1) How could someone come to know the first m/2 or the last m/4 digits of p if it is not part of the public key? Same for d? I don't fully understand the short plaintext attack on RSA. And I still don't really understand why the fraction approximation of decimals works. I understand how to do it, but I don't get why. Do we need to understand that?
2) I am impressed with all of these attacks on RSA but I am wondering if they are ever REALLY used in real world. Are these the only known attacks? Are people still studying RSA and trying to find different attacks? Or is it futile until we have quantum computers?
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