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xmasctf-crypto2.md

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Challenge name: DeFUNct Ransomware

Description:

Santa got infected by a ransomware! His elves managed to extract the public key, but couldn't break it. Help Santa decrypt his memos and save Christmas!

P.S: given files: xmasctf-crypto2-file1.txt, xmasctf-crypto2-file2.enc

Solution:

We take a look at the text file, we see 2 variables named as n nad e. Challenge description is also talking about a public key, so we have a RSA here!

First of all, we try to factorize n. I use Factordb to do it. Seems our n is formed as p^2 * q^2 where p and q are primes. So, we have:

φ(n) = φ(p^2 * q^2)
φ(p^2 * q^2) = φ(p^2) * φ(q^2)  #p^2 and q^2 are co-prime
φ(p^2) = (p - 1) * p            #p is prime

φ(n) = p * q * (p - 1) * (q - 1)

Now all we need is to use a script to find d and calculate plaintext. We define two functions in order to find d:

def egcd(a, b):
    if a == 0:
        return (b, 0, 1)
    else:
        g, y, x = egcd(b % a, a)
        return (g, x - (b // a) * y, y)

def modinv(a, m):
    g, x, y = egcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

We have φ(n) as well, so we decrypt c and try decoding it using ASCII:

p = 167945946509710528501147140850136444757936485900233494350920365296618466491038783888459340376962572176658471433672446105042569166930066764067458760954444542315723029727275896055594485064790247910216515269672809063208736956951590237500845779868099616110730494457247861971337900144361732424961936041908032639503
q = 167945946509710528501147140850136444757936485900233494350920365296618466491038783888459340376962572176658471433672446105042569166930066764067458760954444551181379291048040552484392012079612125237961930510490682072102514499883651342766510399652317335461788686135874608722851478273373669551946245262568601067289

x = int(c, 16)
d = modinv(e, (p-1)*p*(q-1)*q)
m = pow(x, d, n)
t = codecs.decode(hex(m)[2:], 'hex')
print(t)

Output

'TODO\n----\n\n* Stop downloading RAM for the internet.\n* Remove yakuhito from the naughty kids list.\n* Drink all the milk; eat all the cookies\n* Do not forget the flag: X-MAS{yakuhito_should_n0t_b3_0n_th3_n@ughty_l1st_941282a75d89e080}\n'

The Flag

X-MAS{yakuhito_should_n0t_b3_0n_th3_n@ughty_l1st_941282a75d89e080}