Adds sentence suggested by murchandamus to quantum paragraph

Co-authored-by: Mark "Murch" Erhardt <murch@murch.one>

1 files changed, 1 insertions, 1 deletions

diff --git a/bip-0347.mediawiki b/bip-0347.mediawiki
index 88dad57..29d9219 100644
--- a/bip-0347.mediawiki
+++ b/bip-0347.mediawiki
@@ -39,7 +39,7 @@ OP_CAT aims to expand the toolbox of the tapscript developer with a simple, modu
 
 * 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. <ref>R. Linus, "BitStream: Decentralized File Hosting Incentivised via Bitcoin Payments", 2023, https://robinlinus.com/bitstream.pdf</ref>
 * 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 up to 4,294,967,296 public keys. This also enables generalized logical spend conditions. <ref> P. Wuille, "Multisig on steroids using tree signatures", 2015, https://blog.blockstream.com/en-treesignatures/</ref>
-* Post-Quantum Lamport signatures in Bitcoin transactions. Lamport signatures merely require the ability to hash and concatenate values on the stack. <ref>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.html</ref> It is an open question if a tapscript commitment would preserve the quantum resistance of Lamport signatures. Beyond this question, the use of Lamport Signatures in taproot outputs is unlikely to be quantum resistant even if the script spend-path is made quantum resistant. This is because taproot outputs can also be spent with a key. An attacker with a sufficiently powerful quantum computer could bypass the taproot script spend-path by finding the discrete log of the taproot output and thus spending the output using the key spend-path. The use of "Nothing Up My Sleeve" (NUMS) points as described in [[bip-0341.mediawiki|BIP341]] to disable the key spend-path does not disable the key spend-path against a quantum attacker as NUMS relies on the hardness of finding discrete logs. We are not aware of any mechanism which could disable the key spend-path in a taproot output without a softfork change to taproot.
+* Post-Quantum Lamport signatures in Bitcoin transactions. Lamport signatures merely require the ability to hash and concatenate values on the stack. <ref>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.html</ref> It has been proposed that if ECDSA is broken or a powerful computer was on the horizon, there might be an effort to protect ownership of bitcoins by allowing people to mark their taproot outputs as "script-path only" and then move their coins into such outputs with a leaf in the script tree requiring a Lamport signature. It is an open question if a tapscript commitment would preserve the quantum resistance of Lamport signatures. Beyond this question, the use of Lamport Signatures in taproot outputs is unlikely to be quantum resistant even if the script spend-path is made quantum resistant. This is because taproot outputs can also be spent with a key. An attacker with a sufficiently powerful quantum computer could bypass the taproot script spend-path by finding the discrete log of the taproot output and thus spending the output using the key spend-path. The use of "Nothing Up My Sleeve" (NUMS) points as described in [[bip-0341.mediawiki|BIP341]] to disable the key spend-path does not disable the key spend-path against a quantum attacker as NUMS relies on the hardness of finding discrete logs. We are not aware of any mechanism which could disable the key spend-path in a taproot output without a softfork change to taproot.
 * Non-equivocation contracts <ref>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</ref> 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 <ref>M. Moser, I. Eyal, and E. G. Sirer, Bitcoin Covenants, http://fc16.ifca.ai/bitcoin/papers/MES16.pdf</ref> 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 sufficient 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 <ref>R. Linus, "Covenants with CAT and ECDSA", 2023, https://gist.github.com/RobinLinus/9a69f5552be94d13170ec79bf34d5e85#file-covenants_cat_ecdsa-md</ref>.