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Is it true that the "seed words" bruteforce more reliable for to get profit than searching of a "random number" for to open some profitable outputs?

The last one is impossible due to math, but the first one?

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No, it is not true. Both are impossible due to math. The mnemonic is just an encoding of a number that is randomly generated (i.e. just like a private key) so it has the same security properties of that 256-bit number.

If you ignore that it encodes a number, consider this: a seed phrase encoding a 256-bit number needs 24 words in the mnemonic. There are 2048 possible words which means that there are 2048^24 = 2.964... × 10^79 possible mnemonics. There are 2^256 = 1.157... × 10^77 possible 256-bit numbers. There are actually more possible mnemonics than there are values to be encoded in the mnemonic. Thus the mnemonics are just as secure as a randomly generated private key (256-bit number) itself.

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    Assuming BIP39, a 24 word mnemonic actually encodes exactly 256 bits of entropy (2048^24/2^(24/3) = 2^256), since 1 bit of every 3 words is used as a checksum. – Paul Jan 16 '18 at 19:01
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See also this article about Deterministic Cryptocurrency wallets: https://en.wikipedia.org/wiki/Cryptocurrency_wallet#Deterministic_wallet and BIP39 Mnemonic code or sentences on: https://en.wikipedia.org/wiki/Bitcoin_Core#Bitcoin_Improvement_Proposals

  • Please elaborate on the contents of the links as relevant to the question within your answer. As it stands, if the link disappears, or is edited significantly, it may no longer answer the question. – Raghav Sood Nov 29 '18 at 17:25

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