Move/reword tagged hashes motivation

1 files changed, 2 insertions, 2 deletions

diff --git a/bip-taproot.mediawiki b/bip-taproot.mediawiki
index 0823c6b..7a81949 100644
--- a/bip-taproot.mediawiki
+++ b/bip-taproot.mediawiki
@@ -41,7 +41,7 @@ As a result we choose this combination of technologies:
 * Taproot's advantages become apparent under the assumption that most applications involve outputs that could be spent by all parties agreeing. That's where '''Schnorr''' signatures come in, as they permit [https://eprint.iacr.org/2018/068 key aggregation]: a public key can be constructed from multiple participant public keys, and which requires cooperation between all participants to sign for. Such multi-party public keys and signatures are indistinguishable from their single-party equivalents. This means that under this Taproot assumption, the all-parties-agree case can be handled using the key-based spending path, which is both private and efficient using Taproot. This can be generalized to arbitrary M-of-N policies, as Schnorr signatures support threshold signing, at the cost of more complex setup protocols.
 * As Schnorr signatures also permit '''batch validation''', allowing multiple signatures to be validated together more efficiently than validating each one independently, we make sure all parts of the design are compatible with this.
 * Where unused bits appear as a result of the above changes, they are reserved for mechanisms for '''future extensions'''. As a result, every script in the Merkle tree has an associated version such that new script versions can be introduced with a soft fork while remaining compatible with bip-taproot. Additionally, future soft forks can make use of the currently unused <code>annex</code> in the witness (see [[#Rationale]]).
-* While the core semantics of the '''signature hashing algorithm''' are not changed, a number of improvements are included in this proposal. The new signature hashing algorithm fixes the verification capabilities of offline signing devices by including amount and scriptPubKey in the digest, avoids unnecessary hashing, uses '''tagged hashes'''<ref>'''Why use tagged hashes?''' So far, nowhere in the Bitcoin protocol are hashes used where the input of SHA256 starts with two (non-double) SHA256 hashes, making collisions with existing uses of hash functions infeasible.</ref> (according to bip-schnorr) and defines a default sighash byte.
+* While the core semantics of the '''signature hashing algorithm''' are not changed, a number of improvements are included in this proposal. The new signature hashing algorithm fixes the verification capabilities of offline signing devices by including amount and scriptPubKey in the digest, avoids unnecessary hashing, uses '''tagged hashes''' and defines a default sighash byte.
 * The '''public key is directly included in the output''' in contrast to typical earlier constructions which store a hash of the public key or script in the output. This has the same cost for senders and is more space efficient overall if the key-based spending path is taken. <ref>'''Why is the public key directly included in the output?''' While typical earlier constructions store a hash of a script or a public key in the output, this is rather wasteful when a public key is always involved. To guarantee batch verifiability, ''q'' must be known to every verifier, and thus only revealing its hash as an output would imply adding an additional 32 bytes to the witness. Furthermore, to maintain [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2016-January/012198.html 128-bit collision security] for outputs, a 256-bit hash would be required anyway, which is comparable in size (and thus in cost for senders) to revealing the public key directly. While the usage of public key hashes is often said to protect against ECDLP breaks or quantum computers, this protection is very weak at best: transactions are not protected while being confirmed, and a very [https://twitter.com/pwuille/status/1108097835365339136 large portion] of the currency's supply is not under such protection regardless. Actual resistance to such systems can be introduced by relying on different cryptographic assumptions, but this proposal focuses on improvements that do not change the security model. Note that using P2SH-wrapped outputs only have 80-bit collision security. This is considered low, and is relevant whenever the output includes data from more than a single party (public keys, hashes, ...). </ref>.
 
 Not included in this proposal are additional features like new sighash modes or opcodes that can be included with no loss in effectiveness as a future extension. Also not included is cross-input aggregation, as it [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-March/015838.html interacts] in complex ways with upgrade mechanisms and solutions to that are still [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-October/016461.html in flux].
@@ -50,7 +50,7 @@ Not included in this proposal are additional features like new sighash modes or
 
 This section specifies the Taproot consensus rules. Validity is defined by exclusion: a block or transaction is valid if no condition exists that marks it failed.
 
-The notation below follows that of bip-schnorr.
+The notation below follows that of bip-schnorr. This includes the ''hash<sub>tag</sub>(x)'' notation to refer to ''SHA256(SHA256(tag) || SHA256(tag) || x)''. To the best of the authors' knowledge, no existing use of SHA256 in Bitcoin feeds it a message that starts with two single SHA256 outputs, making collisions between ''hash<sub>tag</sub>'' with other hashes extremely unlikely.
 
 === Script validation rules ===