Understanding Bitcoin Root Roots: Can a single address have 160 bits and 4 root roots?
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 root root representation. The root root is a unique fingerprint that represents the validity of an address 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 root root representation of 12345.
Root Roots: A Brief Overview
Bitcoin root roots 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 root is then converted into a human-readable string using algorithms such as 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 hash of the public key. This format is widely used in Bitcoin to reduce the complexity of storing and transmitting addresses.
Converting the root to a P2PKH address
To convert a root to a p2pkh address, you need to perform two separate operations:
- Calculate the hash of each byte in the root.
- Combine these hashes into a single 160-bit number.
Unfortunately, it is not possible to directly convert a single root value (12345) into a p2pkh address. The reason for this lies in the way the Bitcoin public key is generated and stored.
Why primary roots cannot be equivalently represented as P2PKH addresses
When you create an address, its underlying 160-bit number is hashed to produce the primary root representation. This process involves several steps, including:
- Generating a new public key.
- Hashing each byte of the public key.
- Combining these hashes into a single primary root.
To achieve the same result as converting a primary root 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 neither practical nor efficient.
Theoretical Limitations: A single address cannot have 160 bits and 4 hash roots
In theory, there are some limitations to the representation of Bitcoin addresses:
- 256-bit hash roots vs. P2PKH addresses: The size of the hash root (256 bits) is a fundamental property that determines its representation power. A single hash root value cannot be directly converted to 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 restriction limits the possible combinations of hash values for each byte.
In conclusion, while it may seem plausible to create a single address that can represent both its hash root value and the p2pkh format, the underlying mathematical restrictions 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 is 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 such as BIP39 or BIP44, which provide more flexibility for generating private keys and representing addresses.
