the probability of randomly choosing a false prime from a set of 1024-bit numbers is one in 2^60
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What are the consequences of ending up with one? Do you get hacked or something?
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im not totally sure. i think it’s that your key is more easily found because non-prime numbers factor more quickly
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Oh that makes sense since there would be more factorization than you think 🤔
If you misclassify 5, 6 as a prime pair, then 30 has 3 factorizations instead of 1 so 3x weaker... and once you find one factorization the right one is probably easy to get to...
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exactly. i think of primes as being this hardened structure that preserves the independence of all of its children (smaller numbers), in that none of them has a more specialized relationship to it and thus they are all equally protected by “anonymity”
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a non-prime is a ‘weak structure’ that collapses along certain fault lines under questioning. those fault lines are its inherent weakness and are exploitable
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So to answer your original question, to be a false prime would feel like being the crack in dam among several where it ruptures under pressure. You’d feel very unlucky being blamed for a failure that’s really systemic.
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well yes that’s the latent possibility that would exist in a world where you chose a false prime — the possibility for someone to observe this aspect of your number choice would exist. the more likely scenario is that you would never know you ended up in this world
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you can’t observe what you don’t inspect
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