From 9cf4038f17cb566bdc79b5ec12dee5338b1122d1 Mon Sep 17 00:00:00 2001
From: Pieter Wuille <pieter.wuille@gmail.com>
Date: Sun, 19 Jan 2020 14:52:43 -0800
Subject: fix BIP links

---
 bip-0341.mediawiki | 38 +++++++++++++++++++-------------------
 1 file changed, 19 insertions(+), 19 deletions(-)

(limited to 'bip-0341.mediawiki')

diff --git a/bip-0341.mediawiki b/bip-0341.mediawiki
index 44b9818..8f27c35 100644
--- a/bip-0341.mediawiki
+++ b/bip-0341.mediawiki
@@ -31,7 +31,7 @@ This proposal aims to improve privacy, efficiency, and flexibility of Bitcoin's
 
 ==Design==
 
-A number of related ideas for improving Bitcoin's scripting capabilities have been previously proposed: Schnorr signatures ([https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki BIP340), Merkle branches ("MAST", [bip-0114.mediawiki BIP114], [bip-0117.mediawiki BIP117]), new sighash modes ([bip-0118.mediawiki BIP118]), new opcodes like CHECKSIGFROMSTACK, [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-January/015614.html Taproot], [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-February/015700.html Graftroot], [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-July/016249.html G'root], and [https://bitcointalk.org/index.php?topic=1377298.0 cross-input aggregation].
+A number of related ideas for improving Bitcoin's scripting capabilities have been previously proposed: Schnorr signatures ([[bip-0340|BIP340]]), Merkle branches ("MAST", [[bip-0114|BIP114]], [[bip-0117|BIP117]]), new sighash modes ([[bip-0118|BIP118]]), new opcodes like CHECKSIGFROMSTACK, [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-January/015614.html Taproot], [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-February/015700.html Graftroot], [https://lists.linuxfoundation.org/pipermail/bitcoin-dev/2018-July/016249.html G'root], and [https://bitcointalk.org/index.php?topic=1377298.0 cross-input aggregation].
 
 Combining all these ideas in a single proposal would be an extensive change, be hard to review, and likely miss new discoveries that otherwise could have been made along the way. Not all are equally mature as well. For example, cross-input aggregation [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]. On the other hand, separating them all into independent upgrades would reduce the efficiency and privacy gains to be had, and wallet and service providers may not be inclined to go through many incremental updates. Therefore, we're faced with a tradeoff between functionality and scope creep. In this design we strike a balance by focusing on the structural script improvements offered by Taproot and Merkle branches, as well as changes necessary to make them usable and efficient. For things like sighashes and opcodes we include fixes for known problems, but exclude new features that can be added independently with no downsides.
 
@@ -40,7 +40,7 @@ As a result we choose this combination of technologies:
 * '''Taproot''' on top of that lets us merge the traditionally separate pay-to-pubkey and pay-to-scripthash policies, making all outputs spendable by either a key or (optionally) a script, and indistinguishable from each other. As long as the key-based spending path is used for spending, it is not revealed whether a script path was permitted as well, resulting in space savings and an increase in scripting privacy at spending time.
 * 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 with taproot most applications can use the key-based spending path, which is both efficient and private. 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 341. Additionally, future soft forks can make use of the currently unused <code>annex</code> in the witness (see [[#Rationale]]).
+* 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 341. Additionally, future soft forks can make use of the currently unused <code>annex</code> in the witness (see [[bip-0341.mediawiki#Rationale|BIP341]]).
 * 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 signature message, 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, the public key 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.</ref>
 
@@ -50,14 +50,14 @@ Informally, the resulting design is as follows: a new witness version is added (
 
 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-0340.mediawiki#design BIP340]. 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.
+The notation below follows that of [[bip-0340.mediawiki#design|BIP340]]. 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 ===
 
-A Taproot output is a native SegWit output (see [bip-0141.mediawiki BIP141]) with version number 1, and a 32-byte witness program.
+A Taproot output is a native SegWit output (see [[bip-0141.mediawiki|BIP141]]) with version number 1, and a 32-byte witness program.
 The following rules only apply when such an output is being spent. Any other outputs, including version 1 outputs with lengths other than 32 bytes, or P2SH-wrapped version 1 outputs<ref>'''Why is P2SH-wrapping not supported?''' Using P2SH-wrapped outputs only provides 80-bit collision security due to the use of a 160-bit hash. This is considered low, and becomes a security risk whenever the output includes data from more than a single party (public keys, hashes, ...).</ref>, remain unencumbered.
 
