8.18 Show that if P=NP then the RSA cryptosystem (Section 1.4.2) can be broken in polynomial time.
Proof:
We could easily know that the problem of prime factorization belongs to NP,so it means that the problem of prime factorization could be solved within polynomial time if P=NP.
For instance, supposed one user's public key is (N,e) in a application of RSA encryption algorithm,based on the condition of dividing N into pq within polynomial time,its private key( d =e−1 mod(p−1)(q−1) )becomes apparent.
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