Comment by PeeMcGee
16 hours ago
Using RSA as an example, the prime factors are supposed to have the same bit length (plus or minus 1 for carryover) for a similar reason. If the smaller factor has 1 fewer bit than the larger factor, it will be discovered twice as quickly by brute force, and 4x faster if it has 2 fewer bits, 8x faster if it has 3 fewer bits, etc. You could technically create a 4096 bit RSA key where one of the factors is 3 and the other is some other giant prime, but it would be immediately discovered by a naive brute force attack. The algorithm itself isn't concerned with the bit-length difference and operates on the inputs opaquely. The key generator is responsible for selecting prime factors that cannot be easily derived from the algorithm's output.
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