From 4ea021f28c9f919679ae2774890b3061dd13fd6d Mon Sep 17 00:00:00 2001
From: Jonas Nick <jonasd.nick@gmail.com>
Date: Tue, 3 Mar 2020 12:06:55 +0000
Subject: BIP-0341: Avoid decompressing the output public key in script spends

---
 bip-0341.mediawiki | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'bip-0341.mediawiki')

diff --git a/bip-0341.mediawiki b/bip-0341.mediawiki
index c6efaab..6472430 100644
--- a/bip-0341.mediawiki
+++ b/bip-0341.mediawiki
@@ -75,8 +75,8 @@ The following rules only apply when such an output is being spent. Any other out
 **** If ''k<sub>j</sub> &ge; e<sub>j</sub>'': ''k<sub>j+1</sub> = hash<sub>TapBranch</sub>(e<sub>j</sub> || k<sub>j</sub>)''.
 ** Let ''t = hash<sub>TapTweak</sub>(p || k<sub>m</sub>)''.
 ** If ''t &ge; 0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141'' (order of secp256k1), fail.
-** Let ''Q = lift_x_even_y(int(q)) if (c[0] & 1) = 0 and -lift_x_even_y(int(q)) otherwise''<ref>'''Why is it necessary to reveal a bit to indicate if the point represented by the output public key is negated in a script path spend?''' The ''lift_x_even_y'' function (defined in [[bip-0340.mediawiki#design|BIP340]]) always constructs a point with an even Y coordinate, but because ''Q'' is constructed by adding the taproot tweak to the internal public key ''P'', it cannot easily be guaranteed that ''Q'' in fact has such a Y coordinate. Therefore, before verifying the taproot tweak the original point is restored by negating if necessary. We can not ignore the Y coordinate because it would prevent batch verification. Trying out multiple internal keys until there's such a ''Q'' is possible but undesirable and unnecessary since this information about the Y coordinate only consumes an unused bit.</ref>. Fail if this point is not on the curve.
-** If ''Q &ne; P + int(t)G'', fail.
+** Let ''Q = P + int(t)G''.
+** If ''q &ne; x(Q)'' or ''c[0] & 1 &ne; y(Q) mod 2'', fail<ref>'''Why is it necessary to reveal a bit in a script path spend and check that it matches the parity of the Y coordinate of ''Q''?''' The parity of the Y coordinate is necessary to lift the X coordinate ''q'' to a unique point. While this is not strictly necessary for verifying the taproot commitment as described above, it is necessary to allow batch verification. Alternatively, ''Q'' could be forced to have an even Y coordinate, but that would require retrying with different internal public keys (or different messages) until ''Q'' has that property. There is no downside to adding the parity bit because otherwise the control block bit would be unused.</ref>.
 ** Execute the script, according to the applicable script rules<ref>'''What are the applicable script rules in script path spends?''' [[bip-0342.mediawiki|BIP342]] specifies validity rules that apply for leaf version 0xc0, but future proposals can introduce rules for other leaf versions.</ref>, using the witness stack elements excluding the script ''s'', the control block ''c'', and the annex ''a'' if present, as initial stack.
 
 ''q'' is referred to as ''taproot output key'' and ''p'' as ''taproot internal key''.
@@ -87,7 +87,7 @@ We first define a reusable common signature message calculation function, follow
 
 ==== Common signature message ====
 
-The function ''SigMsg(hash_type, ext_flag)'' computes the message being signed as a byte array. It is implicitly also a function of the spending transaction and the outputs it spends, but these are not listed to keep notation simple. 
+The function ''SigMsg(hash_type, ext_flag)'' computes the message being signed as a byte array. It is implicitly also a function of the spending transaction and the outputs it spends, but these are not listed to keep notation simple.
 
 The parameter ''hash_type'' is an 8-bit unsigned value. The <code>SIGHASH</code> encodings from the legacy script system are reused, including <code>SIGHASH_ALL</code>, <code>SIGHASH_NONE</code>, <code>SIGHASH_SINGLE</code>, and <code>SIGHASH_ANYONECANPAY</code>, plus the default ''hash_type'' value ''0x00'' which results in signing over the whole transaction just as for <code>SIGHASH_ALL</code>. The following restrictions apply, which cause validation failure if violated:
 * Using any undefined ''hash_type'' (not ''0x00'', ''0x01'', ''0x02'', ''0x03'', ''0x81'', ''0x82'', or ''0x83''<ref>'''Why reject unknown ''hash_type'' values?''' By doing so, it is easier to reason about the worst case amount of signature hashing an implementation with adequate caching must perform.</ref>).
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