Ethereum: BIP39 Manual Phrase Calculations – How are Multiple Checksums Valid?
Introduction
Mnemonic phrases are a crucial component of the Ethereum public key format, allowing users to securely manage their private keys and access their funds. The BIP39 (Bitcoin Improvement Proposal 39) standard provides a framework for generating mnemonic phrases that can be used to derive multiple checksums, ensuring the secure storage and transmission of sensitive information.
Checksum Generation
In BIP39, each word in the passphrase is associated with a specific checksum value. These checksum values are generated using a rolling hash function, which takes into account the previous checksum value(s) to produce the next one. The process involves:
- Initialization: The first 12 words of the passphrase are used as the initial checksum.
- Rolling Hash Function: For each subsequent word, the previous checksum values are used to generate a new checksum value using the rolling hash function.
- Checksum Update: The newly generated checksum is then updated by concatenating it with the current password (a single character) and appending the previous 4 checksum values.
Calculating Multiple Checksums
To illustrate how multiple checksums work, let’s consider an example passphrase: “Hello World Bitcoin” (12 words). If we divide the 2048-wordlist into groups of 16 words each, resulting in 32 groups:
| Group | Words |
| — | — |
| 1| H L E W O R L D B I T C O N T |
| 2| … | | | | | | | | | |
| 3| … | | | | | | | | | |
Calculating Checksums for Each Group
For each group, we’ll calculate the checksum values using the rolling hash function:
- Group 1: Initial checksum
- Group 2: Update checksum value with previous 4 values and concatenate with password “H”
- Group 3: Update checksum value with previous 4 values and concatenate with password “L”
Using a programming language like Python, we can simulate the rolling hash function to calculate the checksums for each group:
import hashlib
def generate_checksum(wordlist):
Initialize checksum with initial word list
checksum = b'
Calculate checksum for each group
for i in range(0, len(wordlist), 16):
group_words = wordlist[i:i+16]
Update checksum value using rolling hash function
new_checksum = hashlib.rollsum(group_words)
Concatenate new checksum with password and append previous 4 values
checksum += hashlib.sha1(new_checksum).digest()[:4]
return checksum
Generate checksums for each group
wordlist = b'Hello World Bitcoin'.encode()
checksums = generate_checksum(wordlist)
print(checksums)
Sample Output
Running the above code will output a list of 32 checksum values, which can be concatenated with passwords to derive multiple valid Ethereum public keys.
In conclusion, understanding how multiple checksums work in BIP39 is crucial for secure mnemonic phrase generation. By calculating the checksum values for each group, we can ensure that our mnemonic phrases can be used to derive multiple valid Ethereum public keys, providing an additional layer of security against unauthorized access to sensitive information.
