Lost Modulus

Crypto

https://app.hackthebox.com/challenges/lost-modulus

CHALLENGE DESCRIPTION: I encrypted a secret message with RSA but I lost the modulus. Can you help me recover it?

---

In the file given challenge.py we can see that it is RSA encryption and the value of e is 3 Here the e is small and n is too large, so m^e < N When the value of e is as small as 3, we can just do the 3rd root of cipher text and we can get the message

Python code:

import gmpy2
from Crypto.Util.number import long_to_bytes

cipher = int(
    "05c61636499a82088bf4388203a93e67bf046f8c49f62857681ec9aaaa40b4772933e0abc83e938c84ff8e67e5ad85bd6eca167585b0cc03eb1333b1b1462d9d7c25f44e53bcb568f0f05219c0147f7dc3cbad45dec2f34f03bcadcbba866dd0c566035c8122d68255ada7d18954ad604965",
    16,
)
with gmpy2.local_context(gmpy2.context(), precision=800) as ctx:
    ctx.precision += 800
    croot = gmpy2.cbrt(cipher)
    print(long_to_bytes(int(croot)))

Flag: HTB{n3v3r_us3_sm4ll_3xp0n3n7s_f0r_rs4}

:octocat: Happy Hacking :octocat: