Posted on February 14, 2025
Bitcoin Digital Signatures and Ledger Integrity
To understand how Bitcoin uses digital signatures to create a tamper-proof ledger, we need to dive into several key concepts of cryptography and blockchain technology:
Digital Signatures
1. Public Key Cryptography:
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Bitcoin uses public key cryptography, where each user has a pair of keys:
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Public Key: This is openly shared and used to verify signatures.
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Private Key: This is kept secret and used to create signatures.
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2. How Signatures Work:
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When a user wants to send Bitcoin, they sign the transaction with their private key. This signature is a cryptographic proof that the transaction came from the owner of the private key, without revealing the key itself.
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The signature can be verified by anyone using the corresponding public key. This ensures that only the owner of the private key could have created the signature.
3. Signature Algorithm:
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Bitcoin uses the Elliptic Curve Digital Signature Algorithm (ECDSA) for creating signatures. It’s chosen for its security and efficiency, providing strong authentication with relatively small key sizes.
Creating a Tamper-Proof Ledger
1. Transaction Integrity:
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Each transaction includes:
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Inputs: References to previous transactions which are being spent.
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Outputs: Addresses and amounts of Bitcoin being sent.
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Signature: Proof of ownership for each input.
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The digital signature ensures that the transaction cannot be altered after being signed. If any part of the transaction (like the recipient or amount) is changed, the signature would no longer match, making the transaction invalid.
2. Chain of Ownership:
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Transactions are linked in a chain where the output of one transaction becomes the input for another. This chaining ensures:
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Double-Spending Prevention: An output cannot be spent more than once because once spent, it’s removed from the pool of spendable outputs.
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Ownership Proof: Each transaction proves ownership by linking back to previous transactions through signatures.
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3. Blockchain Structure:
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Transactions are grouped into blocks. Each block:
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Contains a list of transactions.
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Includes a cryptographic hash of the previous block, linking it in a chain (hence, blockchain).
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Has its own unique hash based on its contents, including the Merkle root of all transactions within.
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Hash Functions: These ensure that even the slightest change in transaction data would result in a completely different hash, making any alteration easily detectable.
4. Network Verification:
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When a transaction is broadcast to the network, nodes check:
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The validity of the signature against the transaction data.
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That the outputs being spent have not been spent before (using the UTXO set – Unspent Transaction Output).
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Miners confirm transactions by including them in blocks and solving a computational puzzle (Proof of Work), which links the block to the chain.
5. Consensus Mechanism:
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The decentralized nature of Bitcoin means that consensus on the state of the ledger (which transactions have happened) is achieved through widespread agreement among nodes. Any attempt to alter history would require redoing all subsequent work, which is computationally infeasible due to Proof of Work.
Conclusion
The combination of digital signatures, cryptographic hashing, and the structure of the blockchain creates a ledger that is extremely resistant to tampering. Each transaction’s integrity is maintained by its signature, while the blockchain’s structure ensures that altering one transaction would require altering all subsequent blocks, a task made impractical by the network’s consensus and the energy-intensive Proof of Work mechanism. This system collectively ensures that Bitcoin’s ledger is tamper-proof, providing security, transparency, and trustless operation in a decentralized environment.
