Digital signature

Digital signatures are a fundamental building block of blockchain technology, ensuring security, authenticity, and trust in transactions. They provide a way to prove that a particular message or transaction was created by a specific user and has not been tampered with during transmission. In blockchain systems like Bitcoin and Ethereum, digital signatures make it possible for users to securely transfer ownership of digital assets without relying on a central authority.

Concept of Public-Private Key Cryptography

At the heart of digital signatures lies public-private key cryptography, also known as asymmetric cryptography. Each user generates a pair of keys:

• A private key (kept secret and never shared).
• A public key (shared openly).

The private key is used to create a digital signature, while the public key is used by others to verify that signature. This system ensures that only the rightful owner of the private key can sign a transaction, but anyone can verify its authenticity using the corresponding public key.

Example 1: Proving Identity

Imagine Alice has a private key and a public key. If she wants to prove her identity to Bob, she can sign a message like “I am Alice” with her private key. When Bob receives this signed message, he uses Alice’s public key to verify the signature. If the verification succeeds, Bob knows two things:

1. The message was indeed signed by Alice (authenticity).
2. The message wasn’t changed in transit (integrity).

Example 2: Sending a Transaction

Suppose Alice wants to send 2 BTC (Bitcoin) to Bob:

1. Alice creates a transaction: “Send 2 BTC to Bob’s address.”
2. She runs the transaction through a hash function (SHA-256 in Bitcoin).
3. She signs this hash with her private key, creating a digital signature.
4. Alice sends the transaction + her signature to the Bitcoin network.
5. Every node uses Alice’s public key to verify that the signature matches the transaction.
6. If verification passes, the network accepts that only Alice (who holds the private key) could have authorized this transfer.

In this way, Alice never shares her private key, yet the entire network can be confident that the transaction is legitimate.

Signing and Verifying Transactions

The signing process involves taking a transaction’s data (e.g., sender, receiver, and amount) and running it through a hash function (such as SHA-256). The result is a unique, fixed-size hash representing the transaction. This hash is then encrypted using the sender’s private key, creating the digital signature.

Verification happens when the network nodes or the recipient take the transaction hash and the sender’s signature, then use the sender’s public key to decrypt and confirm that the signature matches the transaction data. If the two match, it proves two things:

1. The transaction was created by the owner of the private key.
2. The transaction data has not been altered (since even a small change would create a completely different hash).

Example: If Alice sends 2 ETH to Bob, she signs the transaction with her private key. The Ethereum network validates her signature using her public key before including the transaction in a block.

ECDSA (Elliptic Curve Digital Signature Algorithm)

Most modern blockchain platforms, including Bitcoin and Ethereum, use the Elliptic Curve Digital Signature Algorithm (ECDSA) for generating and verifying digital signatures. ECDSA is a variant of the Digital Signature Algorithm (DSA), but it leverages the mathematics of elliptic curves, which provide the same level of security with much smaller key sizes compared to other algorithms like RSA.

• A 256-bit ECDSA key offers security comparable to a 3072-bit RSA key, making ECDSA efficient for blockchain, where storage and computational resources must be optimized.
• The elliptic curve used in Bitcoin and Ethereum is called secp256k1.
• The security of ECDSA relies on the difficulty of solving the Elliptic Curve Discrete Logarithm Problem (ECDLP), which is computationally infeasible to break with current technology.

Example: How Ethereum Uses ECDSA

Ethereum relies on ECDSA over secp256k1 to secure accounts and transactions. Every Ethereum account is derived from a private key, which generates a corresponding public key, and finally, the Ethereum address (the last 20 bytes of the hashed public key).

When a user sends a transaction (e.g., transferring ETH, deploying a smart contract, or calling a contract function):

1. The transaction details (nonce, gas price, gas limit, recipient, value, and data) are hashed using Keccak-256.
2. The sender signs the hash with their private key using ECDSA.
3. The signature is included in the transaction broadcast to the Ethereum network.
4. Any node can take the transaction data and the signature, use the sender’s public key, and verify that the transaction is valid.
5. The public key also allows nodes to recover the sender’s Ethereum address, ensuring that the transaction indeed came from the rightful account holder.

Example: Suppose Alice wants to send 1 ETH to Bob. She signs the transaction with her private key. The Ethereum network verifies the signature using her public key. If valid, the transaction is added to the blockchain. This process prevents fraud (no one else can spend Alice’s ETH without her private key) and ensures integrity (the transaction cannot be altered after signing).

In summary, digital signatures provide authentication, integrity, and non-repudiation in blockchain. Public-private key cryptography ensures secure ownership, while ECDSA offers strong protection with efficient computation, and Ethereum’s implementation ensures trustless, decentralized verification of transactions.