公钥密码的后量子可证安全理论研究

With the rapid development of quantum computers, the need for post-quantum cryptosystems is extremely urgent. Currently the design of post-quantum public key cryptosystems turns into a very active research area. Meanwhile, the provable security theory, which is an important guideline on the design and parameter setting of public key cryptosystem, also has been extended into the post-quantum era naturally. .The project concerns a systematic research of the post-quantum provable security theory of public key cryptosystems. Firstly, in the aspect of basic primitives, we mainly focus on the existence of several post-quantum one-way trapdoor primitives, and the definition and construction of universal computational extractor. Secondly, in the aspect of security models, we mainly study the security proof of public-key encryption schemes and key exchange protocols in the quantum random oracle model. Thirdly, in the aspect of security notions, we mainly consider the definition of several strong security notions in the quantum setting for public-key encryption and signature schemes, and the construction of corresponding cryptosystems, such as the related-key security and the leakage resilience. The research of the project will promote the development of the post-quantum provable security of public key cryptosystems, aid a reasonable security evaluation of post-quantum public key cryptosystems, and offer references for the parameter setting during their deployment, thus is of important theoretical significance and practical value.

随着量子计算机研制的迅速进展，对后量子密码的需求日益迫切。后量子密码方案的设计与分析已成为十分活跃的研究领域，随之而来的是公钥密码方案的设计以及参数选取的重要指导思想——可证安全理论——也自然地被扩展到后量子时代。.本项目将系统地研究公钥密码的后量子可证安全理论。第一，在基础原语方面，主要关注后量子单向陷门原语的存在性，以及通用计算提取器在量子环境中的定义和构造。第二，在安全模型方面，主要研究公钥加密和密钥交换在量子RO模型中的安全性证明。第三，在安全概念方面，主要考虑加密和签名的相关密钥安全和泄漏容忍等强安全概念在量子环境中的定义以及对应的方案构造。本项目的研究将推进公钥密码后量子可证安全理论的发展，为后量子公钥密码方案的安全性评估和具体实现时的参数选取提供指导，具有重要的理论意义和应用价值。

经典可证安全理论不足以刻画量子环境下公钥密码的安全性，本项目从基础原语、安全模型、安全概念及方案构造等方面系统研究量子环境中公钥密码的可证安全理论，为后量子公钥密码的设计与安全性评估提供理论支撑。.我们取得了如下重要结果: (1)证明了原始的FO变换和OAEP加密方案在量子RO模型下是IND-CCA安全性的。完善了量子RO模型下KEM的IND-qCCA安全性定义，并构造了在量子RO模型下IND-qCCA安全性的FO-KEM方案，它比已有的隐式FO-KEM简洁。（2）构造了多挑战环境下高效的具有紧致归约的CCA安全的IBE方案、具有紧致归约的SO-CCA安全的IBE方案、具有紧凑参数的SO-CCA安全的PKE和确定性IBE方案、CK+安全的认证密钥交换方案。（3）在实用型后量子公钥密码方面，设计了基于同源的认证密钥交换算法SIAKE和基于格的公钥加密算法LAC.PKE，并对多个典型的基于LWE的加密方案的实际安全性给出了较好的评估结果。.本项目中我们共发表12篇有关安全性概念和方案的期刊/会议论文，以及5篇有关椭圆曲线快速计算、离散对数的期刊/会议论文。