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	楕円曲線暗号	格子暗号 (Lattice-Based Cryptography)	zk-STARK
分野	暗号学	暗号学	暗号学
系統	Machine learning	Machine learning	Machine learning
提唱年	1985	1996	2018
提唱者	Neal Koblitz	Miklós Ajtai	Eli Ben-Sasson
種類	asymmetric encryption and key agreement	public-key cryptosystem based on lattice hardness	transparent zero-knowledge argument of knowledge
原典	Miller, V. S. (1985). Use of Elliptic Curves in Cryptography. In Proceedings of the Advances in Cryptology - CRYPTO 1985, LNCS 218, pp. 417-426.	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.	Ben-Sasson, E., Bentov, I., Horesh, Y., & Riabzev, M. (2019). Scalable, transparent, and post-quantum secure computational integrity. In IACR Cryptology ePrint Archive, Report 2018/046.
別名	ECC, elliptic curve cryptosystem	lattice cryptography, post-quantum lattice cryptography	zk-STARK, transparent argument of knowledge, STARK
関連	3	3	3
概要	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.	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.	A zk-STARK (Zero-Knowledge Scalable Transparent Argument of Knowledge) is a cryptographic proof system allowing a prover to convince a verifier of a computation's correctness without trusted setup or revealing computational details. Introduced by Ben-Sasson and colleagues in 2018, zk-STARKs address a key limitation of zk-SNARKs: they require no preprocessing phase vulnerable to corruption. Instead, STARKs rely only on cryptographic hash functions, making them simpler, more transparent, and believed to be post-quantum secure.