Determining the First Byte (Recovery ID) of Ethereum Signatures
As a developer, it is essential to understand how Ethereum works with signatures and private keys. In this article, we will walk through the process of determining the first byte (recovery ID) of Ethereum signatures.
What is a signature?
A signature on a blockchain is a digital representation of a message that confirms its origin and ownership. It consists of three parts: the signature, the signed data, and the associated public key.
How are signatures created and returned?
When a node (such as a miner) wants to verify the authenticity of a transaction or message, it uses a signature to ensure that the sender has control over the data. The process involves:
- Generating a private key (P)
- Using the private key to create a digital signature using the recipient’s public key (K)
- Storing the digital signature in the database
When someone wants to sign a message, they use their private key to create a digital signature and send it along with the message. The first byte of this signature is called the
Recovery ID.
Recovery ID Formula
To determine the Recovery ID, we need to understand how the algorithm works:
- Start with the sender’s public key (K)
- Add the transaction details (including the message and other important information)
- Combine the merged data using a cryptographic hash function (e.g. SHA-256 or Keccak-256)
The resulting hash is then used as input to the
Keccak-256 digital signature scheme.
To recover the sender’s private key, we need to perform the following steps:
- Extract the first byte of the recovered signature
- Use this byte to compute the public key (K_prime) using the formula: “K_prime = K * pow(K^(-1), hash digest)”
- Combine the extracted private key and the computed public key to obtain the sender’s private key (P).
Sample Statements
Suppose we have a transaction that includes the following data:
Message: “Hello, world!”
Sender’s public key: “K=0x1234567890abcdef”
The hash of the merged data is generated as follows:
Transaction data: “message + sender_data”.
Hash digest: “0x1234567890abcdef”.
Using the Keccak-256 digital signature scheme, we get a recovered signature with the first byte (the Recovery ID).
To recover the sender’s private key, we need to calculate the public key using the formula above.
Conclusion
Determining the first byte (Recovery ID) of Ethereum signatures is a critical step in verifying the authenticity of a message. By understanding how this process works, developers can create reliable cryptographic algorithms and applications that rely on digital signatures. This article provides a detailed overview of the Recovery ID formula and its implementation in Ethereum.