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 referred to as “satoshis”) to the receiver, while also providing its own input value (such as a unique identifier or non-cryptographic parameter). This transaction is verified by the Bitcoin node to ensure that it complies with the rules and constraints of the network.

The Hash-Preimage Problem

When verifying a 2-input transaction, the Bitcoin node reconstructs the preimage hash 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 recipient’s input value.

What is the preimage Hash of a 2-input transaction?

To solve this problem, Bitcoin nodes use a combination of hash functions and precompute tables to reconstruct the hash preimage. Specifically, they:

• Precompute hash values ​​​​for all possible inputs x (from 0 to 255) and output hashes H.

• Use these precomputed hash values ​​​​to build a table of “candidate” input values.

• When verifying a transaction, the node reconstructs the hash preimage by finding an input value x in the list of candidates that matches the given output hash H.

The challenge is solvable

The key insight here is that the Bitcoin node has already precomputed and stored the hash values ​​​​for all possible inputs x and output hashes H. This allows them to quickly reconstruct the hash preimage by finding an input value x that corresponds to 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 hash values ​​​​for all possible inputs 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.

Code Example

Here is an example of how a Bitcoin node might reconstruct the hash preimage:

// Precompute hash values ​​​​for all possible inputs x (0-255)
uint256[256] precomputedHashes = {
// ...
};
// Build a candidate list of input values ​​​​that correspond to each output hash H
uint256[] candidateInputs = {
// ...
};
// Reconstruct the hash preimage by finding an input value x in the candidate list that corresponds to the given output hash H
uint256 hashPreimage = 0;
for (uint256 i = 0; i < 256; i++) {
if (hashes precalculated[i] == h) {
hashPreimage = i;
break
}
}

Note: This is a simplified example and the actual implementation may vary depending on the specific requirements of the Bitcoin node.