It's easy to find primes of a given bit length, and it's easy to multiply them together. It's hard to un-multiply a given number (public key) into its unique prime factors (private key).
But if we could more easily find primes, the search space for finding those prime factors would be significantly smaller.
In my mind, it’s not a question of easy vs hard… it’s a question of fast vs slow. The default algorithm for finding primes is pretty simple, but it takes a lot of math and time. If you reduce the time requirements, then we start to get into trouble.
In my mind, it’s not a question of easy vs hard… it’s a question of fast vs slow. The default algorithm for finding primes is pretty simple, but it takes a lot of math and time. If you reduce the time requirements, then we start to get into trouble.