-* Let ''q'' be the 32-byte array containing the witness program (the second push in the scriptPubKey) which represents a public key according to [bip-0340.mediawiki#design BIP340].
+* Let ''q'' be the 32-byte array containing the witness program (the second push in the scriptPubKey) which represents a public key according to [[bip-0340.mediawiki#design|BIP340]].
 * Fail if the witness stack has 0 elements.
 * If there are at least two witness elements, and the first byte of the last element is 0x50<ref>'''Why is the first byte of the annex <code>0x50</code>?''' The <code>0x50</code> is chosen as it could not be confused with a valid P2WPKH or P2WSH spending. As the control block's initial byte's lowest bit is used to indicate the public key's Y squareness, each leaf version needs an even byte value and the immediately following odd byte value that are both not yet used in P2WPKH or P2WSH spending. To indicate the annex, only an "unpaired" available byte is necessary like <code>0x50</code>. This choice maximizes the available options for future script versions.</ref>, this last element is called ''annex'' ''a''<ref>'''What is the purpose of the annex?''' The annex is a reserved space for future extensions, such as indicating the validation costs of computationally expensive new opcodes in a way that is recognizable without knowing the scriptPubKey of the output being spent. Until the meaning of this field is defined by another softfork, users SHOULD NOT include <code>annex</code> in transactions, or it may lead to PERMANENT FUND LOSS.</ref> and is removed from the witness stack. The annex (or the lack of thereof) is always covered by the signature and contributes to transaction weight, but is otherwise ignored during taproot validation.
 * If there is exactly one element left in the witness stack, key path spending is used:
@@ -65,19 +65,19 @@ 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 = point(p)'' where ''point'' 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 = point(p)'' where ''point'' 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]'':
 *** Let ''e<sub>j</sub> = c[33+32j:65+32j]''.
 *** Let ''k<sub>j+1</sub> depend on whether ''k<sub>j</sub> < e<sub>j</sub>'' (lexicographically)<ref>'''Why are child elements sorted before hashing in the Merkle tree?''' By doing so, it is not necessary to reveal the left/right directions along with the hashes in revealed Merkle branches. This is possible because we do not actually care about the position of specific scripts in the tree; only that they are actually committed to.</ref>:
-**** If ''k<sub>j</sub> < e<sub>j</sub>'': ''k<sub>j+1</sub> = hash<sub>TapBranch</sub>(k<sub>j</sub> || e<sub>j</sub>)''<ref>'''Why not use a more efficient hash construction for inner Merkle nodes?''' The chosen construction does require two invocations of the SHA256 compression functions, one of which can be avoided in theory (see [bip-0098.mediawiki BIP98]). However, it seems preferable to stick to constructions that can be implemented using standard cryptographic primitives, both for implementation simplicity and analyzability. If necessary, a significant part of the second compression function can be optimized out by [https://github.com/bitcoin/bitcoin/pull/13191 specialization] for 64-byte inputs.</ref>.
+**** If ''k<sub>j</sub> < e<sub>j</sub>'': ''k<sub>j+1</sub> = hash<sub>TapBranch</sub>(k<sub>j</sub> || e<sub>j</sub>)''<ref>'''Why not use a more efficient hash construction for inner Merkle nodes?''' The chosen construction does require two invocations of the SHA256 compression functions, one of which can be avoided in theory (see [[bip-0098.mediawiki|BIP98]]). However, it seems preferable to stick to constructions that can be implemented using standard cryptographic primitives, both for implementation simplicity and analyzability. If necessary, a significant part of the second compression function can be optimized out by [https://github.com/bitcoin/bitcoin/pull/13191 specialization] for 64-byte inputs.</ref>.
 **** 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 = point(q) if (c[0] & 1) = 1 and -point(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 ''point'' function (defined in [bip-0340.mediawiki#design BIP340]) always constructs a point with a square 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.
+** Let ''Q = point(q) if (c[0] & 1) = 1 and -point(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 ''point'' function (defined in [[bip-0340.mediawiki#design|BIP340]]) always constructs a point with a square 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.
-** Execute the script, according to the applicable script rules<ref>'''What are the applicable script rules in script path spends?''' [bip-0342.mediawiki#design 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.
+** 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''.
 
