标题： 嵌入式系统中后量子密码学的复杂性及其优化策略 显示英文标题

标题： Complexity of Post-Quantum Cryptography in Embedded Systems and Its Optimization Strategies

摘要： 随着量子计算的快速发展，传统的密码方案如 Rivest-Shamir-Adleman (RSA) 和椭圆曲线密码学 (ECC) 正变得脆弱，亟需开发抗量子算法。 国家标准与技术研究院 (NIST) 已启动后量子密码 (PQC) 算法的标准过程，一些候选算法如 CRYSTALS-Kyber 和 McEliece 已进入最后阶段。 本文首先对嵌入式系统中的后量子密码 (PQC) 硬件复杂性进行了全面分析，并根据其底层数学问题将 PQC 算法分类为：基于格的、基于码的、基于哈希的和多变量/同源性的方案。 每个家族呈现出不同的计算、内存和能量特性，使其适用于不同的用例。 为了解决这些挑战，本文讨论了优化策略，如流水线、并行化和高层次综合 (HLS)，可以提高 PQC 实现的性能和能效。 最后，对 CRYSTALS-Kyber 和 McEliece 进行了详细的复杂性分析，比较了它们在密钥生成、加密和解密过程中的计算复杂性。 显示英文摘要

摘要： With the rapid advancements in quantum computing, traditional cryptographic schemes like Rivest-Shamir-Adleman (RSA) and elliptic curve cryptography (ECC) are becoming vulnerable, necessitating the development of quantum-resistant algorithms. The National Institute of Standards and Technology (NIST) has initiated a standardization process for PQC algorithms, and several candidates, including CRYSTALS-Kyber and McEliece, have reached the final stages. This paper first provides a comprehensive analysis of the hardware complexity of post-quantum cryptography (PQC) in embedded systems, categorizing PQC algorithms into families based on their underlying mathematical problems: lattice-based, code-based, hash-based and multivariate / isogeny-based schemes. Each family presents distinct computational, memory, and energy profiles, making them suitable for different use cases. To address these challenges, this paper discusses optimization strategies such as pipelining, parallelization, and high-level synthesis (HLS), which can improve the performance and energy efficiency of PQC implementations. Finally, a detailed complexity analysis of CRYSTALS-Kyber and McEliece, comparing their key generation, encryption, and decryption processes in terms of computational complexity, has been conducted.