In this challenge, we are given a public key with public exponent and public modulus The ciphertext that we are supposed to decrypt is
Using e.g. msieve, this can be factored into three distinct prime factors:
, and .
First, we compute for all . Then, using PARI/GP, we execute the following operation
factor(x^3 - Mod(c_i, p_i)) for each .
For each such operation, we obtain a few roots:
L1 = [13065746773528615679127725156712, 19061253618972528384862766945681, 20754230340289340329043214744501] L2 =  L3 = [19177276190995540727122167162170, 19553467714697919836353088849918, 26432214695116292981336177743006]
Running a CRT for all possible combinations in
L1 x L2 x L3.
m = chinese_remainder(n, [-a,-b,-c])
we find the flag