Design and Application of Codes for Post-Quantum Cryptography

该项目旨在改进基于代码和格的公钥密码学（PKC），以获得高效和安全的后量子系统。它是基于适用于这两种类型的后量子密码系统的新编码理论的发展。我们的目标是：i)改进密钥、密文和签名的大小；Ii)增强解密过程的可靠性；以及iii)提供对算法、侧信道和故障攻击的抵抗。与传统密码学相比，基于代码和格的后量子安全系统最严重的缺点是密钥、密文和签名大小明显更大。为了使后量子系统变得实用，这些数字必须减少，同时满足国家标准与技术研究所（NIST）规定的安全级别。在这个项目中，我们将重点关注代数码和LWE/环-LWE格。我们通过诸如：密钥、密文、签名大小、码率、安全级别和对实现攻击的抵抗力等指标来估计结果的质量。我们将探索潜在的代码并开发适合于基于代码和基于晶格的后量子密码学要求的新代码结构。这个项目的核心是从理论和实现的角度来研究后量子密码学。该理论将提供比目前可能的更小的密钥大小和更大的码率（对于相同的安全级别）的新系统，并分析现有系统的算法安全性。该实现将开发方法、架构和工具，以有效地实现能够抵抗侧信道和故障攻击的基于代码和格子的受保护密码系统。这个项目的主要工具是纠错码，因为它们在基于代码和基于格的密码系统的设计中起着至关重要的作用。这包括等级-度量码、极性码、交错码和LDPC码的修改。

This project aims at improving code- and lattice-based public-key cryptography (PKC) with the goal to obtain efficient and secure post-quantum systems. It is based on the development of new coding theory suitable for these two types of post-quantum cryptosystems. Our goals are hereby: i) improving the key, ciphertext and signature sizes; ii) enhancing the reliability of the decryption process; and iii) providing resistance to algorithmic, side-channel, and fault attacks.The most severe drawback of code- and lattice-based post-quantum secure systems compared to traditional cryptography are the significantly larger key, ciphertext and signature sizes. To turn post-quantum systems practical, these numbers must be decreased while meeting the security levels specified by the National Institute of Standards and Technology (NIST).In this project, we will focus on algebraic codes and LWE/Ring-LWE lattices. We estimatethe quality of the result by metrics such as: key, ciphertext, signature sizes, together with code rates, the security level and resistance to implementation attacks. We will explore potential codes and develop new code constructions that are suitable for the requirements by both, code- and lattice-based post-quantum cryptography.Central to this project is to approach post-quantum cryptography from theory and imple-mentation point of views. The theory will provide new systems with smaller key sizes and larger code rates (for the same security level) than currently possible and analyze existing systems for their algorithmic security. The implementation will develop methods, architectures and tools to efficiently implement code- and lattice-based protected cryptosystems able to resist side-channel and fault attacks. The main tool of this project are error-correcting codes as they play a crucial role in the design of code-based and lattice-based cryptosystems. This includes, amongst others, rank-metric codes, polar codes, interleaved codes, and modifications of LDPC codes.