@@ -93,7 +93,7 @@ The parameter ''hash_type'' is an 8-bit unsigned value. The <code>SIGHASH</code>
 * 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>).
 * Using <code>SIGHASH_SINGLE</code> without a "corresponding output" (an output with the same index as the input being verified).
 
-The parameter ''ext_flag'' is an integer in range 0-127, and is used for indicating (in the message) that extensions are added at the end of the message<ref>'''What extensions use the ''ext_flag'' mechanism?''' [bip-0342.mediawiki#design BIP342] reuses the same common signature message algorithm, but adds BIP342-specific data at the end, which is indicated using ''ext_flag = 1''.</ref>.
+The parameter ''ext_flag'' is an integer in range 0-127, and is used for indicating (in the message) that extensions are added at the end of the message<ref>'''What extensions use the ''ext_flag'' mechanism?''' [[bip-0342.mediawiki|BIP342]] reuses the same common signature message algorithm, but adds BIP342-specific data at the end, which is indicated using ''ext_flag = 1''.</ref>.
 
 If the parameters take acceptable values, the message is the concatenation of the following data, in order(with byte size of each item listed in parentheses). Numerical values in 2, 4, or 8-byte are encoded in little-endian.
 
@@ -125,7 +125,7 @@ If the parameters take acceptable values, the message is the concatenation of th
 
 The total length of ''SigMsg()'' is at most ''209'' bytes<ref>'''What is the output length of ''SigMsg()''?''' The total length of ''SigMsg()'' can be computed using the following formula: ''177 - is_anyonecanpay * 52 - is_none * 32 + has_annex * 32''.</ref>. Note that this does not include the size of sub-hashes such as ''sha_prevouts'', which may be cached across signatures of the same transaction.
 
-In summary, the semantics of the [bip-0143.mediawiki BIP143] sighash types remain unchanged, except the following:
+In summary, the semantics of the [[bip-0143.mediawiki|BIP143]] sighash types remain unchanged, except the following:
 # The way and order of serialization is changed.<ref>'''Why is the serialization in the signature message changed?''' Hashes that go into the signature message and the message itself are now computed with a single SHA256 invocation instead of double SHA256. There is no expected security improvement by doubling SHA256 because this only protects against length-extension attacks against SHA256 which are not a concern for signature messages because there is no secret data. Therefore doubling SHA256 is a waste of resources. The message computation now follows a logical order with transaction level data first, then input data and output data. This allows to efficiently cache the transaction part of the message across different inputs using the SHA256 midstate. Additionally, sub-hashes can be skipped when calculating the message (for example `sha_prevouts` if <code>SIGHASH_ANYONECANPAY</code> is set) instead of setting them to zero and then hashing them as in BIP143. Despite that, collisions are made impossible by committing to the length of the data (implicit in ''hash_type'' and ''spend_type'') before the variable length data.</ref>
 # The signature message commits to the ''scriptPubKey''<ref>'''Why does the signature message commit to the ''scriptPubKey''?''' This prevents lying to offline signing devices about output being spent, even when the actually executed script (''scriptCode'' in BIP143) is correct. This means it's possible to compactly prove to a hardware wallet what (unused) execution paths existed.</ref>.
 # If the <code>SIGHASH_ANYONECANPAY</code> flag is not set, the message commits to the amounts of ''all'' transaction inputs.<ref>'''Why does the signature message commit to the amounts of all transaction inputs?''' This eliminates the possibility to lie to offline signing devices about the fee of a transaction.</ref>
@@ -135,7 +135,7 @@ In summary, the semantics of the [bip-0143.mediawiki BIP143] sighash types remai
 ==== Taproot key path spending signature validation ====
 
