NCW BINUS 2025 - WASSUP TWIN Cryptanalysis

1. Challenge Overview

Challenge Name: WASSUP TWIN
Author: Auric
Event: National Cyber Week (NCW) BINUS 2025
Date: 24 November 2025
Team: TKA LOREM IPSUM

Given chall.py and output.txt containing RSA parameters:

N = 92226959634395542727305870286691824099
e = 65537
c = 81028662439340068660785564873246389821

2. Mathematical Vulnerability Analysis

In standard RSA, the plaintext message m must satisfy m < N. In this challenge:

1. N is generated from 64-bit twin primes (q = p + 2), yielding a 128-bit modulus.
2. The flag length is 23 characters (184 bits), meaning m > N.
3. When encrypting c = m^e mod N, the message wraps around modulus N. Standard decryption calculates:

m_remainder = m mod N

The true message m is related to m_remainder by:

m = k * N + m_remainder  (for integer k >= 1)

Since the flag starts with NCW{ and is exactly 23 bytes long, we can bound the search space of k and search for ASCII printable output.

3. Exploit / Solver Script

import math
from Crypto.Util.number import long_to_bytes, inverse

N = 92226959634395542727305870286691824099
e = 65537
c = 81028662439340068660785564873246389821

# 1. Twin Prime Factorization
val = math.isqrt(N + 1)
p = val - 1
q = val + 1
assert p * q == N

# 2. Decrypt message remainder mod N
phi = (p - 1) * (q - 1)
d = inverse(e, phi)
m_remainder = pow(c, d, N)

# 3. Search bounded range for k
flag_prefix = b"NCW{"
target_len = 23
min_msg = int.from_bytes(flag_prefix + b'\x00' * (target_len - len(flag_prefix)), 'big')
max_msg = int.from_bytes(flag_prefix + b'\xff' * (target_len - len(flag_prefix)), 'big')

min_k = (min_msg - m_remainder) // N
max_k = (max_msg - m_remainder) // N + 1

for k in range(min_k, max_k + 2):
    candidate_m = k * N + m_remainder
    try:
        candidate_bytes = long_to_bytes(candidate_m)
        if candidate_bytes.startswith(b"NCW{") and len(candidate_bytes) == target_len:
            if all(32 <= b <= 126 for b in candidate_bytes):
                print(f"[+] Flag Found: {candidate_bytes.decode()}")
                break
    except Exception:
        continue

4. Flag