bip-p2qrh.mediawiki: Separating discussion about Grovers algorithm into

its own section.

bip-p2qrh.mediawiki

@@ -26,7 +26,7 @@ This document is licensed under the 3-clause BSD license.
 
 This proposal aims to improve the quantum resistance of bitcoin's signature security should the Discrete Logarithm Problem (DLP) which secures Elliptic Curve Cryptography (ECC) no longer prove to be computationally hard, likely through quantum advantage by Cryptoanalytically-Relevant Quantum Computers (CRQCs). [https://arxiv.org/pdf/quant-ph/0301141 A variant of Shor's algorithm] is believed to be capable of deriving the private key from a public key exponentially faster than classical means. The application of this variant of Shor's algorithm is herein referred to as quantum key decryption. Note that doubling the public key length, such as with a hypothetical secp512k1 curve, would only make deriving the private key twice as hard. The computational complexity of this is investigated further in the paper, [https://pubs.aip.org/avs/aqs/article/4/1/013801/2835275/The-impact-of-hardware-specifications-on-reaching ''The impact of hardware specifications on reaching quantum advantage in the fault tolerant regime''].
 
-The primary threat to Bitcoin by CRQCs is [https://en.bitcoin.it/wiki/Quantum_computing_and_Bitcoin#QC_attacks generally considered to be to its breaking of ECC used in signatures and Taproot commitments], hence the focus on a new address format. This is because Shor's algorithm enables a CRQC to break the cryptographic assumptions of ECC in roughly 10^8 quantum operations. While a CRQC could use [https://en.wikipedia.org/wiki/Grover's_algorithm Grover's algorithm] to gain a quadratic speed up on brute force attacks on the hash functions used in Bitcoin, a significantly more powerful CRQC is needed for these attacks to meaningfully impact Bitcoin. For instance, a preimage attack on HASH160<ref>used by P2PKH, P2SH, and P2WPKH addresses, though not P2WSH because it uses 256-bit hashes</ref> using Grover's algorithm would require at least 10^24 quantum operations. As for Grover's application to mining, see [https://quantumcomputing.stackexchange.com/a/12847 Sam Jaques’ post on this].
+The primary threat to Bitcoin by CRQCs is [https://en.bitcoi.it/wiki/Quantum_computing_and_Bitcoin#QC_attacks generally considered to be their potential to break ECC, which is used in signatures and Taproot commitments], hence the focus on a new address format. This is because Shor's algorithm enables a CRQC to break the cryptographic assumptions of ECC in roughly 10^8 quantum operations. 
 
 The vulnerability of existing bitcoin addresses is investigated in [https://web.archive.org/web/20240715101040/https://www2.deloitte.com/nl/nl/pages/innovatie/artikelen/quantum-computers-and-the-bitcoin-blockchain.html this Deloitte report]. The report estimates that in 2020 approximately 25% of the bitcoin supply is held within addresses vulnerable to quantum attack. As of the time of writing, that number is now closer to 20%. Additionally, cryptographer Pieter Wuille [https://x.com/pwuille/status/1108085284862713856 reasons] even more might be vulnerable.
 
@@ -84,6 +84,7 @@ It's for the above reason that, for those who wish to be prepared for quantum em
 
 The Commercial National Security Algorithm Suite (CNSA) 2.0 has a timeline for software and networking equipment to be upgraded by 2030, with browsers and operating systems fully upgraded by 2033. According to NIST IR 8547, Elliptic Curve Cryptography is planned to be disallowed within the US Federal government after 2035. An exception is made for hybrid cryptography, which is the use of ECC and post-quantum algorithms together.
 
+Although CRQCs could pose a threat to the signatures used in Bitcoin, a smaller threat is to Bitcoin's hash algorithms.  In particular, while a CRQC could use [https://en.wikipedia.org/wiki/Grover's_algorithm Grover's algorithm] to gain a quadratic speed up on brute force attacks on the hash functions used in Bitcoin, a significantly more powerful CRQC is needed for these attacks to meaningfully impact Bitcoin. For instance, a preimage attack on HASH160<ref>used by P2PKH, P2SH, and P2WPKH addresses, though not P2WSH because it uses 256-bit hashes</ref> using Grover's algorithm would require at least 10^24 quantum operations. As for Grover's application to mining, see [https://quantumcomputing.stackexchange.com/a/12847 Sam Jaques’ post on this].
 
 === Rationale ===