Taking a number of steps again, it is useful to do not forget that a taproot “deal with” is only a bech32m encoding of a public key. The vast majority of wallets in the present day generate these public keys utilizing BIP32, the place youngster keys are derived from a grasp key. That is probably the place you are getting the quantity “4 billion addresses.” It is vital to level out, nonetheless, all you should create a taproot output is a sound public key.
BIP352 (Silent funds) is completely different in that there isn’t a derivation or pre-generation of addresses by the recipient. The sender creates a public key for the recipient and encodes it as a taproot output. For particulars on how the sender creates this public key for the recipient, I might advocate studying the overview part of BIP352. At a excessive stage, nonetheless, the vital particulars are:
- The sender first creates a shared secret between them and the recipient by multiplying the sum of their personal keys with the recipients scan public key (i.e., Elliptic Curve Diffie-Hellman key alternate)
- This shared secret is become a public key added to the sender’s spend public key, making certain the ensuing output is simply spendable by the recipient
- The ensuing public key (shared secret + recipients spend public key) is encoded as a taproot output within the transaction
The ensuing public secret is distinctive to this transaction. If the sender sends once more to the identical recipient silent fee deal with, they’ll essentially have to make use of completely different UTXOs, which in flip ensures every silent fee output is exclusive to the transaction it’s in.