Nuclear_Disaster.md

Nuclear Disaster

In this task we were given the creds of ssh user. Connecting and looking at the files in the home directory we got the following challenge specifications:

n: 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
e: 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
a: 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
g: 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
c1: 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
c2: 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
DROP US some ETH and you may prevent a nuclear disaster:
0x7b1cA37A0ad47B14e55a1E0d9d882999c0DF1Ee0

And the script to generate ciphertext and encryption parameters:

from Crypto.Util.number import *
from secret import root
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
def generate_keys(nbit):
    p, q, r = [ getPrime(nbit) for _ in range(3)]
    
    n = p * q * r
    
    phi = (p-1)*(q-1)*(r-1)
    
    d = getPrime(1 << 8)
    e = modinv(d, phi)
    a = getPrime(2*nbit)
    while True:
        g = getRandomRange(2, a)
        if pow(g, 2, a) != 1 and pow(g, a//2, a) != 1:
            break
    pub_key = (n, e, a, g)
    priv_key = (n, d, a, g)
    return pub_key, priv_key
def encrypt(m, pub_key):
    n, e, a, g = pub_key
    k = getRandomRange(2, a)
    K = pow(g, k, a)
    c1, c2 = pow(k, e, n), (m * K) % a
    return c1, c2
password = bytes_to_long(root)
pub_key, priv_key = generate_keys(1024)
c1, c2 = encrypt(password, pub_key)
f = open('your_last_hope.txt', 'w')
f.write('n: ' + hex(pub_key[0]) + '\n')
f.write('e: ' + hex(pub_key[1]) + '\n')
f.write('a: ' + hex(pub_key[2]) + '\n')
f.write('g: ' + hex(pub_key[3]) + '\n')
f.write('c1: ' + hex(c1) + '\n')
f.write('c2: ' + hex(c2) + '\n')
f.write('DROP US some ETH if you know what\'s good:\n0x7b1cA37A0ad47B14e55a1E0d9d882999c0DF1Ee0\n')

To recover private exponent, we used the Wiener attack. This can be seen on the Figure 1.

Figure 1 – Wiener attack result

Knowing private exponent, we recovered encrypted password, using the following code:

k = pow(c1, d, n)
K = pow(g, k, a)
print(k)
print(K)
print(c2 * inverse(K, a) % a)
ans = c2 * inverse(K, a) % a
print(long_to_bytes(ans))

Output:

18098846352876641578492621703637624880331428714424686905079101764592280181644093331462690938321592335495484058768969986728411732180570894837745788843183995991823246985343123757080453689951244276523557707327676313359080360775150903286956602511620785151099760705078150354238484251002460234677422962762641306586645834781909131060957678933575054034022557614103110299160082692908096510181005840971132055345278870368033899213507528994430973471900597376519334042400053352516006961034884209317276922080252147616983215686457848394323938861419149438518803049563805423884558690732547210203983368519592760615900150939921381832758
4053492215569828668269107800786425481562377574235838939015694156657899751403202646543157744199205620962570774636969170512021383182400775660020892051476451128344880184590067576167674689076021914088666776790392586671275161649215377032601990904701667864038043839360661893437135206453079737499498364319640266660271736188831773181114938009098796653196592489611009177492177964875944945473422368698169004091606317361059617209668433829729876174385937459981151405210455327742032966781976953852336668891927517060412308363350898889558421967311087999855034773011278504867799344889881695302195754619240397513302233468400643091997
4483715249980043692044294085480048514838642
b'3xtr4H34t1nr34ct0r'

At first, we did not exactly know what to do with recovered password. But then looking at the generator script we got that it is password from root user: “from secret import root”. Then we used recovered password to connect as root and recovered the flag from flag.txt file. This can be seen on the Figure 2.

Figure 2 – Connecting to SSH as root user and displaying the flag

Flag: HTB{s3cur3_y0ur_cr1t1c4l_1nfr4s7ruc7ur3}.