Ethereum: How much is the entropy lost if the alphabetical order is mnemonic?
Let us immerse yourself as an exercise in the world of entropy and its influence on mnemonic systems. In this article we will examine how mnemonic devices for alphabetical management can cause considerable data loss due to the characteristic mathematical properties.
What is the issntropy?
Entropy is a measure of the system disorder or an accident. In the context of computer science, this means the amount of information that is lost when the data is processed or changed. Entropy increases due to the number of bits required for information.
BIP39 Completion: essential concerns
The Brainpool 39 (BIP39) standard is an algorithm with which secure seed words generate in containers that support the mnemonic cryptocurrency repository. Although the BIP39 is supposed to ensure data security, it was criticized that it does not match the BIP32, which is an essential aspect of Ethereum Tocars.
Alphabet mnemonic mix
Let us assume that we have a large collection of mnemonic, each consisting of 12 words (regular mnemonic length). We in the alphabet apparatus. We use this mnemonics the standard order scheme. From a mathematic point of view, this can be presented as a problem of the permutation:
P (12) = σ (n! / (N-i)! * I!), With the number of elements (mnemonics) and I am this generation.
In our example P (12) ≈ 1.94 trillion
Entropy -Conundrum
Now let’s think about how many unique combinations are generated by this passage Mnemonic:
Σ (n! / (N-i)! * I!) Where n = 12 and I range from 1 to 11.
This calculation offers many options: approximately 2.86 quintillions
Since we are in the alphabet of every mnemony, an essential part of this entropy goes through:
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- Symmetry : The alphabet management scheme managed to manage the alphabet can cause a symmetrical distribution if identical permutations are treated as differently.
- Cyclic Character : If we transfer the same sentence from Mnemonisch, they finally increase all possible orders so that data loss is increased exponentially.
consequences and effects
The huge entropy generated by the alphabetical order is of great importance:
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- Save data
: Data loss alone leads to concern about the long -term preservation and availability of historical mnemonics.
In summary, mnemonic devices with alphabetical tournaments are not a harmless practice and have considerable entropy costs. If we understand these mathematical properties, we can better evaluate how important it is to optimize mnemonic systems for efficient storage, the secure production of keys and data maintenance “Ethereum Blockchain” and beyond.