Calculation of combinations from the BIP32 mnemonic list
The BIP32 (Bechanelles Public Key Cryptography) mnemonic list is a critical component of Ethereum’s public key cryptography system. The list consists of 12 words, each of which is a word corresponding 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 that ensures that only valid keys can be generated.
- Combinations
: We are interested in finding out how many unique word combinations are possible from this list.
Calculation of combinations
Assume that each word corresponds to an address or a key (ie, the 12th word is always “0x0 …
2^2048^12
Here are all possible permutations of 12 words, including duplicates.
Allowed Combinations
However, not all these combinations are permissible. 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 12 words (excluding the first word “0x0 …
Let’s denote this checksum as C'. Valid are those combinations that create a unique checksum, which means that 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 possible combinations.
Number of allowed combinations
Unfortunately, there is no direct formula for calculating the exact number of permissible combinations from mnemonic lists BIP32 does not exist. However, we can make a reasonable estimate based on some assumptions:
- Each combination has a unique checksum (C), which excludes duplicates.
- The total number of possible combinations without any restrictions is 2^2048 (provided that 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 number.
Unfortunately, I have not been able to find a reliable source or formula that would give an accurate estimate for this problem. The number of invalid combinations depends on various factors, such as:
- The specific mnemonic list used.
- Length and structure of words.
- Complexity of checksum calculation.
As a result, we can only give an approximate answer:2^2048 – x`, where x is the number of invalid combinations. However, without additional information or clarification of the problem, it is difficult to determine the exact value of x.
Conclusion
In conclusion, it can be said that calculating the actual space on the basis of BIP32 mnemonic lists is not a simple process. Although we can estimate the total number of possible combinations as “2^2048”, determining the exact number of possible combinations requires a deep analysis of the various factors involved in the calculation of the checksum and the process of generating combinations. If you have any specific questions or need additional clarifications, don’t hesitate to ask!
