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rgb-protocol
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rgb-protocol-on-bitcoin

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* `P` is the Internal Public Key of the *Key Path Spend.*
* `G` is the Generator point of [secp256k1](https://en.bitcoin.it/wiki/Secp256k1) elliptic curve.
* `t = tH_TWEAK(P)` = SHA-256(SHA-256(*TapTweak*) || SHA-256(*TapTweak*) || P) is the tweaking factor derived from the tagged hash representing the commitment to the public key `P`. The construction makes use of [BIP86](https://github.com/bitcoin/bips/blob/master/bip-0086.mediawiki#address-derivation) to show that ther...
In order to include the Tapret commitment, **the transaction is modified to include a Script Path Spend containing a single script** according to the following scheme:
```
+---+ +---+ +---+ +---+
| Q | = | P | + | t | * | G |
+---+ +---+ +-^-+ +---+
|
+----------------------------+
| tH_TWEAK(P || Script_root) |
+---------------------^------+
|
+-------------------------+------------+
| tH_BRANCH(64-byte_Tapret_Commitment) |
+--------------------------------------+
```
* `t = tH_TWEAK(P || Script_root)` = SHA-256(SHA-256(*TapTweak*) || SHA-256(*TapTweak*) || P || Script\_root) is the modified tweaking factor.
* `Script_root = tH_BRANCH(`64-byte\_Tapret\_Commitment`)` = SHA256(SHA-256(*TapBranch*) || SHA-256(*TapBranch*) || 64-byte\_Tapret\_Commitment) is the script root of the Script Path Spend.
The proof of inclusion and uniqueness in the Taproot Script Tree is only the internal key `P`.
## **Tapret incorporation in pre-existing Script Path Spend**
To move on to the construction of this more complex case, we show below the structure of a taproot output Key `Q`, which in this example consists of a Spend Key Path with internal key `P` and a 3-script tree in the Spend Script Path.
```
+---+ +---+ +---+ +---+
| Q | = | P | + | t | * | G |
+---+ +---+ +-^-+ +---+
|
+----------------------------+
| tH_TWEAK(P || Script_root) |
+---------------------^------+
|
+-------------+----------+
| tH_BRANCH(tHAB || tHC) |
+------------^-------^---+
| |
+---------+ +---------+
| |
+------------+----------+ +------+-----+
| tH_BRANCH(tHA || tHB) | | tH_LEAF(C) |
+------------^------^---+ +------^-----+
| | |
+------+ +------+ |
| | |
+-----+------+ +-----+------+ |
| tH_LEAF(A) | | tH_LEAF(B) | |
+-----^------+ +-----^------+ |
| | |
+-+-+ +-+-+ +-+-+
| A | | B | | C |
+---+ +---+ +---+
```
Where:
* `tH_LEAF(x)` = SHA-256(SHA-256(*TapLeaf*) || SHA-256(*TapLeaf*) || version\_leaf(x) || size(x) || x) is the standard tagged hash of a script leaf in taproot Script Path Spend.
* `A, B, C` are some Bitcoin scripts of this example taproot script tree.
The RGB Tapret commitment rule imposes the following requirements:
**1) Tapret Commitment is entered as an unspendable script at the 1st level of the Script Tree, shifting all other scripts 1 level below.**
The new Taproot Output Key `Q` including the Tapret commitment is built as follows:
```
+---+ +---+ +---+ +---+
| Q | = | P | + | t | * | G |
+---+ +---+ +-^-+ +---+
|
+--------------------+
|
+---------------+------------+
| tH_TWEAK(P || Script_root) |
+---------------------^------+
|
+--------------+----------+
| tH_BRANCH(tHABC || tHT) |
+-------------^-------^---+
| |
+-------------------------------+ +-------+
| |
+----------+-------------+ +-----------------+--------------------+
| tH_BRANCH(tHAB || tHC) | | tH_BRANCH(64_byte_Tapret_Commitment) |
+------------^-------^---+ +--------------------------------------+
| |
+---------+ +-----------+
| |
+------------+----------+ +------+-----+
| tH_BRANCH(tHA || tHB) | | tH_LEAF(C) |
+------------^------^---+ +------^-----+
| | |
+------+ +------+ |
| | |
+-----+------+ +-----+------+ |