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Ethereum: How to determine first byte (recovery ID) for signatures (message signing)?

Published by Terlumun Aondover on February 5th, 2025.

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Determining the First Byte (Recovery ID) of Signatures on Ethereum

As a developer, it’s essential to understand how Ethereum works with signatures and private keys. In this article, we’ll explore the process of determining the first byte (recovery ID) for signatures in Ethereum.

What is a Signature?

A signature on blockchain is a digital representation of a message that confirms its origin and ownership. It consists of three parts: the signature, the data being signed, and the public key associated with it.

How are Signatures Created and Returned?

When a node (like a miner) wants to verify the authenticity of a transaction or message, it uses the 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 a database

When someone wants to sign a message, they use their own 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

Ethereum: How to determine first byte (recovery ID) for signatures (message signing)?

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The Recovery ID Formula

To determine the recovery ID, we need to understand how the algorithm works:

Start with the sender’s public key (K)

Append the transaction data (including the message and other relevant information)

Hash the concatenated 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 a 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)

Example Walkthrough

Suppose we have a transaction that includes the following data:

Message: “Hello, world!”

Sender’s public key: K = 0x1234567890abcdef

The hash of the concatenated 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 a first byte (`recovery ID’).

Recovering the sender’s private key involves computing the public key using the formula above.

Conclusion

Determining the first byte (recovery ID) of signatures on Ethereum is an essential step in verifying message authenticity. By understanding how this process works, developers can build robust cryptographic algorithms and applications that rely on digital signatures. This article provides a comprehensive overview of the recovery ID formula and its implementation on Ethereum.

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