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Bitcoin: Which is the hash-preimage of a 2-input transaction?

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:

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.

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