助记词24个单词比12个单词对比、转换、安全性分析

我们从密码学角度来聊聊助记词。

随着区块链钱包的发展和分层确定性（HD）钱包技术的普及，越来越多的用户开始熟悉了一个叫“助记词”的概念，很多人都已经习惯了从一开始使用一个钱包的时候，就先抄好单词认真保管，并且他们对于助记词的重要性也有了很深刻的理解。

说到助记词，有人可能会问了，为什么有些钱包是12个单词，另一些则是24个单词的助记词呢？是不是单词越多就越安全呢？

其实，与大部分人的直觉相反，从密码学的角度上讲，12单词的安全强度和24个单词是一样的，12个单词已经足够安全，增加单词数并不能提高安全级别。

虽然按照比特币BIP32/44/39规范，从 2048个单词词库中选择24个助记词的概率空间>2^256，而选择 12 个助记词的概率空间>2^128，从概率空间上看起来24个助记词的安全强度好像是要高很多，但本文将从密码学的角度给你澄清这一事实，即“12个助记词和24个助记词的密码学安全强度是一样的”。

首先我们需要理解一个很著名的数学理论，叫“生日悖论”（Birthday Paradox）。

问大家一个问题，假设一个班级里有 23 个人，问这个班里有两个生日相同的人的概率有多大？直觉上，大家可能会觉得概率很低，几乎不可能，一年有 365 天呢，两个人同一天生的概率得是多小啊。但数学往往就是反直觉的，其真实概率要大于 50%，如果是 30 个人的班级，概率则会大于 70%， 60 个人则大于 99% ，也就是几乎肯定有两个人生日相同，你敢信不？

这就是著名的“生日悖论”

生日悖论这一简单的概率理论对于密码学的影响是巨大的，因为基于这一理论产生了一种名为“生日攻击”的密码学攻击手段，基于这一攻击手段，所有的哈希函数（Hash）的密码学安全强度都会降低到其概率空间位数的1/2，即 2^n 概率空间的密码学安全强度为 2^(n/2)，如果是 2^256，则其安全强度为 2^128。

好了，在进一步讲述生日攻击之前，我们还要做点科普，学习几个密码学基本概念：

• 原像攻击：我们都知道哈希函数是不可逆的，y=hash(x)，知道y，我们是无法得到x的。如果有一种攻击方式能使得您得到x，那这种攻击方式就叫做原像攻击；
• 次原像攻击：如果有一种攻击方式能让你找到另一个x’，使得 hash(x’) 也等于 y，即y=hash(x)=hash(x’)，这种找到了另一个x’的攻击方式叫做次原像攻击；
• 碰撞攻击：碰撞攻击的意思是，虽然我们找不到原像，也找不到次原像，但通过一定范围内的计算，能够找到一对儿碰撞hash(z)=hash(z’)，就像虽然一年有365天，但每23个人就有50%的概率出现一次生日的碰撞，这使得我们不需要遍历365次，而只需随机抽取23个数就有50%的可能性找到一对儿碰撞，这就是碰撞攻击；

对原像攻击、次原像攻击和碰撞攻击有了基本的理解了之后，您就应该能明白，原像或次原像攻击都很难，因为几乎要遍历整个概率空间，如果算法没有漏洞的话，对于 2^256 的概率空间，您就需要遍历几乎 2^256 次才有希望找到一个原像或者次原像。而对于碰撞攻击来说，您只需要遍历 2^128 次，就能找到一对儿碰撞。

那对于密码学签名的碰撞攻击又该如何进行呢？

我们假设你要对一个消息m做密码学签名，攻击者知道m是正确的消息，并且准备了一份伪造的消息m’，毫无疑问，hash(m)<>hash(m’)，拿着m’是骗不了你的。

现在，攻击者准备了大量的稍做修改的m，又准备了大量的稍做修改的m’，这里所提到的“稍作修改”并不影响m的正确性和m’的伪造性。

然后，攻击者再从大量的m和大量的m’中找到一对儿hash(m)=hash(m’)，其难度是2(n/2)，也就是说，对于2256的概率空间，攻击者需要准备2128份正确消息m和2128份伪造消息m’，从中就能找到一对儿碰撞hash(m)=hash(m’)。

最后，攻击者拿碰撞到的m让你做密码学签名，并将m替换为m’，攻击成功。

好了，现在大家应该基本上理解了生日悖论和生日攻击的基本原理了，对于密码学货币来说，2256的概率空间其密码学安全强度为2128，12个单词的助记词的概率空间也是2^128，增加助记词的概率空间并不能提高密码学安全强度，对于钱包助记词来说，12个单词和24个单词一样安全的。

