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If someone or some group found an efficient way to factor large composites with two distinct prime divisors, would this make it easier to decode any messages?

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Please add some details to your question: What cryptosystem are you using? –  Paŭlo Ebermann May 2 at 20:22

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I guess it depends on which scenario you are referring to. If it is RSA, being able to factorize $n = pq$ would compromise the security of that crypto-system.

This is because one could compute $\phi(n) = \phi(p)·\phi(q) = (p-1)·(q-1)$ since $p$, $q$ are two distinct primes and could calculate the private key $d$ from the public key $e$ by using the equation $e \cdot d = 1 \mod \phi(n)$.

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