# Ethereum Addresses ## Ethereum Addresses Ethereum addresses are 40 hexadecimal characters long, excluding the "0x" prefix. This makes each address 20 bytes (160 bits) in length. * **20 Bytes Long**: An Ethereum address is derived from the last 20 bytes of the Keccak-256 hash of the public key. * **160 Bits**: This length provides a vast address space, which helps avoid address collisions and enhances security. ## How to get a Private Key When you got your first Ethereum address, you mostly likely used a tool like MetaMask or a Ledger which gave you a `Seed Phrase`. But that `Seed Phrase` is a string of 12-24 words, so how does that relate to your address? {% code title="Seed Phrase Example" %} ``` twin galaxy such vague current rhythm about laundry upset fatigue fragile whisper ``` {% endcode %} The specific words chosen matter, and the details of how they work can be found here: {% embed url="" %} A single `Seed Phrase` can be used to generate a nearly infinite number of Ethereum addresses. Those addresses are generated using a specific hierarchical deterministic derivation path explained in great detail [here](https://medium.com/myetherwallet/hd-wallets-and-derivation-paths-explained-865a643c7bf2). {% hint style="info" %} What if you want to generate your own `Private Key`? Well since a `Private Key` is simply a binary number 256 digits long, you could flip a coin 256 times counting heads as 1 and tails as 0. {% endhint %} ## Step-by-Step Example
TypeValue
Seed Phrasetwin galaxy such vague current rhythm about laundry upset fatigue fragile whisper
Private Key
Base 2 (Binary)		1010011111101000000011001001111010101100011110010111100010000101110010101101100011010110101111011111101010100110011000111110000100101111100100011101110101100100001110101100000000011111111100111000111001010010111110011100110000110101110010010010010100011011
Private Key
Hexadecimal		0xa7e80c9eac797885cad8d6bdfaa663e12f91dd643ac01ff38e52f9cc35c9251b
{% embed url="" fullWidth="true" %} Live example showing Ethereum address derivation from a private key {% endembed %}
Code to generate an Ethereum address from a private key {% code fullWidth="true" %} ```html Ethereum Public Key Generator 

2. Public Key:
...
3. Keccak-256 Hash of Public Key:
...
4. Ethereum Address:
...
``` {% endcode %}
1. **Generate a Private Key.** This is a random 256-bit number. For simplicity, let's use a hexadecimal representation: {% code title="Private Key" %} ``` 0xa7e80c9eac797885cad8d6bdfaa663e12f91dd643ac01ff38e52f9cc35c9251b ``` {% endcode %} 2. **Generate the Public Key.** The public key is derived from the private key using Elliptic Curve Cryptography (ECC), specifically the secp256k1 curve. The resulting public key is a 512-bit number (128 hexadecimal characters): ```javascript wallet = new ethers.Wallet(privateKey); publicKey = wallet.signingKey.publicKey; ``` {% code title="Public Key" overflow="wrap" %} ``` 0x04f743d6226bab9de56e067f068371bbe1967ab0f8b32c86b0360f5c9a8dfd3fd03994f9babf7b5efcec75c78f9efa4668df930da585b1d57b8c2b4f7de5a6849d ``` {% endcode %} 3. **Keccak-256 Hash of the Public Key.** Ethereum uses the Keccak-256 hash function (a variant of SHA-3) to hash the public key. Note that only the x and y coordinates of the public key (excluding the initial '0x04' byte) are hashed. ```javascript // Slice the `0x04` from the start of the publicKey const publicKeyFormatted = '0x' + publicKey.slice(4); // Convert the public key to a byte array using ethers.getBytes. const publicKeyBytes = ethers.getBytes(publicKeyFormatted); // Perform Keccak-256 hash of the public key const publicKeyHash = ethers.keccak256(publicKeyBytes); ``` {% code title="Public Key (no '0x04')" overflow="wrap" %} ``` 0xf743d6226bab9de56e067f068371bbe1967ab0f8b32c86b0360f5c9a8dfd3fd03994f9babf7b5efcec75c78f9efa4668df930da585b1d57b8c2b4f7de5a6849d ``` {% endcode %} {% code title="Keccak-256 Hash" %} ``` 0x624d10d9dd0d1f68800320293872e96f79890737fcf74aa85d6d760a5a451fe9 ``` {% endcode %} {% hint style="info" %} The initial '0x04' byte is a prefix used in the uncompressed format of an elliptic curve public key. This prefix indicates that the public key is represented in an uncompressed form, which includes both the x and y coordinates of the point on the elliptic curve. **Uncompressed Format**: * The public key consists of a prefix '0x04' followed by the x coordinate and the y coordinate of the elliptic curve point. * The format is: `0x04 ` **Compressed Format**: * The public key consists of a prefix '0x02' or '0x03' followed by only the x coordinate. * The prefix '0x02' is used if the y coordinate is even, and '0x03' is used if the y coordinate is odd. The '0x04' prefix is removed because it is not part of the essential elliptic curve point data (x and y coordinates). It merely indicates that the data following it is an uncompressed public key. For the purpose of hashing and deriving the Ethereum address, only the actual coordinates of the elliptic curve point are relevant, and thus the prefix is excluded. {% endhint %} 4. **Ethereum Address.** The Ethereum address is derived from the last 20 bytes of the Keccak-256 hash. ```javascript const ethereumAddress = wallet.address ``` {% code title="Ethereum Address" %} ``` 0x3872E96F79890737fCf74aa85D6d760a5a451Fe9 ``` {% endcode %} --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://docs.eridian.xyz/ethereum-dev/ethereum-notes/ethereum-addresses.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.