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From: Ethan Heilman <eth3rs@gmail.com>
Date: Sat, 21 Oct 2023 01:08:03 -0400
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To: Bitcoin Dev <bitcoin-dev@lists.linuxfoundation.org>
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Subject: [bitcoin-dev] Proposed BIP for OP_CAT
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Hi everyone,

We've posted a draft BIP to propose enabling OP_CAT as Tapscript opcode.
https://github.com/EthanHeilman/op_cat_draft/blob/main/cat.mediawiki

OP_CAT was available in early versions of Bitcoin. It was disabled as
it allowed the construction of a script whose evaluation could create
stack elements exponential in the size of the script. This is no
longer an issue in the current age as tapscript enforces a maximum
stack element size of 520 Bytes.

Thanks,
Ethan

=3D=3DAbstract=3D=3D

This BIP defines OP_CAT a new tapscript opcode which allows the
concatenation of two values on the stack. This opcode would be
activated via a soft fork by redefining the opcode OP_SUCCESS80.

When evaluated the OP_CAT instruction:
# Pops the top two values off the stack,
# concatenate the popped values together,
# and then pushes the concatenated value on the top of the stack.

OP_CAT fails if there are less than two values on the stack or if a
concatenated value would have a combined size of greater than the
maximum script element size of 520 Bytes.

=3D=3DMotivation=3D=3D
Bitcoin tapscript lacks a general purpose way of combining objects on
the stack restricting the expressiveness and power of tapscript. For
instance this prevents among many other things the ability to
construct and evaluate merkle trees and other hashed data structures
in tapscript. OP_CAT by adding a general purpose way to concatenate
stack values would overcome this limitation and greatly increase the
functionality of tapscript.

OP_CAT aims to expand the toolbox of the tapscript developer with a
simple, modular and useful opcode in the spirit of Unix[1]. To
demonstrate the usefulness of OP_CAT below we provide a non-exhaustive
list of some usecases that OP_CAT would enable:

* Tree Signatures provide a multisignature script whose size can be
logarithmic in the number of public keys and can encode spend
conditions beyond n-of-m. For instance a transaction less than 1KB in
size could support tree signatures with a thousand public keys. This
also enables generalized logical spend conditions. [2]
* Post-Quantum Lamport Signatures in Bitcoin transactions. Lamport
signatures merely requires the ability to hash and concatenate values
on the stack. [3]
* Non-equivocation contracts [4] in tapscript provide a mechanism to
punish equivocation/double spending in Bitcoin payment channels.
OP_CAT enables this by enforcing rules on the spending transaction's
nonce. The capability is a useful building block for payment channels
and other Bitcoin protocols.
* Vaults [5] which are a specialized covenant that allows a user to
block a malicious party who has compromised the user's secret key from
stealing the funds in that output. As shown in <ref>A. Poelstra, "CAT
and Schnorr Tricks II", 2021,
https://www.wpsoftware.net/andrew/blog/cat-and-schnorr-tricks-ii.html</ref>
OP_CAT is sufficent to build vaults in Bitcoin.
* Replicating CheckSigFromStack <ref> A. Poelstra, "CAT and Schnorr
Tricks I", 2021,
https://medium.com/blockstream/cat-and-schnorr-tricks-i-faf1b59bd298
</ref> which would allow the creation of simple covenants and other
advanced contracts without having to presign spending transactions,
possibly reducing complexity and the amount of data that needs to be
stored. Originally shown to work with Schnorr signatures, this result
has been extended to ECDSA signatures. [6]

The opcode OP_CAT was available in early versions of Bitcoin. However
OP_CAT was removed because it enabled the construction of a script for
which an evaluation could have memory usage exponential in the size of
the script.
For instance a script which pushed an 1 Byte value on the stack then
repeated the opcodes OP_DUP, OP_CAT 40 times would result in a stack
value whose size was greater than 1 Terabyte. This is no longer an
issue because tapscript enforces a maximum stack element size of 520
Bytes.

=3D=3DSpecification=3D=3D

Implementation
<pre>
  if (stack.size() < 2)
    return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);
  valtype vch1 =3D stacktop(-2);
  valtype vch2 =3D stacktop(-1);

  if (vch1.size() + vch2.size() > MAX_SCRIPT_ELEMENT_SIZE)
      return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);

  valtype vch3;
  vch3.reserve(vch1.size() + vch2.size());
  vch3.insert(vch3.end(), vch1.begin(), vch1.end());
  vch3.insert(vch3.end(), vch2.begin(), vch2.end());

  popstack(stack);
  popstack(stack);
  stack.push_back(vch3);
</pre>

The value of MAX_SCRIPT_ELEMENT_SIZE is 520 Bytes

=3D=3D Reference Implementation =3D=3D
[Elements](https://github.com/ElementsProject/elements/blob/master/src/scri=
pt/interpreter.cpp#L1043)

=3D=3DReferences=3D=3D

[1]: R. Pike and B. Kernighan, "Program design in the UNIX
environment", 1983,
https://harmful.cat-v.org/cat-v/unix_prog_design.pdf
[2]: P. Wuille, "Multisig on steroids using tree signatures", 2015,
https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2021-July/019233.ht=
ml
[3]: J. Rubin, "[bitcoin-dev] OP_CAT Makes Bitcoin Quantum Secure [was
CheckSigFromStack for Arithmetic Values]", 2021,
https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2021-July/019233.ht=
ml
[4]: T. Ruffing, A. Kate, D. Schr=C3=B6der, "Liar, Liar, Coins on Fire:
Penalizing Equivocation by Loss of Bitcoins", 2015,
https://citeseerx.ist.psu.edu/viewdoc/download?doi=3D10.1.1.727.6262&rep=3D=
rep1&type=3Dpdf
[5]: M. Moser, I. Eyal, and E. G. Sirer, Bitcoin Covenants,
http://fc16.ifca.ai/bitcoin/papers/MES16.pdf
[6]: R. Linus, "Covenants with CAT and ECDSA", 2023,
https://gist.github.com/RobinLinus/9a69f5552be94d13170ec79bf34d5e85#file-co=
venants_cat_ecdsa-md