Subject: Re: [bitcoindev] On (in)ability to embed data into Schnorr

From: Peter Todd <[email-masked]>
Date: Fri, 3 Oct 2025 13:24:38 +0000

On Wed, Oct 01, 2025 at 07:24:50AM -0700, waxwing/ AdamISZ wrote:
> Hi all,
> 
> https://github.com/AdamISZ/schnorr-unembeddability/
> 
> Here I'm analyzing whether the following statement is true: "if you can 
> embed data into a (P, R, s) tuple (Schnorr pubkey and signature, BIP340 
> style), without grinding or using a sidechannel to "inform" the reader, you 
> must be leaking your private key".
> 
> See the abstract for a slightly more fleshed out context.
> 
> I'm curious about the case of P, R, s published in utxos to prevent usage 
> of utxos as data. I think this answers in the half-affirmative: you can 
> only embed data by leaking the privkey so that it (can) immediately fall 
> out of the utxo set.
> 
> (To emphasize, this is different to the earlier observations (including by 
> me!) that just say it is *possible* to leak data by leaking the private 
> key; here I'm trying to prove that there is *no other way*).

You can probably use timelock encryption to ensure that the leak of the private
key only happens in the future, after the funds are recovered by the owner in a
subsequent transaction.

-- 
https://petertodd.org 'peter'[:-1]@petertodd.org

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