1. (40 points) the security of rsa public key cryptosystem relies on the fact that prime factorization of large integers is practically unsolvable due to the high time-complexity of its solution. here is the reason: part of rsa's public key is a semiprime number n that is the product of two very large prime numbers p and q. although n is publicly available, both pand q must remain secret; otherwise, rsa's private key can be easily calculated and rsa's security gets compromised.