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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?

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  • Wiener's 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

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