Re: [bitcoindev] Signing a Bitcoin Transaction with Lamport Signatures (no changes needed)

[Xiaohui Liu <x.liu@scrypt.io>]

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Hi,

How does covenant work without OP_CAT here, assuming no size limit? Don't 
you still need OP_CAT to parse/introspect fields (e.g., input/output) of 
the spending transaction?

Regards,
sCrypt

On Tuesday, April 30, 2024 at 7:22:54 AM UTC-7 Andrew Poelstra wrote:

> On Tue, Apr 30, 2024 at 08:32:42AM -0400, Matthew Zipkin wrote:
> > > if an attacker managed to grind a 23-byte r-value at a cost of 2^72
> > computations, it would provide the attacker some advantage.
> > 
> > If we are assuming discrete log is still hard, why do we need Lamport
> > signatures at all? In a post-quantum world, finding k such that r is 21
> > bytes or less is efficient for the attacker.
> >
>
> Aside from Ethan's point that a variant of this technique is still
> secure in the case that discrete log is totally broken (or even
> partially broken...all we need is that _somebody_ is able to find the
> discrete log of the x=1 point and for them to publish this).
>
> Another reason this is useful is that if you have a Lamport signature on
> the stack which is composed of SIZE values, all of which are small
> enough to be manipulated with the numeric script opcodes, then you can
> do covenants in Script.
>
> (Sadly(?), I think none of this works in the context of the 201-opcode
> limit...and absent BitVM challenge-response tricks it's unlikely you can
> do much in the context of the 4MWu block size limit..), but IMO it's a
> pretty big deal that size limits are now the only reason that Bitcoin
> doesn't have covenants.)
>
> -- 
> Andrew Poelstra
> Director, Blockstream Research
> Email: apoelstra at wpsoftware.net
> Web: https://www.wpsoftware.net/andrew
>
> The sun is always shining in space
> -Justin Lewis-Webster
>
>

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