我們從密碼學(xué)角度來(lái)聊聊助記詞。

隨著區(qū)塊鏈錢包的發(fā)展和分層確定性（HD）錢包技術(shù)的普及，越來(lái)越多的用戶開始熟悉了一個(gè)叫“助記詞”的概念，很多人都已經(jīng)習(xí)慣了從一開始使用一個(gè)錢包的時(shí)候，就先抄好單詞認(rèn)真保管，并且他們對(duì)于助記詞的重要性也有了很深刻的理解。

說(shuō)到助記詞，有人可能會(huì)問(wèn)了，為什么有些錢包是12個(gè)單詞，另一些則是24個(gè)單詞的助記詞呢？是不是單詞越多就越安全呢？

其實(shí)，與大部分人的直覺(jué)相反，從密碼學(xué)的角度上講，12單詞的安全強(qiáng)度和24個(gè)單詞是一樣的，12個(gè)單詞已經(jīng)足夠安全，增加單詞數(shù)并不能提高安全級(jí)別。

雖然按照比特幣BIP32/44/39規(guī)范，從 2048個(gè)單詞詞庫(kù)中選擇24個(gè)助記詞的概率空間>2^256，而選擇 12 個(gè)助記詞的概率空間>2^128，從概率空間上看起來(lái)24個(gè)助記詞的安全強(qiáng)度好像是要高很多，但本文將從密碼學(xué)的角度給你澄清這一事實(shí)，即“12個(gè)助記詞和24個(gè)助記詞的密碼學(xué)安全強(qiáng)度是一樣的”。

首先我們需要理解一個(gè)很著名的數(shù)學(xué)理論，叫“生日悖論”（Birthday Paradox）。

問(wèn)大家一個(gè)問(wèn)題，假設(shè)一個(gè)班級(jí)里有 23 個(gè)人，問(wèn)這個(gè)班里有兩個(gè)生日相同的人的概率有多大？直覺(jué)上，大家可能會(huì)覺(jué)得概率很低，幾乎不可能，一年有 365 天呢，兩個(gè)人同一天生的概率得是多小啊。但數(shù)學(xué)往往就是反直覺(jué)的，其真實(shí)概率要大于 50%，如果是 30 個(gè)人的班級(jí)，概率則會(huì)大于 70%， 60 個(gè)人則大于 99% ，也就是幾乎肯定有兩個(gè)人生日相同，你敢信不？

這就是著名的“生日悖論”

生日悖論這一簡(jiǎn)單的概率理論對(duì)于密碼學(xué)的影響是巨大的，因?yàn)榛谶@一理論產(chǎn)生了一種名為“生日攻擊”的密碼學(xué)攻擊手段，基于這一攻擊手段，所有的哈希函數(shù)（Hash）的密碼學(xué)安全強(qiáng)度都會(huì)降低到其概率空間位數(shù)的1/2，即 2^n 概率空間的密碼學(xué)安全強(qiáng)度為 2^(n/2)，如果是 2^256，則其安全強(qiáng)度為 2^128。

好了，在進(jìn)一步講述生日攻擊之前，我們還要做點(diǎn)科普，學(xué)習(xí)幾個(gè)密碼學(xué)基本概念：

• 原像攻擊：我們都知道哈希函數(shù)是不可逆的，y=hash(x)，知道y，我們是無(wú)法得到x的。如果有一種攻擊方式能使得您得到x，那這種攻擊方式就叫做原像攻擊；
• 次原像攻擊：如果有一種攻擊方式能讓你找到另一個(gè)x’，使得 hash(x’) 也等于 y，即y=hash(x)=hash(x’)，這種找到了另一個(gè)x’的攻擊方式叫做次原像攻擊；
• 碰撞攻擊：碰撞攻擊的意思是，雖然我們找不到原像，也找不到次原像，但通過(guò)一定范圍內(nèi)的計(jì)算，能夠找到一對(duì)兒碰撞hash(z)=hash(z’)，就像雖然一年有365天，但每23個(gè)人就有50%的概率出現(xiàn)一次生日的碰撞，這使得我們不需要遍歷365次，而只需隨機(jī)抽取23個(gè)數(shù)就有50%的可能性找到一對(duì)兒碰撞，這就是碰撞攻擊；

對(duì)原像攻擊、次原像攻擊和碰撞攻擊有了基本的理解了之后，您就應(yīng)該能明白，原像或次原像攻擊都很難，因?yàn)閹缀跻闅v整個(gè)概率空間，如果算法沒(méi)有漏洞的話，對(duì)于 2^256 的概率空間，您就需要遍歷幾乎 2^256 次才有希望找到一個(gè)原像或者次原像。而對(duì)于碰撞攻擊來(lái)說(shuō)，您只需要遍歷 2^128 次，就能找到一對(duì)兒碰撞。

