I think it is possible to get past the 201 op code limit doing it in tapscript. I don't think it would have the same quantum security but could maybe be a path to covenants. My understanding is that you're using the OP_SIZE of the sig to basically decide to verify if the bit is a 0 or a 1, then do that verification. You could do the same trick with schnorr sigs, just for 0 bits don't include the sighash_all flag, and for 1 bits include it. This would allow you to get around all the resource limits that taproot lifted. This still should be safe since the the signature commits to if it is SIGHASH_DEFAULT vs SIGHASH_ALL. I am not sure if this will enable very complex things or just let you do it on 1 bit of information in tapscript.

On Tuesday, April 30, 2024 at 9:22:54 AM UTC-5 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