Ron Was Wrong, Whit Is Right

Long challenge name, but short story. We are given an article at this link, outlining the difficulties in generating RSA keys such that there are no two public keys using the same prime. Because if that’s the case, one can very efficiently recover the factorisation by doing Euclid’s Algorithm, which runs in polynomial time (and thus much faster compared to factorising), to obtain one of the two primes used in the modulus....