24个助记词更安全

理论上 24 个助记词的更难以破解，但是实际使用中无论 12 个还是 24 个都是安全。

12 个助记词的概率空间 > 2^128,换成数字就是: 340282366920938463463374607431768211456

24 个单词的概率空间 > 2^256，换成数字就是已经超出计算机范围了，2 的 256 次方也就是 8 个 2^32 次方相乘。

2^256 = 2^32 * 2^32 * 2^32 * 2^32 * 2^32 * 2^32 * 2^32 * 2^32

精确计算现在计算机还做不到，我们一般采取估算：2 的 32 次方约等于 40 亿。40 亿连续相乘 8 次。

40 亿 * 40 亿 * 40 亿 * 40 亿 * 40 亿 * 40 亿 * 40 亿 * 40 亿

最终的数是:1.1579208923732e+77，如果说破解 2^128 是在地球中寻找一粒沙子，那么 2^256 就相当于在我们所认知的宇宙中寻找一粒沙子。

从密码学上来说肯定是单词越多越安全，因为更多的数字拥有更多的排列组合。24 个单词的排列组合是完全碾压 12 个单词组合的，完全不在一个数量级上。但是从实际角度出发，到这个量级的概率，加密本身已经不存在安全问题了，无论 12 个，还是 24 个，或者 240 个，你脑袋都记不住，只可能写下来，或者记录下来。也就是说这时候的危险是来自你助记词储存是否安全了，已经不是 12 个单词的安全问题了；

如果你的记录丢了，或者被木马病毒窃取了了，别说你是 24 个单词，你就是 240 个单词也是白搭.所以从实际场景来说，我们通常认为 12 个单词和 24 个单词安全性是一样的。考虑到未来几十年的科技发展，我更认为 24 个助记词是更让人放心的，也体现了你对钱包安全方面的态度。要搞就搞最安全的，哪怕只是理论上的更加安全。

为什么助记词钢板每个单词只给了4个字母的空位（后附完整BIP-39助记词表）

通常没买过助记词板或者初次拿到助记词板的朋友会有这样的疑问。

我们所提到的助记词，一般分为12个、18个和24个，其中，大部分软件钱包一般会生成12个助记词，而大部分硬件钱包会生成24个助记词。在使用区块链钱包的过程中，助记词是管理资产的核心，也就是说，谁拥有助记词，谁才是这个钱包账户的真正拥有者。

为了保护好这个核心部分，很多人选择使用助记词钢板，当然也有人选择记在纸上或者存在其他任何觉得保险的地方。如果你用过软件钱包或者硬件钱包，你就会发现或者应该知道如下事实：

1、所有接触到的助记词的前四位都是不同的，这也是助记词钢板只给了4个空位的最根本原因；

2、助记词的总数是有限的，根据BIP-39，这个数量是2048个，每一个单词都对应一个唯一的编号，比如Abandon是0001， Ability是0002，Able是0003，以此类推，单词表详见附件。

3、有些钱包软件在用助记词导入账户的时候，往往只需输入3个或者4个字母，就会出现几个单词的备选项，在这些备选项里，一定有你要输入的单词。

4、同一套助记词导入到不同的钱包，得到的以太坊的地址往往是相同的，但BTC的地址却不太相同。就比如用Ledger钱包生成的助记词导入到OKX WEB3钱包里面，原有的BTC资产很难直接出现在OKX钱包里面，因为所用的导出规则不同。所以如果Ledger的钱包故障了，想导出里面的资产，最稳妥的方法还是买一个新的Ledger钱包，同理换做其他品牌的硬件钱包也是一样。

5、相比于软件钱包，硬件钱包往往还有一个Passphrase的功能，就是在第24个助记词之外，你可以自定义一个助记词，然后会生成一个完全不同的账户来，也就是说，别人即使知道了你的24个助记词，因为不知道你的Passphrase，他还是拿不走你的资产。

最后，再强调一遍，千万别随便告诉别人你的助记词，谁拥有助记词，谁就拥有这个账户的管理权限。

附件：BIP-39完整版助记词表
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助记词12个单词和24个如何互转

助记词从12个单词转换为24个单词，或者从24个单词转换为12个单词，可以通过使用特定的工具或算法来实现。 例如，最近发布的开源工具"BIP39Colors"就可以实现这种转换。这个工具不仅可以将助记词转换为一组颜色，还可以实现颜色到助记词的逆转换。这意味着，通过这个工具，你可以将12个单词的助记词扩展为24个单词，或者反之，将24个单词的助记词缩减为12个单词。这种转换是基于BIP39标准进行的，该标准规定了如何从一个熵池中生成助记词，并且要求助记词必须满足一定的熵值和校验和要求，以确保它们的安全性和唯一性。