方法对比

	基于格的密码学	椭圆曲线密码学	后量子密码学（Kyber）
领域	密码学	密码学	密码学
方法族	Machine learning	Machine learning	Machine learning
起源年份	1996	1985	2022
提出者	Miklós Ajtai	Neal Koblitz	NIST PQC Standardization Project
类型	public-key cryptosystem based on lattice hardness	asymmetric encryption and key agreement	post-quantum key encapsulation mechanism
开创性文献	Ajtai, M. (1996). Generating hard instances of the short basis problem. In Proceedings of the 28th Annual ACM Symposium on Theory of Computing, pp. 99-108.	Miller, V. S. (1985). Use of Elliptic Curves in Cryptography. In Proceedings of the Advances in Cryptology - CRYPTO 1985, LNCS 218, pp. 417-426.	Avanzi, R., Bos, J., Ducas, L., & Kiltz, E. (2022). CRYSTALS-Kyber algorithm specification and supporting documentation. NIST Post-Quantum Cryptography Project.
别名	lattice cryptography, post-quantum lattice cryptography	ECC, elliptic curve cryptosystem	PQC, quantum-resistant cryptography, quantum-safe
相关	3	3	3
摘要	Lattice-based cryptography is a class of cryptosystems whose security is derived from the computational hardness of lattice problems, particularly the shortest vector problem (SVP) and learning with errors (LWE). First proposed by Miklós Ajtai in 1996, lattice-based approaches have gained prominence as the leading candidates for post-quantum cryptography. Unlike RSA and ECC, which are vulnerable to quantum computers, lattice problems are believed to remain hard even against quantum algorithms.	Elliptic Curve Cryptography (ECC) is a public-key cryptosystem based on the algebraic structure of elliptic curves over finite fields. Proposed independently by Neal Koblitz and Victor Miller in 1985, ECC offers equivalent security to RSA with much smaller key sizes. Modern cryptography increasingly favors ECC for its efficiency: a 256-bit ECC key provides security comparable to a 2048-bit RSA key, making it ideal for constrained environments and high-performance systems.	Post-quantum cryptography comprises cryptographic algorithms believed to be secure against both classical and quantum computers. In 2022, NIST standardized post-quantum algorithms including ML-KEM (CRYSTALS-Kyber) for key encapsulation and ML-DSA (CRYSTALS-Dilithium) for signatures. Post-quantum cryptography is essential for systems requiring long-term confidentiality, as adversaries may record encrypted communications today and decrypt them once quantum computers become available.