Good morning Burak,

I have not gone through the deep dive fully yet, but I find myself confused 
about this particular claim:

> A pool transaction can be double-spent by the Ark service provider while it 
> remains in the mempool. However, in the meantime, the recipient can pay a 
> lightning invoice with their incoming zero-conf vTXOs, so it’s a footgun for 
> the service operator to double-spend in this case. 

Given that you make this claim:

> ASPs on Ark are both (1) liquidity providers, (2) blinded coinjoin 
> coordinators, and (3) Lightning service providers. ASPs main job is to create 
> rapid, blinded coinjoin sessions every five seconds, also known as pools.

As the access to Lightning is also by the (same?) ASP, it seems to me that the 
ASP will simply fail to forward the payment on the broader Lightning network 
after it has replaced the in-mempool transaction, preventing recipients from 
actually being able to rely on any received funds existing until the next pool 
transaction is confirmed.

Even if the Lightning access is somehow different from the ASP you are 
receiving funds on, one ASP cannot prove that another ASP is not its sockpuppet 
except via some expensive process (i.e. locking funds or doing proof-of-work).

Regards,
ZmnSCPxj

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