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To: Matt Bell <mappum@gmail.com>
From: ZmnSCPxj <ZmnSCPxj@protonmail.com>
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Cc: Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
Subject: Re: [bitcoin-dev] Proof-of-Stake Bitcoin Sidechains
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Good Morning Matt,

> ### ZmnSCPxj,
>
> I'm intrigued by this mechanism of using fixed R values to prevent multip=
le signatures, but how do we derive the R values in a way where they are
unique for each blockheight but still can be used to create signatures or v=
erify?

One possibility is to derive `R` using standard hierarchical derivation.
Then require that the staking pubkey be revealed to the sidechain network a=
s actually being `staking_pubkey =3D P + hash(P || parent_R) * G` (possibly=
 with some trivial protection against Taproot).
To sign for a blockheight `h`, you must use your public key `P` and the spe=
cific `R` we get from hierarchical derivation from `parent_R` and the block=
height as index.



Regards,
ZmnSCPxj