Date: Tue, 19 Jan 2021 17:57:08 +0000
To: nakagat <nakagat@gmail.com>
From: Pieter Wuille <bitcoin-dev@wuille.net>
Reply-To: Pieter Wuille <bitcoin-dev@wuille.net>
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Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] Bech32m BIP: new checksum,
	and usage for segwit address
Precedence: list

On Sunday, January 17, 2021 9:59 PM, nakagat <nakagat@gmail.com> wrote:

> I thought that BECH32M_CONST could be created from hrp and data
> instead of constants.
>
> I thought that the error position would be the same as bech32 by
> recalculating the value created from hrp and data.

So, bech32 can be written as:

* checksum =3D polymod(expand(hrp) + data) xor 1

Bech32m changes that to:

* checksum =3D polymod(expand(hrp) + data) xor 0x2bc830a3

I believe that your idea is:

* checksum =3D polymod(expand(hrp) + data) xor hash(hrp, data)

That has exactly the same error detecting capabilities as:

* checksum =3D hash(hrp, data)

The hashing makes all types of errors uniform, and it doesn't matter what o=
ther things are added to the checksum. Once you hash the data, the checksum=
 is uniformly random, and you can't make it "less random" anymore.

In this case, we *want* non-uniformity. The polymod function as a checksum =
detects some kinds of errors much better than others, and this is what we w=
ant.

Does that clarify things?

Cheers,

--
Pieter