To get from the seed to the BIP84 tackle (meant for the P2WPKH), you could comply with the derivation path defines in BIP84 commonplace and apply the suitable derivation operation.
The derivation path outlined on this commonplace is: m/84’/0’/0’/0/0 the place m stands for the grasp key, the signal / denotes the extent of the tree and the quantity between the / denote the index of key in that stage. With the ' signal, it’s indicated that the important thing was of hardened kind (hardened derivation was utilized). If there is no such thing as a such signal, the important thing a results of the traditional derivation.
So first what we have to do is to get the grasp key from the seed. To do that, we comply with the BIP32 part for the grasp key era. It says that after producing the seed, we have to use the HMAC-SHA512 perform the place the hot button is Bitcoin seed and the info is the seed. In our case:
KEY: Bitcoin seed
DATA: 59dc4d5348b364f9024e2af7d6bcd6fd115a95a5dfe33b213ddac6d1ed4b77175b05e727605c62c98bd110d0952dcb38de9f16c94e55b82603af77d5226be5f5
For this objective, you should utilize a web based device like this. Set the values as I did within the following picture. I hold mentioning on-line instruments (it was simpler for me to make use of them when writing the reply), nonetheless, you can even use well-tested programming libraries in numerous programming languages.
The result’s the next:
f36ab72ee8ddc6c9288a3a26dc5f1009198bd37169dfb6ddc93b7c237b63b231c547d66d20e80779c2b7a48e9d59f989ae8c3e2bf3e8eb752aae9fb555ad5123
Left 32 bytes symbolize grasp/root non-public key and the best 32 bytes symbolize grasp/root chain code. Thus:
MASTER PRIVATE KEY: f36ab72ee8ddc6c9288a3a26dc5f1009198bd37169dfb6ddc93b7c237b63b231
MASTER CHAIN CODE: c547d66d20e80779c2b7a48e9d59f989ae8c3e2bf3e8eb752aae9fb555ad5123
On the positioning you supplied they symbolize BIP32 Root Key as a zprv base58check encoded prolonged non-public key. However that is only a manner of presenting it, nothing else.
Now that we’ve our grasp non-public key, we have to generate its youngster keys. Trying on the derivation path, we will see that subsequent what we have to generate is the eighty fifth key on the second stage. The hardened derivation is used (it has the signal ').
Earlier than we proceed, it is necessary to notice that the indexes for hardened youngsters begin at 2^31. So the index for the eighty fifth hardened youngster is definitely 2147483732 (hex: 80000054). For the first youngster it might be 2147483648 (hex: 80000000).
So to get the eighty fifth hardened youngster, following the BIP32 part to derive the hardened youngster non-public key from the mum or dad’s non-public key, the very first thing we have to do is use the HMAC-SHA512 perform the place the hot button is the mum or dad’s chain code and the date is the concatenation of 0x00, the mum or dad’s non-public key and youngster index. So the inputs for the HMAC-SHA512 are:
KEY: c547d66d20e80779c2b7a48e9d59f989ae8c3e2bf3e8eb752aae9fb555ad5123
DATA: 00f36ab72ee8ddc6c9288a3a26dc5f1009198bd37169dfb6ddc93b7c237b63b23180000054
You may once more use the identical on-line device. The result’s:
4eb98f36d3bd9c27c2d74ae497e2dba29e3af8365b1de8fc29dd2f39b8111017841d3b7767023d0d985618d4a6b8d466aaac220155cb1fb18739836a86f2c223
Subsequent, following BIP32, the best 32 bytes symbolize the kid’s chain key, and to get the kid’s non-public key, the subsequent factor we have to do is add the left half of the end result (4eb98f36d3bd9c27c2d74ae497e2dba29e3af8365b1de8fc29dd2f39b8111017) and the mum or dad’s non-public key (f36ab72ee8ddc6c9288a3a26dc5f1009198bd37169dfb6ddc93b7c237b63b231). Additionally, the MOD operation needs to be carried out on the obtained end result. The secp256k1 elliptic curve order is used for this. Order of the secp256k1 elliptic curve is FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE BAAEDCE6 AF48A03B BFD25E8C D0364141. Subsequent two photos present how to do that utilizing this on-line device.
