# Does Hinek and Lam's Paper prove that Common Modulus Attacks is possible with non-coprime public exponents?

We know that Common Modulus Attacks work with coprime public exponents $$(e',s)$$ such that $${e_1}s+{e_2}t=\gcd(e_1,e_2)=1$$

I am reading Hinek and Lam's Paper: Common Modulus Attacks on Small Private Exponent RSA and Some Fast Variants (in Practice). Got confused, it seems they proved that Common Modulus Attacks would work with non-coprime public exponents, with the condition of "Small Private Exponent RSA".

Is my understanding correct? Is there some example for this?

• BTW this is related to an ongoing CTF ctf.dicega.ng Feb 6 at 22:39
• Mmm..., good to know this is related to CTF challenge happening now. I did not know that, I was just writing some blog for my RSA attack survey and got puzzle on this. Feb 7 at 6:36

and if there is a common modulus and the public exponents are relatively prime (i.e. $$\gcd(e_1,e_2)=1$$) then recovering the message is easy ( no factoring).