An small question about RSA algorithm

[zetafunction]

on the RSA algorithm

http://en.wikipedia.org/wiki/RSA

why simply we can not choose e=1 or e=2 ? it would simplify the calculations a lot.

 

[Santa1]

Does'nt that go against the purpose of the RSA?

edit: shady comma

 

[adriank]

If e = 1, then the ciphertext is the same as the plaintext, making the algorithm useless.

It's required that e is coprime to φ(n) = (p - 1)(q - 1), so that there exists d such that ed = 1 mod φ(n). However, if p and q are distinct primes, then one of them is odd, so φ(n) is even. Thus e can't be 2.

 

[zetafunction]

thanks a lot adriank , nice forum