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Ethereum: Nonce usage in ECDSA signing algorithm

Published by Terlumun Aondover on February 8th, 2025.

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Understanding Nonce Usage in Ethereum’s ECDSA Signing Algorithm

When it comes to cryptographic operations, understanding the details of how various algorithms work can be crucial for ensuring security and robustness. In this article, we’ll dive into the specifics of nonce usage in Ethereum’s ECDSA signing algorithm, which is employed by the secp256k1_ecdsa_sig_sign() function.

ECDSA Overview

Ethereum: Nonce usage in ECDSA signing algorithm

Ethereum’s ECDSA (Elliptic Curve Digital Signature Algorithm) is a widely used cryptographic standard for secure data transmission. It relies on the Elliptic Curve Discrete Logarithm problem (ECDLP), which provides a fast and efficient method for generating signatures from private keys.

Secp256k1 ECDSA

The secp256k1 ECDSA implementation provided by Ethereum is one of the most widely used variants in the ecosystem. It uses a variant of the Elliptic Curve Digital Signature Algorithm, optimized for performance on the Ethereum blockchain.

ECDSA Signatures and Nonce Usage

In an ECDSA signature generation process, the following steps are typically performed:

Private key initialization: The user’s private key is initialized with a random value.

Hashing: The user’s input data (also known as the message) is hashed using the SHA-256 hash function to produce a unique digest.

Private key derivation: A cryptographic hash function (e.g., Argon2) is applied to the private key and the hashed message, producing a new value.

Signature generation: The output of step 3 is used to generate an ECDSA signature.

The secp256k1_ecdsa_sig_sign() function takes several parameters, including:

ctx: An instance of the secp256k1_ecmult_gen_context structure, which represents the elliptic curve and other cryptographic context.

data: The input message to be signed.

d: A random value used for signature generation.

s: The ECDSA signature generated by the function.

Nonce Usage

One of the key features of nonces in cryptographic algorithms is their ability to prevent replay attacks. In the context of ECDSA, a nonce (short for “number”) is a unique value added to each transaction or message that allows it to be verified and authenticated.

In Ethereum’s secp256k1 ECDSA implementation, the secp256k1_ecdsa_sig_sign() function uses a mechanism called “nonce padding” to prevent replay attacks. Here’s how:

Each time a new transaction is sent, a random nonce value is generated using the SHA-256 hash of the transaction data.

The nonce value is appended to each transaction using padding (e.g., concatenation) and then hashed with another cryptographic function (e.g., Argon2).

The resulting padded hash value serves as the signature for that transaction.

The secp256k1_ecdsa_sig_sign() function does not explicitly use a nonce. Instead, it relies on the implementation of the secp256k1_ecdsa_sig_sign() function to generate and manage the nonce values used in each transaction.

Example Use Case

To illustrate how nonces work in Ethereum’s ECDSA signing algorithm, let’s consider an example:

Suppose we want to sign a message “Hello, World!” with a private key that has a random nonce value generated using the SHA-256 hash of the message. The resulting signature would be something like 0x..., where the ellipsis represents the padded hash value.

Here is some sample code demonstrating how to generate and verify an ECDSA signature in Ethereum using the secp256k1_ecdsa_sig_sign() function:

“`c

#include

#include <ethers/hasher.