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本文将介绍与区块链技术相关的一些重要加密主题，包括公钥加密，散列和Merkle树。
This article will cover some important cryptography topics that relate to blockchain technology including public-key cryptography, hashing, and Merkle trees.所以即使Merkle树包含了大量的块，我们仍然可以在相对较短的时间内证明成员资格。
And so even if the Merkle tree contains a very large number of blocks, we can still prove membership in a relatively short time.每个以太坊区块头不是包括一个Merkle树，而是为三种对象设计的三棵树.
Every block header in Ethereum contains not just one Merkle tree, but three 这个清单是控件的一个Merkle树，确保每个步骤都可以用哈希的证据来证明。
The manifest is a Merkle tree of controls, assuring every step is provable with just the evidence of the hash.用简单的英语，这意味着Merkle树提供了对大量数据的有效和安全的验证。
In plain English, this means Merkle trees provide for efficient and secure verification of large amounts of data.第二个Merkle树增加了区块复杂性，有些人认为它对整体系统来说是不利的。
The second Merkle tree increases complexity, which some may consider a disadvantage.Merkle树最常见和最简单的形式是二分Merkle树，其中一个桶总是由两个相邻的块或散列组成;
The most common and simple form of Merkle Vault的区块链，在Merkle树中存储交易，但它被分成分配给不同用户组的片段。
Vault's blockchain, like Bitcoin, stores transactions in a Merkle tree, but it is divided into fragments assigned to different groups of users.更准确地说，Merkle树旨在确保数据块可以从对等网络中的其他对等体接收。
To be more precise, a Merkle tree is designed to ensure blocks of data can receive from other peers in 如果你最近在Ethereum研究所社区工作，那你可能听说过一种叫做稀疏Merkle树的东西。
If you have been around the Ethereum research community lately, you might have heard of something called a sparse Merkle tree.每个块包含前一个块的加密哈希值(时间戳)和事交易数据(通常表示为Merkle树)。
Each block contains 上面提到的两个变化，重组Merkle树和UTXO证明，可能会引入一个新的部分验证操作模式。
Two of Merkle树确保在p2p网络上交换的数据块是正确的、没有受到损害的和未被修改的。
Merkle trees ensure that data blocks exchanged on p2p networks are correct, undamaged and unaltered.这篇文章将详细解释什么是稀疏的Merkle树，为什么它们很酷，以及它们目前被用来做什么。
This post will explain exactly what a sparse Merkle tree is, why they're cool, and what they're currently being used for.年，他们升级了他们的系统，采用了Merkle树，提高了效率，从而可以在一个区块内收集更多文件。
In 1992, they upgraded their system to incorporate Merkle trees that enhanced efficiency by enabling the collection of more documents on a single block.为了以一种安全的方式实现共享，Vault使用了一种众所周知的数据结构，称为二进制Merkle树。
To implement sharing in 基于散列的签名的极端低效导致区块链使用Merkle树来减少空间消耗（是的，比特币中使用的相同Merkle树）。
This extreme inefficiency of hash-based signatures led to use of 结合已被证明的工作保护下的适当复制和交易链，Merkle树可以通过协商使如交易之类的数据变的不可伪造。
Combined with a proper replication and chains of transaction blocks protected by proof-of-work, Merkle trees can make data such as transactions post-unforgeable by consensus.例如，RalphMerkle在1979年引入了哈希值二叉树(现在称为Merkle树)的概念。
Ralph Merkle树最常见和最简单的形式是如下所示的二进制Merkle树。
