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There are multiple reasons, RSA uses a Modulo multiplication group with modulus $PQ$. Due to the nature of groups, this group does not contain all natural numbers between 1 and $PQ$, rather it only contains the numbers that are coprime with $PQ$. Coinsidentaly, the number of elements happens to be $(P-1)(Q-1)$. But that is when $P$ and $Q$ are prime. If ...


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Very large exponents $e$ Assuming that $e > 2^t$ where $t > 514$ we may use Coppersmith's attack to factorize $N$ efficiently. By this answer I only intend to exemplify that for some public exponents $e$ the given condition on the primes makes it significantly easier to factorize the RSA modulus. In particular it is worth noting that public exponents $...


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