 To validate a signature ''sig'' with public key ''q'':
-* If the ''sig'' is 64 bytes long, return ''Verify(q, hash<sub>TapSigHash</sub>(0x00 || SigMsg(0x00, 0)), sig)''<ref>'''Why is the input to ''hash<sub>TapSigHash</sub>'' prefixed with 0x00?''' This prefix is called the sighash epoch, and allows reusing the ''hash<sub>TapSigHash</sub>'' tagged hash in future signature algorithms that make invasive changes to how hashing is performed (as opposed to the ''ext_flag'' mechanism that is used for incremental extensions). An alternative is having them use a different tag, but supporting a growing number of tags may become undesirable.</ref>, where ''Verify'' is defined in [bip-0340.mediawiki#design BIP340].
+* If the ''sig'' is 64 bytes long, return ''Verify(q, hash<sub>TapSigHash</sub>(0x00 || SigMsg(0x00, 0)), sig)''<ref>'''Why is the input to ''hash<sub>TapSigHash</sub>'' prefixed with 0x00?''' This prefix is called the sighash epoch, and allows reusing the ''hash<sub>TapSigHash</sub>'' tagged hash in future signature algorithms that make invasive changes to how hashing is performed (as opposed to the ''ext_flag'' mechanism that is used for incremental extensions). An alternative is having them use a different tag, but supporting a growing number of tags may become undesirable.</ref>, where ''Verify'' is defined in [[bip-0340.mediawiki#design|BIP340]].
 * If the ''sig'' is 65 bytes long, return ''sig[64] &ne; 0x00<ref>'''Why can the <code>hash_type</code> not be <code>0x00</code> in 65-byte signatures?''' Permitting that would enable malleating (by third parties, including miners) 64-byte signatures into 65-byte ones, resulting in a different `wtxid` and a different fee rate than the creator intended</ref> and Verify(q, hash<sub>TapSighash</sub>(0x00 || SigMsg(sig[64], 0)), sig[0:64])''.
 * Otherwise, fail<ref>'''Why permit two signature lengths?''' By making the most common type of <code>hash_type</code> implicit, a byte can often be saved.</ref>.
 
@@ -167,7 +167,7 @@ Alice will not be able to notice the script path, but Mallory can unilaterally s
 
 '''Computing the output script''' Once the spending conditions are split into an internal key <code>internal_pubkey</code> and a binary tree whose leaves are (leaf_version, script) tuples, the output script can be computed using the Python3 algorithms below. These algorithms take advantage of helper functions from the [bip-0340/referency.py BIP340 reference code] for integer conversion, point multiplication, and tagged hashes.
 
-First, we define <code>taproot_tweak_pubkey</code> for 32-byte [bip-0340.mediawiki#design BIP340] public key arrays.
+First, we define <code>taproot_tweak_pubkey</code> for 32-byte [[bip-0340.mediawiki|BIP340]] public key arrays.
 In addition to the tweaked public key byte array, the function returns a boolean indicating whether the public key represents the tweaked point or its negation.
 This will be required for spending the output with a script path.
 In order to allow spending with the key path, we define <code>taproot_tweak_seckey</code> to compute the secret key for a tweaked public key.
@@ -191,7 +191,7 @@ def taproot_tweak_seckey(seckey0, h):
     return (seckey + t) % SECP256K1_ORDER
 </source>
 
-The following function, <code>taproot_output_script</code>, returns a byte array with the scriptPubKey (see BIP141).
+The following function, <code>taproot_output_script</code>, returns a byte array with the scriptPubKey (see [[bip-0141.mediawiki|BIP141]]).
 <code>ser_script</code> refers to a function that prefixes its input with a CCompactSize-encoded length.
 
