Ethereum: How many combinations are there from the BIP32 mnemonic list?

Calculating Combinations from BIP32 Mnemonic List

The BIP32 (Bechanelles Public Key Cryptography) mnemonic list is a crucial component in Ethereum’s public key cryptography system. The list consists of 12 words, each representing a word that corresponds to an address or key in the Ethereum network.

To calculate the actual space from these combinations, we need to consider two factors:

  • Checksum: Each combination has a checksum, which ensures that only valid keys can be generated.

  • Combinations: We’re interested in finding out how many unique combinations of words are possible from this list.

Calculating Combinations

Assuming each word corresponds to an address or key (i.e., the 12th word is always “0x00000000000000000000000000000000000000000000000000000000000000”), we can calculate the total number of combinations by raising 2048 to the power of 12:

2^2048^12

This represents all possible permutations of the 12 words, including duplicates.

Valid Combinations

However, not all these combinations are valid. A checksum is applied to each combination to ensure that only keys with a specific signature can be generated. This checksum is calculated by combining the 12 words (excluding the first word “0x00000000000000000000000000000000000000000000000000000000000000”) and the remaining 11 words.

Let’s denote this checksum as C. The valid combinations are those that produce a unique checksum, which means they can be used to generate keys with the desired signature. To calculate the actual space from these combinations, we need to consider the number of valid combinations.

Number of Valid Combinations

Unfortunately, there is no direct formula to calculate the exact number of valid combinations from BIP32 mnemonic lists. However, we can make an educated estimate based on some assumptions:

  • Each combination has a unique checksum (C), which eliminates duplicates.

  • The total number of possible combinations without any restrictions is 2^2048 (assuming each word can be used independently).

  • Since not all combinations are valid due to the checksum, we need to subtract the number of invalid combinations from the total.

Unfortunately, I couldn’t find a reliable source or formula that provides an exact estimate for this problem. The number of invalid combinations depends on various factors, such as:

  • The specific mnemonic list used.

  • The length and structure of the words.

  • The complexity of the checksum calculation.

As a result, we can only provide an approximate answer: 2^2048 - x, where x represents the number of invalid combinations. However, without further information or clarification on the problem, it’s challenging to determine the exact value of x.

Conclusion

In summary, calculating the actual space from BIP32 mnemonic lists is not a straightforward process. While we can estimate the total number of possible combinations as 2^2048, determining the exact number of valid combinations requires an in-depth analysis of various factors involved in the checksum calculation and combination generation process. If you have any specific questions or need further clarification, feel free to ask!

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