那對(duì)于密碼學(xué)簽名的碰撞攻擊又該如何進(jìn)行呢？

我們假設(shè)你要對(duì)一個(gè)消息m做密碼學(xué)簽名，攻擊者知道m(xù)是正確的消息，并且準(zhǔn)備了一份偽造的消息m’，毫無(wú)疑問(wèn)，hash(m)<>hash(m’)，拿著m’是騙不了你的。

現(xiàn)在，攻擊者準(zhǔn)備了大量的稍做修改的m，又準(zhǔn)備了大量的稍做修改的m’，這里所提到的“稍作修改”并不影響m的正確性和m’的偽造性。

然后，攻擊者再?gòu)拇罅康膍和大量的m’中找到一對(duì)兒hash(m)=hash(m’)，其難度是2(n/2)，也就是說(shuō)，對(duì)于2256的概率空間，攻擊者需要準(zhǔn)備2128份正確消息m和2128份偽造消息m’，從中就能找到一對(duì)兒碰撞hash(m)=hash(m’)。

最后，攻擊者拿碰撞到的m讓你做密碼學(xué)簽名，并將m替換為m’，攻擊成功。

好了，現(xiàn)在大家應(yīng)該基本上理解了生日悖論和生日攻擊的基本原理了，對(duì)于密碼學(xué)貨幣來(lái)說(shuō)，2256的概率空間其密碼學(xué)安全強(qiáng)度為2128，12個(gè)單詞的助記詞的概率空間也是2^128，增加助記詞的概率空間并不能提高密碼學(xué)安全強(qiáng)度，對(duì)于錢包助記詞來(lái)說(shuō)，12個(gè)單詞和24個(gè)單詞一樣安全的。

24個(gè)助記詞更安全

理論上 24 個(gè)助記詞的更難以破解，但是實(shí)際使用中無(wú)論 12 個(gè)還是 24 個(gè)都是安全。

12 個(gè)助記詞的概率空間 > 2^128,換成數(shù)字就是: 340282366920938463463374607431768211456

24 個(gè)單詞的概率空間 > 2^256，換成數(shù)字就是已經(jīng)超出計(jì)算機(jī)范圍了，2 的 256 次方也就是 8 個(gè) 2^32 次方相乘。

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

精確計(jì)算現(xiàn)在計(jì)算機(jī)還做不到，我們一般采取估算：2 的 32 次方約等于 40 億。40 億連續(xù)相乘 8 次。

40 億 * 40 億 * 40 億 * 40 億 * 40 億 * 40 億 * 40 億 * 40 億

最終的數(shù)是:1.1579208923732e+77，如果說(shuō)破解 2^128 是在地球中尋找一粒沙子，那么 2^256 就相當(dāng)于在我們所認(rèn)知的宇宙中尋找一粒沙子。

從密碼學(xué)上來(lái)說(shuō)肯定是單詞越多越安全，因?yàn)楦嗟臄?shù)字擁有更多的排列組合。24 個(gè)單詞的排列組合是完全碾壓 12 個(gè)單詞組合的，完全不在一個(gè)數(shù)量級(jí)上。但是從實(shí)際角度出發(fā)，到這個(gè)量級(jí)的概率，加密本身已經(jīng)不存在安全問(wèn)題了，無(wú)論 12 個(gè)，還是 24 個(gè)，或者 240 個(gè)，你腦袋都記不住，只可能寫下來(lái)，或者記錄下來(lái)。也就是說(shuō)這時(shí)候的危險(xiǎn)是來(lái)自你助記詞儲(chǔ)存是否安全了，已經(jīng)不是 12 個(gè)單詞的安全問(wèn)題了；

如果你的記錄丟了，或者被木馬病毒竊取了了，別說(shuō)你是 24 個(gè)單詞，你就是 240 個(gè)單詞也是白搭.所以從實(shí)際場(chǎng)景來(lái)說(shuō)，我們通常認(rèn)為 12 個(gè)單詞和 24 個(gè)單詞安全性是一樣的?？紤]到未來(lái)幾十年的科技發(fā)展，我更認(rèn)為 24 個(gè)助記詞是更讓人放心的，也體現(xiàn)了你對(duì)錢包安全方面的態(tài)度。要搞就搞最安全的，哪怕只是理論上的更加安全。

