From 8a3db73a84bf8856e651b40a0df5684992563a3b Mon Sep 17 00:00:00 2001
From: Pieter Wuille <pieter@wuille.net>
Date: Tue, 18 Aug 2020 10:56:05 -0700
Subject: Rename lift_x_even_y to lift_x

---
 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 6c71b8d..f5e4e90 100644
--- a/bip-0341.mediawiki
+++ b/bip-0341.mediawiki
@@ -66,7 +66,7 @@ The following rules only apply when such an output is being spent. Any other out
 * If there are at least two witness elements left, script path spending is used:
 ** Call the second-to-last stack element ''s'', the script.
 ** The last stack element is called the control block ''c'', and must have length ''33 + 32m'', for a value of ''m'' that is an integer between 0 and 128<ref>'''Why is the Merkle path length limited to 128?''' The optimally space-efficient Merkle tree can be constructed based on the probabilities of the scripts in the leaves, using the Huffman algorithm. This algorithm will construct branches with lengths approximately equal to ''log<sub>2</sub>(1/probability)'', but to have branches longer than 128 you would need to have scripts with an execution chance below 1 in ''2<sup>128</sup>''. As that is our security bound, scripts that truly have such a low chance can probably be removed entirely.</ref>, inclusive. Fail if it does not have such a length.
-** Let ''p = c[1:33]'' and let ''P = lift_x_even_y(int(p))'' where ''lift_x_even_y'' and ''[:]'' are defined as in [[bip-0340.mediawiki#design|BIP340]]. Fail if this point is not on the curve.
+** Let ''p = c[1:33]'' and let ''P = lift_x(int(p))'' where ''lift_x'' and ''[:]'' are defined as in [[bip-0340.mediawiki#design|BIP340]]. Fail if this point is not on the curve.
 ** Let ''v = c[0] & 0xfe'' and call it the ''leaf version''<ref>'''What constraints are there on the leaf version?''' First, the leaf version cannot be odd as ''c[0] & 0xfe'' will always be even, and cannot be ''0x50'' as that would result in ambiguity with the annex. In addition, in order to support some forms of static analysis that rely on being able to identify script spends without access to the output being spent, it is recommended to avoid using any leaf versions that would conflict with a valid first byte of either a valid P2WPKH pubkey or a valid P2WSH script (that is, both ''v'' and ''v | 1'' should be an undefined, invalid or disabled opcode or an opcode that is not valid as the first opcode). The values that comply to this rule are the 32 even values between ''0xc0'' and ''0xfe'' and also ''0x66'', ''0x7e'', ''0x80'', ''0x84'', ''0x96'', ''0x98'', ''0xba'', ''0xbc'', ''0xbe''. Note also that this constraint implies that leaf versions should be shared amongst different witness versions, as knowing the witness version requires access to the output being spent.</ref>.
 ** Let ''k<sub>0</sub> = hash<sub>TapLeaf</sub>(v || compact_size(size of s) || s)''; also call it the ''tapleaf hash''.
 ** For ''j'' in ''[0,1,...,m-1]'':
@@ -152,7 +152,7 @@ Satisfying any of these conditions is sufficient to spend the output.
 '''Initial steps''' The first step is determining what the internal key and the organization of the rest of the scripts should be. The specifics are likely application dependent, but here are some general guidelines:
 * When deciding between scripts with conditionals (<code>OP_IF</code> etc.) and splitting them up into multiple scripts (each corresponding to one execution path through the original script), it is generally preferable to pick the latter.
 * When a single condition requires signatures with multiple keys, key aggregation techniques like MuSig can be used to combine them into a single key. The details are out of scope for this document, but note that this may complicate the signing procedure.
-* If one or more of the spending conditions consist of just a single key (after aggregation), the most likely one should be made the internal key. If no such condition exists, it may be worthwhile adding one that consists of an aggregation of all keys participating in all scripts combined; effectively adding an "everyone agrees" branch. If that is inacceptable, pick as internal key a point with unknown discrete logarithm. One example of such a point is ''H = lift_x_even_y(0x0250929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0)'' which is [https://github.com/ElementsProject/secp256k1-zkp/blob/11af7015de624b010424273be3d91f117f172c82/src/modules/rangeproof/main_impl.h#L16 constructed] by taking the hash of the standard uncompressed encoding of the [https://www.secg.org/sec2-v2.pdf secp256k1] base point ''G'' as X coordinate. In order to avoid leaking the information that key path spending is not possible it is recommended to pick a fresh integer ''r'' in the range ''0...n-1'' uniformly at random and use ''H + rG'' as internal key. It is possible to prove that this internal key does not have a known discrete logarithm with respect to ''G'' by revealing ''r'' to a verifier who can then reconstruct how the internal key was created.
+* If one or more of the spending conditions consist of just a single key (after aggregation), the most likely one should be made the internal key. If no such condition exists, it may be worthwhile adding one that consists of an aggregation of all keys participating in all scripts combined; effectively adding an "everyone agrees" branch. If that is inacceptable, pick as internal key a point with unknown discrete logarithm. One example of such a point is ''H = lift_x(0x0250929b74c1a04954b78b4b6035e97a5e078a5a0f28ec96d547bfee9ace803ac0)'' which is [https://github.com/ElementsProject/secp256k1-zkp/blob/11af7015de624b010424273be3d91f117f172c82/src/modules/rangeproof/main_impl.h#L16 constructed] by taking the hash of the standard uncompressed encoding of the [https://www.secg.org/sec2-v2.pdf secp256k1] base point ''G'' as X coordinate. In order to avoid leaking the information that key path spending is not possible it is recommended to pick a fresh integer ''r'' in the range ''0...n-1'' uniformly at random and use ''H + rG'' as internal key. It is possible to prove that this internal key does not have a known discrete logarithm with respect to ''G'' by revealing ''r'' to a verifier who can then reconstruct how the internal key was created.
 * If the spending conditions do not require a script path, the output key should commit to an unspendable script path instead of having no script path. This can be achieved by computing the output key point as ''Q = P + int(hash<sub>TapTweak</sub>(bytes(P)))G''. <ref>'''Why should the output key always have a taproot commitment, even if there is no script path?'''
 If the taproot output key is an aggregate of keys, there is the possibility for a malicious party to add a script path without being noticed by the other parties.
 This allows to bypass the multiparty policy and to steal the coin.
@@ -180,7 +180,7 @@ def taproot_tweak_pubkey(pubkey, h):
     t = int_from_bytes(tagged_hash("TapTweak", pubkey + h))
     if t >= SECP256K1_ORDER:
         raise ValueError
-    Q = point_add(lift_x_even_y(int_from_bytes(pubkey)), point_mul(G, t))
+    Q = point_add(lift_x(int_from_bytes(pubkey)), point_mul(G, t))
     return 0 if has_even_y(Q) else 1, bytes_from_int(x(Q))
 
 def taproot_tweak_seckey(seckey0, h):
-- 
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