<p>BIP39 uses a dictionary of 2048 words. Each word is indexable with 11 bits (2^11).</p>

<p>The combined entropy and checksum is represented as a sequence of words from the dictionary, and therefore must have a length which is evenly divisible by 11.</p>

<p>If you take any integer N where N mod 32 = 0, then (N + N/32) mod 11 = 0.</p>

<p>So <code>ENT/32</code> simply provides the number of bits which must be used for the checksum.</p>

CC BY-SA 4.0
2020-04-21T11:25:28.067Z
2020-04-21T11:25:28.067Z
Mark H
<p>I want to create a Seed-Phrase (mnemonics) from entropy. One aspect of <code>BIP39</code>  is to create the checksum and describes it as follows (<a href="https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki" rel="nofollow noreferrer">Link BIP39</a>):</p>

<hr>

<blockquote>
  <p>The mnemonic must encode entropy in a multiple of <code>32</code> bits. With more
  entropy, security is improved but the sentence length increases. We
  refer to the initial entropy length as ENT. The allowed size of <code>ENT</code> is
  <code>128-256 bits</code> First, an initial entropy of <code>ENT</code> bits is generated. A
  checksum is generated by taking the first  <code>ENT / 32</code></p>
</blockquote>

<hr>

<p>This <a href="https://bitcoin.stackexchange.com/questions/89814/how-does-bip-39-mnemonic-work">thread</a> describes a lot of details but not why divider <code>32</code> (or I don't understand it).
I am not a cryptographer and I did not find any detailed description why the divider <code>32</code> has been chosen. My guess is entropy. But why exactly? </p>

<mnemonic-seed>
Why Entropie is divided by 32 (Seed to MNEMONICS)
0xjacobb
# Why Entropie is divided by 32 (Seed to MNEMONICS)

(Asked by: username_0 on 2020-04-21)

I want to create a Seed-Phrase (mnemonics) from entropy. One aspect of `BIP39` is to create the checksum and describes it as follows ([Link BIP39](https://github.com/bitcoin/bips/blob/master/bip-0039.mediawiki)):

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> The mnemonic must encode entropy in a multiple of `32` bits. With more
> entropy, security is improved but the sentence length increases. We
> refer to the initial entropy length as ENT. The allowed size of `ENT` is
> `128-256 bits` First, an initial entropy of `ENT` bits is generated. A
> checksum is generated by taking the first `ENT / 32`

---

This [thread](https://bitcoin.stackexchange.com/questions/89814/how-does-bip-39-mnemonic-work) describes a lot of details but not why divider `32` (or I don't understand it).
I am not a cryptographer and I did not find any detailed description why the divider `32` has been chosen. My guess is entropy. But why exactly?

**Tags:** mnemonic-seed


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## 1 answers

### Answer by username_1 on 2020-04-21. Score: 1 | Accepted answer

BIP39 uses a dictionary of 2048 words. Each word is indexable with 11 bits (2^11).

The combined entropy and checksum is represented as a sequence of words from the dictionary, and therefore must have a length which is evenly divisible by 11.

If you take any integer N where N mod 32 = 0, then (N + N/32) mod 11 = 0.

So `ENT/32` simply provides the number of bits which must be used for the checksum.


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