為什么助記詞鋼板每個(gè)單詞只給了4個(gè)字母的空位（后附完整BIP-39助記詞表）

通常沒(méi)買過(guò)助記詞板或者初次拿到助記詞板的朋友會(huì)有這樣的疑問(wèn)。

我們所提到的助記詞，一般分為12個(gè)、18個(gè)和24個(gè)，其中，大部分軟件錢包一般會(huì)生成12個(gè)助記詞，而大部分硬件錢包會(huì)生成24個(gè)助記詞。在使用區(qū)塊鏈錢包的過(guò)程中，助記詞是管理資產(chǎn)的核心，也就是說(shuō)，誰(shuí)擁有助記詞，誰(shuí)才是這個(gè)錢包賬戶的真正擁有者。

為了保護(hù)好這個(gè)核心部分，很多人選擇使用助記詞鋼板，當(dāng)然也有人選擇記在紙上或者存在其他任何覺(jué)得保險(xiǎn)的地方。如果你用過(guò)軟件錢包或者硬件錢包，你就會(huì)發(fā)現(xiàn)或者應(yīng)該知道如下事實(shí)：

1、所有接觸到的助記詞的前四位都是不同的，這也是助記詞鋼板只給了4個(gè)空位的最根本原因；

2、助記詞的總數(shù)是有限的，根據(jù)BIP-39，這個(gè)數(shù)量是2048個(gè)，每一個(gè)單詞都對(duì)應(yīng)一個(gè)唯一的編號(hào)，比如Abandon是0001， Ability是0002，Able是0003，以此類推，單詞表詳見附件。

3、有些錢包軟件在用助記詞導(dǎo)入賬戶的時(shí)候，往往只需輸入3個(gè)或者4個(gè)字母，就會(huì)出現(xiàn)幾個(gè)單詞的備選項(xiàng)，在這些備選項(xiàng)里，一定有你要輸入的單詞。

4、同一套助記詞導(dǎo)入到不同的錢包，得到的以太坊的地址往往是相同的，但BTC的地址卻不太相同。就比如用Ledger錢包生成的助記詞導(dǎo)入到OKX WEB3錢包里面，原有的BTC資產(chǎn)很難直接出現(xiàn)在OKX錢包里面，因?yàn)樗玫膶?dǎo)出規(guī)則不同。所以如果Ledger的錢包故障了，想導(dǎo)出里面的資產(chǎn)，最穩(wěn)妥的方法還是買一個(gè)新的Ledger錢包，同理?yè)Q做其他品牌的硬件錢包也是一樣。

5、相比于軟件錢包，硬件錢包往往還有一個(gè)Passphrase的功能，就是在第24個(gè)助記詞之外，你可以自定義一個(gè)助記詞，然后會(huì)生成一個(gè)完全不同的賬戶來(lái)，也就是說(shuō)，別人即使知道了你的24個(gè)助記詞，因?yàn)椴恢滥愕腜assphrase，他還是拿不走你的資產(chǎn)。

最后，再?gòu)?qiáng)調(diào)一遍，千萬(wàn)別隨便告訴別人你的助記詞，誰(shuí)擁有助記詞，誰(shuí)就擁有這個(gè)賬戶的管理權(quán)限。

附件：BIP-39完整版助記詞表
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There is one very good use of this list. If you have lost your recovery key, and you think you might have it on your computer or in an email somewhere, you can search your computer for these words. If you are able to find any of them, it is worth exploring the document and seeing if you might have used it to write down the other 11. These are the words that we suggest you backup with one of our seed cassette devices. This 12 word phrase or sometimes 24/25 is worth the entire value of your wallet. With a seed phrase, you can setup a new wallet and move millions of dollars in less than a minute.

助記詞12個(gè)單詞和24個(gè)如何互轉(zhuǎn)

助記詞從12個(gè)單詞轉(zhuǎn)換為24個(gè)單詞，或者從24個(gè)單詞轉(zhuǎn)換為12個(gè)單詞，可以通過(guò)使用特定的工具或算法來(lái)實(shí)現(xiàn)。 例如，最近發(fā)布的開源工具"BIP39Colors"就可以實(shí)現(xiàn)這種轉(zhuǎn)換。這個(gè)工具不僅可以將助記詞轉(zhuǎn)換為一組顏色，還可以實(shí)現(xiàn)顏色到助記詞的逆轉(zhuǎn)換。這意味著，通過(guò)這個(gè)工具，你可以將12個(gè)單詞的助記詞擴(kuò)展為24個(gè)單詞，或者反之，將24個(gè)單詞的助記詞縮減為12個(gè)單詞。這種轉(zhuǎn)換是基于BIP39標(biāo)準(zhǔn)進(jìn)行的，該標(biāo)準(zhǔn)規(guī)定了如何從一個(gè)熵池中生成助記詞，并且要求助記詞必須滿足一定的熵值和校驗(yàn)和要求，以確保它們的安全性和唯一性。

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