From 97635f5c094709dd18f4afee017e33face886f5b Mon Sep 17 00:00:00 2001
From: Ethan Heilman <ethan.r.heilman@gmail.com>
Date: Sun, 17 Dec 2023 12:49:46 -0500
Subject: Lowercase the signatures

---
 bip-???-cat.mediawiki | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

(limited to 'bip-???-cat.mediawiki')

diff --git a/bip-???-cat.mediawiki b/bip-???-cat.mediawiki
index 8709f7b..68c24c9 100644
--- a/bip-???-cat.mediawiki
+++ b/bip-???-cat.mediawiki
@@ -28,8 +28,8 @@ Bitcoin tapscript lacks a general purpose way of combining objects on the stack
 OP_CAT aims to expands the toolbox of the tapscript developer with a simple, modular and useful opcode in the spirit of Unix <ref>R. Pike and B. Kernighan, "Program design in the UNIX environment", 1983, https://harmful.cat-v.org/cat-v/unix_prog_design.pdf</ref>. 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. <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 a thousand 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 the quantum resistance of Lamport Signatures can be preserved when used in a taproot output.
+* 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. <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 the quantum resistance of Lamport signatures can be preserved when used in a taproot output.
 * 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 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 <ref>R. Linus, "Covenants with CAT and ECDSA", 2023, https://gist.github.com/RobinLinus/9a69f5552be94d13170ec79bf34d5e85#file-covenants_cat_ecdsa-md</ref>.
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