# Are the Common modulus attack, Common Factor Attack, and Wiener's attack different?

Is there a difference between:

• Common modulus attack

• Common Factor attack

• Wiener's attack

or are these just a different name for the same attack?

• In Wiener's attack, an attacker may efficiently find $$d$$ when $$d < (1/3) N^{1/4}$$

• Coppersmith's attack

The Wiener attack works on low $$d$$, but Coppersmith attack works on small $$e$$. In general case, the Håstad's broadcast attack uses The Coppersmith method. In the simplest form, it uses CRT when the sender sent the same messages to different parties.

• Common modulus attack

In Common modulus attack, the modulus is the same but the public exponents are different.

As a result, they are different attacks with different names.

And, here a nice paper from Dan Boneh; Twenty Years of Attacks on the RSA Cryptosystem