xiyu
xiyu|Aug 06, 2026 13:16
Every once in a while, people ask: With more and more people using mnemonic words, will two people draw the same set? No. But this concern was misplaced. The effective combination of 12 mnemonic words is 2 ^ 128, approximately 3.4 × 10 ^ 38. According to the birthday paradox, to increase the probability of "any two sets colliding" to 50%, approximately 2 ^ 64 sets of independently generated seeds -180 billion sets - are needed. Currently, there are approximately 600-700 million global cryptocurrency holders (a16z caliber), with only a few million truly active. Even if we zoom in to the dead, the 10 billion people on Earth each generate 1000 sets, which is only 10-13, six orders of magnitude away from that threshold. Moreover, there are far fewer independent seeds actually in use: a set of seeds can generate thousands of addresses through BIP32, and the exchange has several sets of seeds to manage all assets. The real loser is never a collision of words, but the collapse of the random number at the moment of generation. Milk Sad (CVE-2023-39910) in July 2023, the bx seed of LibBitcoin Explorer generates entropy using Mersenne Twister, using system time as the seed, leaving only 32 bits of internal entropy. The space of 2 ^ 128 instantly shrinks to 4.3 billion candidates, which can be filled with just one consumer grade graphics card. Researchers have confirmed that 227000 addresses were affected and over 900000 US dollars were taken off the chain. The Trust Wallet browser plugin fell into the same category in 2022 (CVE-2023-31290), which was discovered by the same group of researchers, Shunto. So don't merge arrays anymore. What should be asked is: How much true entropy did the device that generated these 12 words have in its hands at that time?
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