Why Entropie is divided by 32 (Seed to MNEMONICS)

Question

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):

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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

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This thread 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?

Answer 1

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.