[openssl-dev] common factors in (p-1) and (q-1)

[mancha]

On Fri, Jul 31, 2015 at 02:36:03AM +0000, paul at securecottage.com wrote:
> 
> Hi there,
> 
> I have looked at the RSA protocol a bit and have concluded that
> 
> 1) common factors in (p-1) and (q-1) are also in the factorisation of
> (p*q-1).  2) by factoring (p*q-1) you can come up with candidates for
> squares in the totient.  3) you can also come up with d mod
> commonfactor^2 if there is a common factor.
> 
> the math is shown in my wikipedia users page math blog at:
> 
> https://en.wikipedia.org/wiki/User:Endo999#The_Bad_Stuff_That_Happens_When_There_Are_Common_Factors_Between_.28P-1.29_and_.28Q-1.29

[SNIP]

Hi. How are you finding a common factor f such that f|(p-1) and f|(q-1)?

Thanks.

--mancha

-- https://twitter.com/mancha140
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