So, the eighty fifth hardened youngster non-public key and its chain code are:
CHILD PRIVATE KEY: 42244665bc9b62f0eb61850b7441ebacfd17eec115b4ff9e33464cd0633e8107
CHILD CHAIN CODE: 841d3b7767023d0d985618d4a6b8d466aaac220155cb1fb18739836a86f2c223
Completely the identical mechanism is used to get the subsequent two youngsters within the BIP84 derivation path. The one distinction is that the index of the kid is 0, that’s 2147483648 (hex: 80000000) since it’s a hardened derivation. That is why I’ll write solely the outcomes.
m/84’/0′
CHILD PRIVATE KEY: 68155c2b225b592f73e2f812a307d9a15f4cb352cf3fc12e80fea185c63a176e
CHILD CHAIN CODE: 52da1bc66383744a78001a8b504d5d28c1fea7b98a95c361a8d8cc23fb371345
m/84’/0’/0′
CHILD PRIVATE KEY: f4f8cb21aae3e6b3df7acee3f65bb592824b770ecbbc6ebe1efa4479d4950978
CHILD CHAIN CODE: f871e9c89e2ad059573dbd49bc14f6d1d2b1d444027ec12c23d2ede7b921175f
The remaining two youngsters we have to discover (m/84’/0’/0’/0 and m/84’/0’/0’/0/0) are derived utilizing non-hardened (regular) derivation. The process is kind of the identical, with the truth that within the HMAC-SHA512 perform, the non-public key just isn’t forwarded, however the public key. Subsequently, based mostly on the non-public key, it’s first crucial to search out its public key. I can’t go into the main points of this.
To discover a public key from a personal key, you should utilize this on-line device.
So, for the non-public key f4f8cb21aae3e6b3df7acee3f65bb592824b770ecbbc6ebe1efa4479d4950978, the corresponding uncompressed public secret is:
04576DF6CA4FA6D5347899277169CD38646F74E35A391F85DBDAFD3DE697F106979CDEA7B904A7B6F254BD3635ABEDCB140CBBDBBC2A81E7CB7223259B846E7BB2
The issue right here is that we’d like a compressed public key, so we will once more use one of many on-line device. So the compressed public secret is:
PRIVATE KEY: f4f8cb21aae3e6b3df7acee3f65bb592824b770ecbbc6ebe1efa4479d4950978
PUBLIC KEY: 02576df6ca4fa6d5347899277169cd38646f74e35a391f85dbdafd3de697f10697
Now we’ve all the pieces we have to discover a non-hardened youngster non-public key. BIP32 says that we have to use HMAC-SHA512 perform the place the hot button is mum or dad chain code, and the date is the concatenation of the (now) mum or dad public key and the kid index. So the inputs to the HMAC-SHA512 are:
KEY: f871e9c89e2ad059573dbd49bc14f6d1d2b1d444027ec12c23d2ede7b921175f
DATA: 02576df6ca4fa6d5347899277169cd38646f74e35a391f85dbdafd3de697f1069700000000
The additional course of is strictly the identical as with hardened derivation. The left half of the result’s added with the mum or dad’s non-public key, after which the MOD operation is carried out. On this manner, the kid’s non-public secret is obtained. The proper facet of the end result represents the chain code of the kid. Thus:
RESULT: ef2ca2404a289aefb8ed2327215ed0660524d470394e06d4c6cd665e23191ffd1ba81f4c432bba50b8c1089b4030e4edf71ada1ac83962f745dc3769525d004c
CHILD PRIVATE KEY: e4256d61f50c81a39867f20b17ba85f9ccc16e9855c1d55725f54c4b2777e834
CHILD CHAIN CODE: 1ba81f4c432bba50b8c1089b4030e4edf71ada1ac83962f745dc3769525d004c
And for the final youngster (m/84’/0’/0’/0/0):
PARENT PRIVATE KEY: e4256d61f50c81a39867f20b17ba85f9ccc16e9855c1d55725f54c4b2777e834
PARENT PUBLIC KEY: 03ad87f5eb4b30ba3aa1b4713cacb4d722b47d729ac0b24c4c9810d4d2d11981ed
CHILD PRIVATE KEY: 879bef1ec302343d2c722fbfbd313165f2e1ef4828b0e74249bcef6e15ec55db
CHILD CHAIN CODE: f0aebf37903b4bd76d90456771c6673ff2b09bbd58435d54afb69089e30791ca
CHILD PUBLIC KEY: 0299c5b020a59dbe0059292b9c78f869ed82768de29184cd60feafd33db3f4e0e2
And that’s that. Now we have obtained the general public key for the trail m/84’/0’/0’/0/0. The one factor left is to calculate the tackle and encode it with bech32. To get a P2WPKH tackle in Bitcoin, it’s worthwhile to do RIPEMD160 (SHA256 (public key)). So we’ve the next:
PUBLIC KEY: 0299c5b020a59dbe0059292b9c78f869ed82768de29184cd60feafd33db3f4e0e2
SHA256(PUBLIC KEY): 2152377138127c59daf69fc627325d1b1b76c775a3c1e5063dd6f265cf7bb4b1
RIPEMD160(SHA256(PUBLIC KEY)): a791cf441333a2ecfafeb144342994c31146fa4f
On the finish we simply have to encode a791cf441333a2ecfafeb144342994c31146fa4f in bech32. For that, we will use this on-line device.
This fashion we get the tackle you requested for (bc1q57gu73qnxw3we7h7k9zrg2v5cvg5d7j0g5y6d4).
