https://app.hackthebox.com/challenges/232

Description

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

Exploitation

#!/usr/bin/env python3
from Crypto.Util.number import long_to_bytes
import gmpy2

def int_to_bytes(n):
    return n.to_bytes((n.bit_length() + 7) // 8, byteorder='big')

def hex_to_int(hex_str):
    return int(hex_str, 16)

def small_exponent_attack(ct_hex, e=3):
    ct = hex_to_int(ct_hex)
    root, is_perfect = gmpy2.iroot(ct, e)
    return int_to_bytes(root)

def main():
    encrypted_flag = "05c61636499a82088bf4388203a93e67bf046f8c49f62857681ec9aaaa40b4772933e0abc83e938c84ff8e67e5ad85bd6eca167585b0cc03eb1333b1b1462d9d7c25f44e53bcb568f0f05219c0147f7dc3cbad45dec2f34f03bcadcbba866dd0c566035c8122d68255ada7d18954ad604965"
    try:
        decrypted = small_exponent_attack(encrypted_flag)
        print(f"[+] Flag: {decrypted.decode()}")
    except Exception as e:
        print(f"[-] Attack failed: {str(e)}")

if __name__ == "__main__":
    main()

Summary

Lost Modulus: exploit the RSA structure, recover the missing secret, and decrypt the flag.