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+++ title = "The Cyber Grabs CTF: Unbr34k4bl3 (942)" draft = true date = 2022-02-02 tags = ["ctf", "crypto"] languages = ["python"] layout = "single" math = true +++
Crypto challenge Unbr34k4bl3 from the Cyber Grabs CTF.
No one can break my rsa encryption, prove me wrong !!
Flag Format: cybergrabs{}
Author: Mritunjya
Looking at the source code, this challenge looks like a typical RSA challenge at first, but there are some important differences to note:
N = pqr(line 34). This is a twist but RSA strategies can easily be extended to 3 prime components.p, q \equiv 3 \mod 4(line 19). This suggests that the cryptosystem is actually a Rabin cryptosystem.- We're not given the public keys
e_1ande_2, but they are related throughx.
Finding e_1 and e_2
We know that e_1 and e_2 are related through x, which is some even number
greater than 2, but we're not given any of their real values. We're also given
through an oddly-named functor function that:
\begin{aligned}
1 + e_1 + e_1^2 + \cdots + e_1^x &= 1 + e_2 + e_2^2 \\
\frac{1 - e_1^x}{1 - e_1} &= 1 + e_2 + e_2^2
\end{aligned}
Interestingly enough, since e_1 and e_2 are primes, that means
I'd like to thank @10, @sahuang, and @thebishop in the Project Sekai discord for their help throughout this challenge.