asepharyana
0de2458955
- Deleted all 14 dummy docs from DB + filesystem - Created 14 Gemastik warmup writeups + index via create_document API (DB-first) - ch1-ch12: encoding/stego/web/pwn basics - ch13: RSA small factors - ch14: RSA special integers via paper-search (GCD with paper appendix primes) - All 15 docs indexed and live at wiki.asepharyana.my.id
88 lines
2.5 KiB
Markdown
88 lines
2.5 KiB
Markdown
---
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title: "Slopped wave-2 — RSA Special Integers (Paper Search)"
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type: "writeup"
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section: "writeups"
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status: "published"
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author: "asep"
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tags: ["gemastik", "ctf", "warmup", "crypto"]
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path: "writeups/gemastik-2026-warmup/ch14-slopped-wave2.md"
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created_at: "2026-08-21T07:25:51.729Z"
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updated_at: "2026-08-21T07:25:51.729Z"
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event: "GEMASTIK 2026 Warmup"
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challenge: "Slopped wave-2 — RSA Special Integers (Paper Search)"
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category: "crypto"
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points: 501
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difficulty: "hard"
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flag: "GEMASTIK19{test_vector_of_listP_on_quant}"
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---
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# Slopped wave-2 (501 pts) — Crypto / RSA "special integers"
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**File:** `chals.py` — Kategori: `crypto, misc`
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## Challenge
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```python
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p = #### (hidden_length)
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q = #### (hidden_length)
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n = p * q
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print(n)
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e = 0x10001
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p = bytes_to_long(b'GEMASTIK19{...}') # flag hijacked as 'p'
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c = pow(p, e, n)
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print(c)
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```
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`c = pow(p, e, n)` dengan `p = bytes_to_long(flag)`, `e = 0x10001`, `n` 2048-bit.
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## Analisis Serangan
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Semua serangan standar gagal:
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- **Fermat** (close primes): gap > 1.2×10^159
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- **ECM**: tidak smooth (B1=43M)
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- **Pollard p-1**: B=2M — tidak smooth
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- **ROCA**: n mod M bukan pangkat 65537
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- **Wiener / Boneh-Durfee**: e kecil berarti d besar
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- **Trial division** ke 10M: bersih
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### Hint "paper search"
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Hint dari ch13 ("you should use paper search mcp skill") mengarah ke paper akademik.
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Paper: **[Wang et al., "A First Successful Factorization of RSA-2048 Integer by D-Wave Quantum Computer (TST 2024.9010028)"](https://www.sciopen.com/article/10.26599/TST.2024.9010028)**.
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Paper 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** — inilah "sloppiness" wave-2: modulus challenge merekonstruksi ulang dua prima dari dua contoh berbeda.
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## Solusi
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Hitung `gcd(n, P_i)` untuk setiap prima `P_i` di 10 contoh paper:
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```python
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import math
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from Crypto.Util.number import long_to_bytes
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n = <2048-bit modulus from challenge>
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e = 0x10001
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c = <ciphertext>
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# 10 contoh dari appendix paper, setiap contoh punya (p, q)
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paper_examples = [...]
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for ex in paper_examples:
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for P in (ex.p, ex.q):
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g = math.gcd(n, int(P))
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if 1 < g < n:
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p_factor = g
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q_factor = n // g
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break
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phi = (p_factor - 1) * (q_factor - 1)
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d = pow(e, -1, phi)
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flag = pow(c, d, n)
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print(long_to_bytes(flag))
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# GEMASTIK19{test_vector_of_listP_on_quant}
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```
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## Flag
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`GEMASTIK19{test_vector_of_listP_on_quant}` |