encryption - How can I decrypt an RSA cipher knowing only p and q? -

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knowing p , q, how can definitively find e , d in order able decrypt ciphertext?

given "well aware" of rsa algorithm (i'm assuming textbook rsa) aware e can chosen value between 1 , φ(n), provided both e , φ(n) co-prime.

if question boils down can determine, 100% certainty, values of e , d given p , q? answer no.

this because valid value of e selected decrypt ciphertext something, not neccessarily original, something. you'd have have indication of plaintext's context, e.g. english? if knew this, , provided p , q relatively small, could test possible values of e until received result in english.

in practice, e chosen 3 or 65537.


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