HackTheBox Mayday Mayday Challenge

Explore the basics of cybersecurity in the Mayday Mayday Challenge on Hack The Box. This medium-level Challenge introduces encryption reversal and file handling concepts in a clear and accessible way, perfect for beginners.

https://app.hackthebox.com/challenges/628

Description

After successfully obtaining the research papers by extracting the encryption key, a new obstacle arises. The essential information regarding potential cures, including formulas and test results, is shielded by another layer of encryption. Can you overcome this additional challenge to reveal the final formula, enabling you to initiate the cure creation process?

Exploitation

#!/usr/bin/env python3
from Crypto.Util.number import *
from sage.all import *

def decrypt_rsa():
    N = 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
    e = 0x447a951fc908492e818cad6d6f0ab1b0212b57f952575e391bec5ad43
    c = 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
    dp = 0xc8c6f6c4408d9d34b18948d976313329f4e09e722df217fe8dbd0684dbe52bccdcf4de9e6697d788601d753221886b1bc689e68e9745d1297a39cdd2de9bdcdf
    dq = 0x230ba63327b3480c4cf80369f10af726baacf61e631b07178d5aa62dc4b9017b30bf28c5ada9486817d71f0587dd23eea5162ff60880eb0cf7f866c695e1b369
    A = (2**1024 * e**2 * dp * dq) // N + 1
    PR = PolynomialRing(Zmod(e), 'x')
    x = PR.gen()
    f = x**2 - (1 - A*(N - 1))*x + A
    k, l = [int(c[0]) for c in f.roots()]
    PR_kN = PolynomialRing(Zmod(k*N), 'x')
    x = PR_kN.gen()
    a = ((e*dp*2**512 + k - 1) * pow(e, -1, k * N)) % (k * N)
    g = x + a
    dp_low = int(g.small_roots(X=2**512, beta=0.5)[0])
    kp = int(g(dp_low))
    p = gcd(kp, N)
    q = N // p
    assert p * q == N
    d = pow(e, -1, (p - 1)*(q - 1))
    m = pow(c, d, N)
    return long_to_bytes(int(m))

if __name__ == '__main__':
    try:
        flag = decrypt_rsa()
        print(f"\033[92mDecrypted Flag\033[0m: {flag.decode()}")
    except Exception as e:
        print(f"\033[91mError\033[0m: {str(e)}")

Summary

The Mayday Mayday Challenge on Hack The Box is a medium-level cryptography challenge centered around reversing a flawed RSA encryption implementation. Participants must leverage mathematical insights into RSA parameters and use polynomial equations to recover the decryption key. The provided exploit script demonstrates techniques for deducing private keys using low-level decryption parameters, performing factorization, and recovering the plaintext from the ciphertext. This challenge is an excellent exploration of advanced cryptographic attack methods, particularly involving RSA vulnerabilities.