 <source lang="python">
@@ -210,7 +210,7 @@ def taproot_tree_helper(script_tree):
 def taproot_output_script(internal_pubkey, script_tree):
     """Given a internal public key and a tree of scripts, compute the output script.
     script_tree is either:
-     - a (leaf_version, script) tuple (leaf_version is 0xc0 for [bip-0342.mediawiki#design BIP342] scripts)
+     - a (leaf_version, script) tuple (leaf_version is 0xc0 for [[bip-0342.mediawiki|BIP342]] scripts)
      - a list of two elements, each with the same structure as script_tree itself
      - None
     """
@@ -222,13 +222,13 @@ def taproot_output_script(internal_pubkey, script_tree):
     return bytes([0x51, 0x20]) + output_pubkey
 </source>
 
-[[File:bip-0342/tree.png|frame|This diagram shows the hashing structure to obtain the tweak from an internal key ''P'' and a Merkle tree consisting of 5 script leaves. ''A'', ''B'', ''C'' and ''E'' are ''TapLeaf'' hashes similar to ''D'' and ''AB'' is a ''TapBranch'' hash. Note that when ''CDE'' is computed ''E'' is hashed first because ''E'' is less than ''CD''.]]
+[[File:bip-0341/tree.png|frame|This diagram shows the hashing structure to obtain the tweak from an internal key ''P'' and a Merkle tree consisting of 5 script leaves. ''A'', ''B'', ''C'' and ''E'' are ''TapLeaf'' hashes similar to ''D'' and ''AB'' is a ''TapBranch'' hash. Note that when ''CDE'' is computed ''E'' is hashed first because ''E'' is less than ''CD''.]]
 
 To spend this output using script ''D'', the control block would contain the following data in this order:
 
      <control byte with leaf version and negation bit> <internal key p> <C> <E> <AB>
 
-The TapTweak would then be computed as described in [[#script-validation-rules]] like so:
+The TapTweak would then be computed as described [[bip-0341.mediawiki#script-validation-rules|above]] like so:
 
 <source>
 D = tagged_hash("TapLeaf", bytes([leaf_version]) + ser_script(script))
@@ -238,7 +238,7 @@ ABCDE = tagged_hash("TapBranch", AB + CDE)
 TapTweak = tagged_hash("TapTweak", p + ABCDE)
 </source>
 
-'''Spending using the key path''' A Taproot output can be spent with the secret key corresponding to the <code>internal_pubkey</code>. To do so, a witness stack consists of a single element: a bip-schnorr signature on the signature hash as defined above, with the secret key tweaked by the same <code>h</code> as in the above snippet. See the code below:
+'''Spending using the key path''' A Taproot output can be spent with the secret key corresponding to the <code>internal_pubkey</code>. To do so, a witness stack consists of a single element: a [[bip-0340.mediawiki|BIP340]] signature on the signature hash as defined above, with the secret key tweaked by the same <code>h</code> as in the above snippet. See the code below:
 
 <source lang="python">
 def taproot_sign_key(script_tree, internal_seckey, hash_type):
@@ -302,7 +302,7 @@ Non-upgraded nodes, however, will consider all SegWit version 1 witness programs
 They are strongly encouraged to upgrade in order to fully validate the new programs.
 
 Non-upgraded wallets can receive and send bitcoin from non-upgraded and upgraded wallets using SegWit version 0 programs, traditional pay-to-pubkey-hash, etc.
-Depending on the implementation non-upgraded wallets may be able to send to Segwit version 1 programs if they support sending to [https://github.com/bitcoin/bips/blob/master/bip-0173.mediawiki BIP173] Bech32 addresses.
+Depending on the implementation non-upgraded wallets may be able to send to Segwit version 1 programs if they support sending to [[bip-0173.mediawiki|BIP173]] Bech32 addresses.
 
 == Acknowledgements ==
 
-- 
cgit v1.2.3

