RSA notes

1, Does RSA work for any message M?

Yes.

Even if message m and modulus n is not co-prime, ist gcd{m, n} !=1

2, 

Common modulus attack on RSA when the 2 public exponents differ by a single bit

3, Common n attack

Multiple parties cannot share the same n. Because for one person, knowing {e1, d1} = knowing Phi{n} = can factor n = can find another d2 according to e2 = know plain text sent to person2