Originally posted by Qaridarium
(Someone check if I make a mistake in the following)
Let's say the amount of transistors in year 0 is k. The amount in year 2 by Moore's law would be 2^1 * k. Original effort required to break the encryption is p. Effort after increasing p by one is p^2. If we assumed the password was crackable with transistors k, then p = k. Let's say i is the amount of two year cycles it takes to catch up after a single increment in password size. 2^i * k = k^2 (divided by k) => 2^i = k <=> i = log2(k). You quickly notice from that that you can't indefinitely keep up with the password length increases. Like if it took a two-billion-transistor CPU to break a password with length n, it would take 61.794705708 years by my calculations before you could create a computer that could break a password with length n+1.
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