Bitcoin transactions are verified through a decentralized process involving multiple nodes in the Bitcoin network. This verification process ensures that transactions are legitimate, preventing double-spending and maintaining the integrity of the blockchain. Here’s a detailed explanation of how Bitcoin transactions are verified.

Steps in the Verification Process

1. Transaction Creation:

   A user creates a transaction by specifying the amount to send, the recipient's address, and the inputs (previous transaction outputs being spent). The transaction is then signed with the sender's private key, creating a digital signature.

2. Broadcasting the Transaction:

   The signed transaction is broadcast to the Bitcoin network, where it is propagated to all connected nodes.

3. Transaction Validation by Nodes:

   Each node that receives the transaction performs several checks:

   • Signature Verification:

     Nodes verify the digital signature to ensure that the sender is authorized to spend the Bitcoin. This is done using the sender's public key.

   • Input Validation:

     Nodes check that the inputs referenced in the transaction are valid and have not been spent. They confirm that the transaction ID and output index correspond to existing, unspent outputs.

   • Sufficient Funds:

     Nodes ensure that the sender has enough Bitcoin in their wallet to cover the amount being sent plus any transaction fees.

4. Inclusion in a Block:

   Once validated, the transaction enters the mempool (memory pool) of the node, where it waits to be included in a block. Miners select transactions from the mempool based on transaction fees and other criteria.

5. Mining and Consensus:

   Miners compete to solve a complex mathematical puzzle (Proof of Work) to create a new block. When a miner successfully mines a block containing the transaction, the block is added to the blockchain. The consensus mechanism ensures that all nodes agree on the state of the blockchain.

6. Confirmation:

   Once a transaction is included in a block, it receives its first confirmation. As more blocks are added on top of that block, the transaction receives additional confirmations, increasing its security and finality.

Sample Code: Verifying a Bitcoin Transaction

The following sample code demonstrates how to verify a Bitcoin transaction using the bitcoinjs-lib library in JavaScript. This example focuses on signature verification:

    const bitcoin = require('bitcoinjs-lib');
    const bitcoinMessage = require('bitcoinjs-message');

    // Example transaction details
    const txDetails = {
        txid: 'previous_transaction_id', // Replace with actual TXID
        vout: 0, // Output index
        amount: 100000, // Amount in satoshis
        recipient: 'recipient_address', // Replace with actual recipient address
    };

    // Sender's private and public keys
    const senderKeyPair = bitcoin.ECPair.fromPrivateKey(Buffer.from('your_private_key', 'hex')); // Replace with actual private key
    const senderAddress = bitcoin.payments.p2pkh({ pubkey: senderKeyPair.publicKey }).address;

    // Create a transaction
    const txb = new bitcoin.TransactionBuilder(bitcoin.networks.bitcoin);
    txb.addInput(txDetails.txid, txDetails.vout);
    txb.addOutput(txDetails.recipient, txDetails.amount);
    
    // Sign the transaction
    txb.sign(0, senderKeyPair);
    
    // Get the transaction hex
    const transactionHex = txb.build().toHex();

    // Verify the signature
    const isValid = bitcoinMessage.verify(transactionHex, senderAddress, txDetails.amount, senderKeyPair);
    console.log('Transaction is valid:', isValid);