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

From: Ethan Heilman <[email-masked]>
Date: Sat, 16 Nov 2024 09:55:48 -0500

I don't think it is clear how to turn this into a covenant. The bits you
are extracting using OP_SIZE are only related to the sighash via a random
function.

That said, I don't see any reason that with an unlimited number of opcodes
you can build an small script that's uses SPV to introspect into the entire
blockchains and enforce anything without having to use OP_SIZE or OP_CAT.
You could build snarks in small script so the size of the small script
would be large but constant in the size of the blockchains.

On Fri, Nov 15, 2024, 5:02 PM Xiaohui Liu <[email-masked]> wrote:

> 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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