Ethereum: the Mnemonic Bip39 construction avoids repeated words?

The decentralized Ethreum network is based on a complex system of cryptographic keys and mnemonic phrases to ensure the safe storage of private keys. At the center of this system there is the proposal to improve Bitcoin (BIP) 39, also known as bip39 or the derivation of seed phrases. This protocol allows users to generate unique seeds, which can be used for different purposes, including the signature of transactions, the creation of wallets and the interaction with third services.

A common concern when it comes to mnemonic construction is whether all 24 words of a seed phrase will be unique through the specifications. In other words, is there the possibility that a word can occupy two positions in the valid seed, which could lead to duplicate or incomplete keys?

Mnemonico Bip39

construction algorithm

Bip39 uses a simple but effective algorithm to generate mnemonic phrases. The process provides for the random selection of 12 words from a predefined set of possible words, which is usually represented as a list of letters and symbols (for example, capital and tiny letters, figures, punctuation signs). These 12 words are used to create the seed phrase.

The algorithm selects every random word, ensuring that two selected words are not identical. However, it is essential to note that the selection process does not guarantee uniqueness in all possible combinations of 12 words. There is still the possibility that some orders of words or even specific apparitions of words bring to duplicate keys.

Duplica Word and Keys

To illustrate this point, consider an example using the default list of 256 possible words (a more realistic number of 128, which is often mentioned as a maximum dimension of a Mnemonica phrase). The Bip39 algorithm selects 12 random words in this list. In the worst case, all 24 seed positions could be occupied by these same words, which leads to duplicate keys.

For example, if we consider two possible orders of words:

Word Command A:
Tool

-> #8 and #20

Word B command:
Tool -> #10 and #12

In both cases, the word “tool” appears twice in a phrase of valid seeds. This shows that, yes, it is technically possible that a mnemonic construction leads to duplicate keys.

Conclusion

While Bip39 offers an effective algorithm to generate unique phrases, there is still the possibility of duplicate keys in specific circumstances (for example some orders or words). To mitigate this risk, users can consider the following good practices:

• Use a random numbers generator to select words from a large predefined list.

• Avoid selecting words too similar in the spelling model or in letters.

• Consider the use of a password manager that generates and stores unique mnemonic phrases.

By understanding how bip39 construction algorithms and adopting measures to minimize the risk of duplicate keys, users can enjoy a safe and private archive in the Ethereum network.

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