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

Calculating Combinations from a BIP32 Mnemonic List

The BIP32 (Bechanelle Public Key Cryptography) mnemonic list is an essential part of the Ethereum public key cryptography system. The list consists of 12 words, each of which represents a word that corresponds to an address or key on the Ethereum network.

To calculate the actual space of these combinations, two factors must be taken into account:

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

• Combinations: We want to know how many unique combinations of words are possible from this list.

Combination Calculation

Assuming that each word corresponds to an address or key (i.e. the 12th word is always “0x0

“2^2048^12”.

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

Valid Combinations

However, not all of 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 (except for the first word “0x0

Let’s denote this checksum as “C”. Valid combinations are those that produce a unique checksum, meaning that they can be used to generate keys with the desired signature. To calculate the actual position of these combinations, we need to consider the number of valid combinations.

Number of Valid Combinations

Unfortunately, there is no direct formula for calculating the exact number of valid combinations of BIP32 mnemonic lists. However, we can make a reasonable guess based on a few assumptions:

• Each combination has a unique checksum (C) that prevents duplication.

• The total number of possible combinations without limits is 2^2048 (assuming that each word can be used individually).

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

Unfortunately, I have not been able to find a reliable source or formula that gives an accurate 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 word.

• The complexity of calculating the checksum.

As a result, we can only give an approximate answer: “2^2048 – x”, where x represents the number of invalid combinations. However, without further information or explanation of the problem, it is difficult to determine the exact value of x.

Conclusion

In summary, calculating the actual space of BIP32 mnemonic lists is not an easy process. Although we can estimate the total number of possible combinations as “2^2048”, determining the exact number of valid combinations requires a thorough analysis of the various factors involved in the checksum calculation and the combination generation process. If you have specific questions or need further clarification, please ask!