asepharyana
7a6e717c28
- Deleted all previous dummy docs (defcon-quals-2024, infra/cloudflare-525, debugging/websocket-timeout, template, docs/*, notes/*, research/*) - Added 14 Gemastik warmup writeups covering encoding, stego, web, pwn, crypto - ch13: RSA small factors; ch14: RSA special integers via paper-search (GCD with paper appendix primes) - All flags recovered and documented with solution methods
1.4 KiB
1.4 KiB
title, event, challenge, category, points, difficulty, flag
| title | event | challenge | category | points | difficulty | flag |
|---|---|---|---|---|---|---|
| Slopped — RSA Small Factors | GEMASTIK 2026 Warmup | Slopped | crypto | 500 | medium | GEMASTIK19{qu4ntum_c0mput3r_br0k3_rs4_y0u_sh0uld_us3_p4p3r_s34rch_mcp_sk1ll} |
Slopped (500 pts) — Crypto / RSA small factors
File: chall.py
import random
p = random.randint(1, 10**4) # tiny prime candidates
q = random.randint(1, 10**4)
# ... find small primes, multiply
n = p * q * (big prime)
e = 0x10001
c = pow(flag, e, n)
Analisis
RSA dengan e = 0x10001, n 2048-bit, c = pow(flag, e, n).
n dibangun dari faktor prima kecil (sloppy primes — "my AI broke RSA with 1 billion qubits"). Faktorisasi temukan prima kecil lewat trial division, lalu phi = prod(p_i - 1), d = e⁻¹ mod phi, dan m = pow(c, d, n).
Solusi
from Crypto.Util.number import long_to_bytes
from sympy import factorint
e = 0x10001
n = 0xdb... # 2048-bit modulus
c = 0x...
# Trial division menemukan faktor kecil
factors = factorint(n)
print(factors)
# {83: 1, 233: 1, 9679: 1, <big_prime>: 1}
phi = 1
for p, exp in factors.items():
phi *= (p - 1) * p**(exp - 1)
d = pow(e, -1, phi)
m = pow(c, d, n)
print(long_to_bytes(m))
# GEMASTIK19{qu4ntum_c0mput3r_br0k3_rs4_y0u_sh0uld_us3_p4p3r_s34rch_mcp_sk1ll}
Flag
GEMASTIK19{qu4ntum_c0mput3r_br0k3_rs4_y0u_sh0uld_us3_p4p3r_s34rch_mcp_sk1ll}
Flag ini adalah petunjuk untuk ch14 ("you should use paper search").