PicoCTF_2017: weirderRSA

Category: Master Points: 175 Description:

Another message encrypted with RSA. It looks like some parameters are missing. Can you still decrypt it? Message

Hint:

Is there some way to create a multiple of p given the values you have? Fermat's Little Theorem may be helpful

Write-up

Fermat's Little Theorem is an interesting thing that took me awhile to understand, being new to cryptography but essentially what we have to do to break this involves just playing with dp to get p

r = 123456
p = gmpy2.gcd(n, pow(r, (e*dp), n) - r)

With p found, we can just divide n with p to get q.

q = gmpy2.div(n, p)

With q found, we can calculate d to be the inverse of (p-1)(q-1)

phi = (p-1) * (q-1)
d = gmpy2.invert(e, phi)

With d found, the challenge is solved.

Therefore, the flag is flag{wow_leaking_dp_breaks_rsa?_64151418169}.

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