Understanding Bitcoin Taproots: Can a Single Address Be Both 160-Bit and 4-Taproot?
When you create a new Bitcoin address, it is represented in two different ways: as a human-readable string (e.g., “1A2B3C4D5E6F7G8H9I0J”) and as a taproot representation. The taproot is a unique digital fingerprint that represents an address’s validity and allows for efficient storage and retrieval of Bitcoin data. In this article, we will explore whether Bob can send his BTC to user “Alice” using a p2pkh address whose underlying 160-bit number is equivalent to the Taproot representation of 12345.
Taproots: A Brief Overview
Bitcoin taproots are created by computing the hash of each byte in an address’s public key. This process results in a unique, 256-bit (or 32-byte) value that represents the entire address. The resulting taproot is then converted into a human-readable string using algorithms like BIP39 or BIP44.
P2PKH Addresses: A Simplified Representation
A p2pkh (Public Key Address) is a simplified representation of an address, consisting of a single 160-bit number followed by the public key’s hash. This format is widely used in Bitcoin to reduce the complexity of storing and transmitting addresses.
Converting Taproot to P2PKH Address
To convert a taproot to a p2pkh address, you need to perform two separate operations:
- Compute the hash of each byte in the taproot.
- Combine these hashes into a single 160-bit number.
Unfortunately, it is not possible to directly convert a single taproot value (12345) into a p2pkh address. The reason for this lies in the way Bitcoin’s public key is generated and stored.
Why Taproots Can’t Be Equivalently Represented as P2PKH Addresses
When you create an address, its underlying 160-bit number is hashed to produce the taproot representation. This process involves multiple steps, including:
- Generating a new public key.
- Hashing each byte of the public key.
- Combining these hashes into a single taproot.
To achieve the same result as converting a taproot directly into a p2pkh address, you would need to generate a new Bitcoin private key and hash it multiple times to produce different 160-bit numbers. However, this approach is not practical or efficient.
Theoretical Limitations: A Single Address Can’t Be Both 160-Bit and 4-Taproot
In theory, there are some limitations on the representation of Bitcoin addresses:
- 256-bit Taproots vs. P2PKH Addresses: The taproot’s size (256 bits) is a fundamental property that determines its representational power. A single taproot value cannot be directly converted into a p2pkh address because it exceeds the capacity of a 160-bit number.
- Address Length and Structure
: Bitcoin addresses have a maximum length of 64 characters, which includes the first byte (the seed). This constraint limits the possible combinations of hash values for each byte.
In conclusion, while it might seem plausible to create a single address that can represent both its taproot value and p2pkh format, the underlying mathematical constraints make this impossible. Bob cannot send his BTC to Alice using a p2pkh address whose underlying 160-bit number is equivalent to the Taproot representation of 12345.
Recommendation: Use Standard P2PKH Addresses
For most practical purposes, it’s recommended to use standard p2pkh addresses when interacting with Bitcoin. These formats are efficient, easy to understand, and provide a clear representation of an address’s validity.
If you need to implement specific requirements or optimizations for your Bitcoin-related applications, consider using additional tools like BIP39 or BIP44, which provide more flexibility in generating private keys and representing addresses.
