The Hash Preimage Problem in Bitcoin Transactions
The hash preimage problem is a fundamental aspect of block verification in the Bitcoin network. It refers to the challenge of determining the input value for a given output hash in a 2-input transaction, without knowing the corresponding preimage hash.
What is a 2-input transaction?
In Bitcoin, transactions are 2-input transactions, meaning that two inputs are required: a sender and a receiver. The sender provides a certain amount of bitcoins (often called “satoshis”) to the receiver, in addition to providing their own input value (such as a unique identifier or a non-cryptographic parameter). This transaction is verified by the Bitcoin node to ensure that it complies with the rules and restrictions of the network.
The Hash Preimage Problem
When verifying a 2-input transaction, the Bitcoin node reconstructs the hash preimage of the transaction from the provided input value. In other words, given a transaction with an output hash H
, we need to find an input value x
such that:
H = m + x
where m
is the sender’s signature for the transaction and x
is the receiver’s input value.
What is the hash preimage of a 2-input transaction?
To solve this problem, Bitcoin nodes use a combination of hash functions and precomputation tables to reconstruct the hash preimage. Specifically, they:
- Precompute hash values for all possible inputs
x
(from 0 to 255) and the output hashesH
.
- Use these precomputed hash values to create a table of “candidate” input values.
- When verifying a transaction, the node reconstructs the hash preimage by finding an input value
x
in the candidate list that matches the given output hashH
.
The challenge is solvable
The key point here is that the Bitcoin node has already precomputed and stored the hash values for all possible input x
and output hashes H
. This allows them to quickly reconstruct the hash preimage by finding an input value x
that matches the given output hash H
.
Conclusion
In conclusion, the hash-preimage problem is a critical aspect of block verification in Bitcoin transactions. By precomputing and storing the hash values for all possible input x
and output hashes H
, Bitcoin nodes can quickly reconstruct the hash preimage and verify 2-input transactions without requiring extensive computations or hash table lookups.
Example code
Here is an example of how a Bitcoin node can reconstruct the hash preimage:
// Precompute hash values for all possible inputs x (0-255)
uint256[256] Precomputed Hashes = {
// ...
};
// Create a candidate list of input values that match each output hash H
uint256[] candidate inputs = {
// ...
};
// Reconstruct the hash-preimage by finding an input value x in the candidate list that matches the given output hash H
uint256 hashPreimage = 0;
for (uint256 i = 0; i < 256; i++) {
if (precomputedHashes[i] == h) {
hashPreimage = i;
break;
}
}
Note: This is a simplified example and the actual implementation may vary depending on the specific Bitcoin node requirements.