BIP: 420
  Layer: Consensus (soft fork)
  Title: OP_CAT
  Author: Ethan Heilman <ethan.r.heilman@gmail.com>
          Armin Sabouri <arminsdev@gmail.com>
  Comments-URI: https://github.com/bitcoin/bips/wiki/Comments:BIP-op-cat
  Status: Draft
  Type: Standards Track
  Created: 2023-10-21
  License: BSD-3-Clause

Table of Contents Abstract Copyright Specification Motivation Rationale Backwards Compatibility Reference implementation References Acknowledgements

Abstract

This BIP introduces OP_CAT as a tapscript opcode which allows the concatenation of two values on the stack. OP_CAT would be activated via a soft fork by redefining the opcode OP_SUCCESS126 (126 in decimal and 0x7e in hexadecimal). This is the same opcode value used by the original OP_CAT.

Copyright

This document is licensed under the 3-clause BSD license.

Specification

When evaluated the OP_CAT instruction:

1. Pops the top two values off the stack,
2. concatenates the popped values together in stack order,
3. and then pushes the concatenated value on the top of the stack.

Given the stack [x1, x2], where x2 is at the top of the stack, OP_CAT will push x1 || x2 onto the stack. By || we denote concatenation. OP_CAT fails if there are fewer than two values on the stack or if a concatenated value would have a combined size greater than the maximum script element size of 520 bytes.

This opcode would be activated via a soft fork by redefining the tapscript opcode OP_SUCCESS126 (126 in decimal and 0x7e in hexadecimal) to OP_CAT.

Motivation

Bitcoin tapscript lacks a general purpose way of combining objects on the stack restricting the expressiveness and power of tapscript. 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:

• Bitstream, a protocol for the atomic swap (fair exchange) of bitcoins for decryption keys, that enables decentralized file hosting systems paid in Bitcoin. While such swaps are currently possible on Bitcoin without OP_CAT they require the use of complex and computationally expensive Verifiable Computation cryptographic techniques. OP_CAT would remove this requirement on Verifiable Computation, making such protocols far more practical to build in Bitcoin. ^[2]
• 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. ^[3]
• Post-Quantum Lamport signatures in Bitcoin transactions. Lamport signatures merely require the ability to hash and concatenate values on the stack. ^[4] It is an open question if the quantum resistance of Lamport signatures can be preserved when used in a taproot output.
• Non-equivocation contracts ^[5] 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 ^[6] 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 ^[7] OP_CAT is sufficient to build vaults in Bitcoin.
• Replicating CheckSigFromStack ^[8] 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 ^[9].

The opcode OP_CAT was available in early versions of Bitcoin. However, OP_CAT was removed because it enabled the construction of a script whose evaluation could have memory usage exponential in the size of the script. For example, a script that pushed a 1-byte value on the stack and 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.

Rationale

Our decision to reenable OP_CAT by redefining a tapscript OP_SUCCESSx opcode to OP_CAT was motivated to leverage the tapscript softfork opcode upgrade path introduced in BIP342.

We specifically choose to use OP_SUCCESS126 rather than another OP_SUCCESSx as OP_SUCCESS126 uses the same opcode value (126 in decimal and 0x7e in hexadecimal) that was used for OP_CAT prior to it being disabled in Bitcoin. This removes a potential source of confusion that would exist if we had a opcode value different from the one used in the original OP_CAT opcode.

While the OP_SUCCESSx opcode upgrade path could enable us to increase the stack element size while reenabling OP_CAT, we wanted to separate the decision to change the stack element size limit from the decision to reenable OP_CAT. This BIP takes no position in favor or against increasing the stack element size limit.

Backwards Compatibility

OP_CAT usage in an non-tapscript script will continue to trigger the SCRIPT_ERR_DISABLED_OPCODE. The only change would be to OP_CAT usage in tapscript. This change to tapscript would be activated a soft fork that redefines an OP_SUCCESSx opcode (OP_SUCCESS126) to OP_CAT.

Reference implementation

case OP_CAT:
{
  if (stack.size() < 2)
    return set_error(serror, SCRIPT_ERR_INVALID_STACK_OPERATION);
  valtype& vch1 = stacktop(-2);
  valtype& vch2 = stacktop(-1);
  if (vch1.size() + vch2.size() > MAX_SCRIPT_ELEMENT_SIZE)
    return set_error(serror, SCRIPT_ERR_PUSH_SIZE);
  vch1.insert(vch1.end(), vch2.begin(), vch2.end());
  stack.pop_back();
}
break;

The value of MAX_SCRIPT_ELEMENT_SIZE is 520.

This implementation is inspired by the original implementation of OP_CAT as it existed in the Bitcoin codebase prior to the commit "misc changes" 4bd188c^[10] which disabled it:

case OP_CAT:
{
    // (x1 x2 -- out)
    if (stack.size() < 2)
        return false;
    valtype& vch1 = stacktop(-2);
    valtype& vch2 = stacktop(-1);
    vch1.insert(vch1.end(), vch2.begin(), vch2.end());
    stack.pop_back();
    if (stacktop(-1).size() > 5000)
        return false;
}
break;

An alternative implementation of OP_CAT can be found in Elements ^[11].

References

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. ^ R. Linus, "BitStream: Decentralized File Hosting Incentivised via Bitcoin Payments", 2023, https://robinlinus.com/bitstream.pdf
3. ^ P. Wuille, "Multisig on steroids using tree signatures", 2015, https://blog.blockstream.com/en-treesignatures/
4. ^ J. Rubin, "[bitcoin-dev] OP_CAT Makes Bitcoin Quantum Secure [was]", 2021, https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2021-July/019233.html
5. ^ T. Ruffing, A. Kate, D. Schröder, "Liar, Liar, Coins on Fire: Penalizing Equivocation by Loss of Bitcoins", 2015, https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.727.6262&rep=rep1&type=pdf
6. ^ M. Moser, I. Eyal, and E. G. Sirer, Bitcoin Covenants, http://fc16.ifca.ai/bitcoin/papers/MES16.pdf
7. ^ A. Poelstra, "CAT and Schnorr Tricks II", 2021, https://www.wpsoftware.net/andrew/blog/cat-and-schnorr-tricks-ii.html
8. ^ A. Poelstra, "CAT and Schnorr Tricks I", 2021, https://medium.com/blockstream/cat-and-schnorr-tricks-i-faf1b59bd298
9. ^ R. Linus, "Covenants with CAT and ECDSA", 2023, https://gist.github.com/RobinLinus/9a69f5552be94d13170ec79bf34d5e85#file-covenants_cat_ecdsa-md
10. ^ S. Nakamoto, "misc changes", Aug 25 2010, https://github.com/bitcoin/bitcoin/commit/4bd188c4383d6e614e18f79dc337fbabe8464c82#diff-27496895958ca30c47bbb873299a2ad7a7ea1003a9faa96b317250e3b7aa1fefR94
11. ^ Roose S., Elements Project, "Re-enable several disabled opcodes", 2019, https://github.com/ElementsProject/elements/commit/13e1103abe3e328c5a4e2039b51a546f8be6c60a#diff-a0337ffd7259e8c7c9a7786d6dbd420c80abfa1afdb34ebae3261109d9ae3c19R740-R759

Acknowledgements

We wish to acknowledge Dan Gould for encouraging and helping review this effort. We also want to thank Madars Virza, Jeremy Rubin, Andrew Poelstra, Bob Summerwill for their feedback, review and helpful comments.