Description
                            This vault should unlock in a week - can you crack it faster, in time to submit the flag?
                            Attachments
                            https://imaginaryctf.org/f/XUw2X#vault.txt
https://imaginaryctf.org/f/N8V83#gen.py
                            Writeup 
                            
                                from Crypto.Util.number import *
exec('\n'.join(list(open('vault.txt'))[2:]))
fac = {
    2:14,
    3:12,
    5:6,
    7:1,
    17:1,
    19:2,
    31:1,
    41:1,
    227:1,
    433:1,
    467:1,
    2309:1,
    5527:1,
    13591:1,
    36985379:1,
    259726127:1,
    481626029:1,
    701899711:1,
    927093907:1,
    1392514213:1,
    3492606209:1,
    127172501513:1,
    34926936182669:1,
    36411945668431:1,
    62634262995527:1,
}
diff = 95026205724
phi = 1
for key in fac:
    phi *= key**(2*fac[key]) * (key-1)
e = pow(71, diff, phi)
print(long_to_bytes(pow(c, e, n)))
You can get the factors of p-1 and q-1 with a site like Alpertron, as all of them are relatively small. You can then use that to calculate phi and figure out the effective exponent after raising the ciphertext to 71 that many times.
                             
                            Flag 
                            
                                ictf{just_another_rsa_problem_in_disguise_:<}