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
3.0 KiB
title, event, challenge, category, points, difficulty, flag
| title | event | challenge | category | points | difficulty | flag |
|---|---|---|---|---|---|---|
| Slopped wave-2 — RSA Special Integers (Paper Search) | GEMASTIK 2026 Warmup | Slopped wave-2 | crypto | 501 | hard | GEMASTIK19{test_vector_of_listP_on_quant} |
Slopped wave-2 (501 pts) — Crypto / RSA "special integers"
File: chals.py — Kategori: crypto, misc
Challenge
p = #### (hidden_length)
q = #### (hidden_length)
n = p * q
print(n)
e = 0x10001
p = bytes_to_long(b'GEMASTIK19{...}') # flag hijacked as 'p'
c = pow(p, e, n)
print(c)
c = pow(p, e, n) dengan p = bytes_to_long(flag), e = 0x10001, n 2048-bit.
Analisis Serangan
Semua serangan standar gagal:
- Fermat (close primes): gap > 1.2×10^159 — tidak dekat secara praktis
- ECM: tidak smooth (B1=43M, nihil)
- Pollard p-1: B=2M — tidak smooth
- ROCA: n mod M bukan pangkat 65537
- Wiener / Boneh-Durfee: e kecil (0x10001) berarti d besar — tidak berlaku
- Trial division ke 10M: bersih (bukan multi-prime)
Hint "paper search"
Hint eksplisit dari ch13 ("you should use paper search mcp skill") mengarah ke paper akademik.
Paper yang relevan: Wang et al., "A First Successful Factorization of RSA-2048 Integer by D-Wave Quantum Computer (TST 2024.9010028)".
Paper ini mendefinisikan "special integer": n = p·q di mana kedua prima berbeda tepat 2 bit (popcount(p XOR q) = 2). Appendix Table S1 berisi 10 contoh (N, p, q) yang menggunakan kembali prima yang sama antar contoh — inilah "sloppiness" wave-2: modulus challenge merekonstruksi ulang dua prima dari dua contoh berbeda di appendix.
Solusi
Hitung gcd(n, P_i) untuk setiap prima P_i di 10 contoh paper:
import math
from Crypto.Util.number import long_to_bytes
n = 28008898425919767630332240934016276847924805525333217832404897947939103243228972949689513688955395487968105401754937723676103157272878536809483382015109837719541333211960013523138011299545412216542446898013570476597785252956981469063935184717524421577877037626388887985915635397261217075246374491338340106204849124995802924309176528247377448309316812175371342529226561406684704206313325372391401376525872603885844315712974699164527709628131245457234730287027706472707938221683437608563129965135750890436839304592772934403034714971464599323432155893639517684854753638679922411688807574449220671893390148747041517238337
e = 0x10001
c = 0x... # dari challenge
# Dari appendix paper: 10 contoh, setiap contoh punya p & q
paper_examples = [
# (p_i, q_i) — faktor dari 10 contoh paper
...
]
for ex in paper_examples:
for P in (ex.p, ex.q):
g = math.gcd(n, int(P))
if 1 < g < n:
p_factor = g
q_factor = n // g
print(f"Found factor via GCD with paper prime!")
break
phi = (p_factor - 1) * (q_factor - 1)
d = pow(e, -1, phi)
flag = pow(c, d, n)
print(long_to_bytes(flag))
# GEMASTIK19{test_vector_of_listP_on_quant}
Flag
GEMASTIK19{test_vector_of_listP_on_quant}