Calculation of combinations from the bip32
mnemonic list
The bip32 mnemonic list (Key Cryptography Public Bechanets) is a crucial element in the Ethereum public cryptography system. The list consists of 12 words, each representing a word which corresponds to an address or a key to the Ethereum network.
To calculate the real space from these combinations, we must consider two factors:
- Verification : Each combination has a sum of control, which guarantees that only the valid keys can be generated.
- Combinations : We want to discover the number of combinations unique of possible words from this list.
Calculation of combinations
Assuming that each word corresponds to an address or a key (that is to say that the 12th word is still “0x0000000000000000000000000000000000000000000000000000000000”), we can calculate the total number of combinations by increasing 2048 with the power of 12:
2 ^ 2048 ^ 12 '
This represents all the possible permutations of the 12 words, including duplicates.
Valid combinations
However, all these combinations are not valid. A sum of control is applied to each combination to ensure that only the keys with a specific signature can be generated. This sum of control is calculated by combining the 12 words (excluding the first word "0x0000000000000000000000000000000000000000000000000000000000") and the remaining 11 words.
Indicate this sum of control as "C". Valid combinations are those that produce a single sum of control, which means that they can be used to generate keys with the desired signature. To calculate the real space from these combinations, we must 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 certain hypotheses:
- Each combination has a single sum of control (C), which eliminates duplicates.
- The total number of possible combinations without any restriction is 2 ^ 2048 (assuming that each word can be used independently).
- Since not all combinations are valid due to the sum of control, we must subtract the number of non -valid combinations of the total.
Unfortunately, I did not find a reliable source or formula which provides an exact estimate for this problem. The number of non -valid combinations depends on various factors, such as:
- The specific mnemonic list used.
- The length and structure of words.
- The complexity of the calculation of the sum of control.
Consequently, we can only provide an approximate response:2 ^ 2048 – X`, where X represents the number of non -valid combinations. However, without more information or more clarification on the problem, it is difficult to determine the exact value of X.
Conclusion
In summary, the calculation of the real space from the bip32 mnemonic lists is not a simple process. Although we can estimate the total number of possible combinations such as “2 ^ 2048”, the determination of the exact number of valid combinations requires an in -depth analysis of various factors involved in the calculation of the sum of control and the combination generation process. If you have specific questions or if you need additional clarifications, do not hesitate to ask!