# Merkle 树与认证数据结构：包含证明、一致性证明与构造陷阱

DevFeed: [Merkle 树与认证数据结构：包含证明、一致性证明与构造陷阱](<https://devfeed.tech/articles/merkle-60347.md>)

Original publisher: [Read original article](<https://quant67.com/post/algorithms/22-merkle-auth-ds/merkle-auth-ds.html>)

Author: Liao Tonglang

Published: 2026-04-24T00:00:00Z

Content type: tutorial

Language: zh

Sources: [土法炼钢 - 系统与基础设施](<https://devfeed.tech/sources/source-4.md>)

Topics: [Data structures](<https://devfeed.tech/topics/data-structures.md>), [Cryptography](<https://devfeed.tech/topics/cryptography.md>), [Certificate Transparency](<https://devfeed.tech/topics/certificate-transparency.md>), [Security](<https://devfeed.tech/topics/security.md>), [systems](<https://devfeed.tech/topics/systems.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [authenticated-data-structure](<https://devfeed.tech/tags/authenticated-data-structure.md>), [certificate-transparency](<https://devfeed.tech/tags/certificate-transparency.md>), [consistency-proof](<https://devfeed.tech/tags/consistency-proof.md>), [crypto](<https://devfeed.tech/tags/crypto.md>), [cryptography](<https://devfeed.tech/tags/cryptography.md>), [cve-2012-2459](<https://devfeed.tech/tags/cve-2012-2459.md>), [data-structure](<https://devfeed.tech/tags/data-structure.md>), [git](<https://devfeed.tech/tags/git.md>), [merkle-patricia-trie](<https://devfeed.tech/tags/merkle-patricia-trie.md>), [merkle-tree](<https://devfeed.tech/tags/merkle-tree.md>), [paper](<https://devfeed.tech/tags/paper.md>), [rfc9162](<https://devfeed.tech/tags/rfc9162.md>), [security](<https://devfeed.tech/tags/security.md>), [sparse-merkle-tree](<https://devfeed.tech/tags/sparse-merkle-tree.md>), [verkle-tree](<https://devfeed.tech/tags/verkle-tree.md>)

## AI overview

A technical tutorial on Merkle trees and authenticated data structures. It explains tree hashing, inclusion and consistency proofs, verification algorithms, historical development, construction flaws including Bitcoin's CVE-2012-2459, proof-size measurements for branching tries, Merkle DAGs, Verkle trees, and unresolved Certificate Transparency issues.

## Source excerpt

按 RFC 9162 实现 Merkle 树哈希、包含证明与一致性证明并用公开向量验证，复现域分离缺失与 Bitcoin CVE-2012-2459 两类缺陷，实测 k 叉 trie 证明大小，梳理从 Merkle 1979 到 Verkle 与二叉状态树之争。