BIP341: Define c[0] = leaf version + pubkey parity

Add explicit definition of _c[0]_ as the _leaf version_ and the public
key _parity bit_.

Prior to this change that interesting fact is only implicit in the code
of `taproot_tweak_pubkey` and `taproot_sign_script`.  Making it explicit
will help reader understanding of the control block and the script
validation rules.

Author: david-bakin

bip-0341.mediawiki

@@ -66,8 +66,10 @@ 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 ''c[0]'' be the ''control byte'' consisting of:
+*** 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 ''ppar = c[0] & 0x01'' and call it the ''public key parity''<ref>'''What is the public key parity?''' The encoding of whether the ''y''-coordinate of the EC point is even or odd, in the standard way that compressed keys are formed. See also the return value of <code>taproot_tweak_pubkey</code>.</ref>
 ** 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]'':
 *** Let ''e<sub>j</sub> = c[33+32j:65+32j]''.
@@ -77,7 +79,7 @@ The following rules only apply when such an output is being spent. Any other out
 ** 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 = 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>.
+** If ''q &ne; x(Q)'' or ''ppar &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. This implies that for the future leaf versions (non-''0xC0'') the execution must succeed.<ref>'''Why we need to success on future leaf version validation''' This is required to enable future leaf versions as soft forks</ref>.
 
 ''q'' is referred to as ''taproot output key'' and ''p'' as ''taproot internal key''.
@@ -350,6 +352,6 @@ Depending on the implementation non-upgraded wallets may be able to send to Segw
 
 == Acknowledgements ==
 
-This document is the result of discussions around script and signature improvements with many people, and had direct contributions from Greg Maxwell and others. It further builds on top of earlier published proposals such as Taproot by Greg Maxwell, and Merkle branch constructions by Russell O'Connor, Johnson Lau, and Mark Friedenbach. 
+This document is the result of discussions around script and signature improvements with many people, and had direct contributions from Greg Maxwell and others. It further builds on top of earlier published proposals such as Taproot by Greg Maxwell, and Merkle branch constructions by Russell O'Connor, Johnson Lau, and Mark Friedenbach.
 
 The authors wish the thank Arik Sosman for suggesting to sort Merkle node children before hashes, removing the need to transfer the position in the tree, as well as all those who provided valuable feedback and reviews, including the participants of the [https://github.com/ajtowns/taproot-review structured reviews].