On Thu, Oct 03, 2019 at 11:05:52AM -0400, Ethan Heilman wrote:
> To avoid derailing the NO_INPUT conversation, I have changed the
> subject to OP_CAT.
> 
> Responding to:
> """
> * `SIGHASH` flags attached to signatures are a misdesign, sadly
> retained from the original BitCoin 0.1.0 Alpha for Windows design, on
> par with:
> [..]
> * `OP_CAT` and `OP_MULT` and `OP_ADD` and friends
> [..]
> """
> 
> OP_CAT is an extremely valuable op code. I understand why it was
> removed as the situation at the time with scripts was dire. However
> most of the protocols I've wanted to build on Bitcoin run into the
> limitation that stack values can not be concatenated. For instance
> TumbleBit would have far smaller transaction sizes if OP_CAT was
> supported in Bitcoin. If it happens to me as a researcher it is
> probably holding other people back as well. If I could wave a magic
> wand and turn on one of the disabled op codes it would be OP_CAT.  Of
> course with the change that size of each concatenated value must be 64
> Bytes or less.
>

Just throwing my two cents in here - as others have noted, OP_CAT
lets you create Merkle trees (allowing e.g. log-sized accountable
threshold sigs, at least in a post-Schnorr future).

It also allows manipulating signatures - e.g. forcing the revelation
of discrete logs by requiring the user use the (1/2) point as a nonce
(this starts with 11 zero bytes, which no other computationally
accessible point does), or by requiring two sigs with the same nonce.

It also lets you do proof-of-work-like computations on hashes or
curvepoints; or enforce that EC points come from a hash and have
no known discrete log. You can also switch on hashes, something
currently impossible because of the 4-byte limitation on numeric
opcodes. I don't have specific application of these in mind but
definitely have cut off many lines of inquiry because they were
impossible.

You could build a crappy Lamport signature, though the key would
be so big that you'd never do this pre-MAST :P.


-- 
Andrew Poelstra
Director of Research, Blockstream
Email: apoelstra at wpsoftware.net
Web:   https://www.wpsoftware.net/andrew

The sun is always shining in space
    -Justin Lewis-Webster