that corresponds the security of cryptography schemes to hard math problems, which is widely used in the study of public key encryption. One important approach to achieve IND-CCA security is constructing framework through hash proof systems, then giving instantiations under concrete assumptions. Besides, hash proof systems are also used in constructions of lossy trapdoor functions, public key encryptions with leakage resistant security, selective opening security, related-key security and identity based encryptions..In this project we focus on the study of hash proof systems, refine properties of hash proof systems through concrete schemes, and use them to build schemes satisfying new-type security requirements. The first aim of our is to give extensions of hash proof systems through investigation of problems such as LWE, LPN. The second aim is to find conditions for mutual transformations of universal hash proof systems and extractable hash proof systems. The third aim is to build new framework from hash proof systems to match the new-type security requirements in application. This project is helpful in unifying the methods of non-interactive proof of “well-formedness” and “all-but-one” simulation technique, understanding relations between different security notions and constructing practical encryption schemes.

可证明安全理论将密码方案的安全性与底层数学问题的困难性相关联，是密码学的一个重要研究方向。实现可证明IND-CCA安全的公钥加密方案的重要方法之一是通过哈希证明系统构造加密框架，进而基于具体困难假设实例化。除此应用外，哈希证明系统在构造有损陷门函数以及满足泄露容忍安全性、选择公开安全性、相关密钥安全性等新型密码学需求的公钥加密方案和基于身份的加密方案中也有广泛应用。.本项目以哈希证明系统为研究核心，围绕公钥加密的方案构造，通过分析已有方案的安全特性，提炼哈希证明系统的结构特征。主要研究：哈希证明系统蕴含范围的扩展，使其可以在LWE，LPN等困难假设下实例化；普适哈希证明系统和可提取哈希证明系统相互转化的条件；哈希证明系统在新型密码需求中的应用三个方面。本项目的开展有助于促进公钥加密方案不同证明方法的统一，加强对公钥加密不同安全概念间关系的理解，得到现实中高效的加密方案。

本项目属理论密码学研究领域，主要研究哈希证明系统的含义及其在公钥密码中的应用。研究结果包括在经典DDH类假设和抗量子的LWE假设下满足多种安全性的公钥加密方案、基于身份的加密方案和双系统加密方案。