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
87 lines
3.0 KiB
Markdown
87 lines
3.0 KiB
Markdown
---
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title: "Slopped wave-2 — RSA Special Integers (Paper Search)"
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event: "GEMASTIK 2026 Warmup"
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challenge: "Slopped wave-2"
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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 — tidak dekat secara praktis
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- **ECM**: tidak smooth (B1=43M, nihil)
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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 (0x10001) berarti d besar — tidak berlaku
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- **Trial division** ke 10M: bersih (bukan multi-prime)
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### Hint "paper search"
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Hint eksplisit dari ch13 (`"you should use paper search mcp skill"`) mengarah ke paper akademik.
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Paper yang relevan: **[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 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.
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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 = 28008898425919767630332240934016276847924805525333217832404897947939103243228972949689513688955395487968105401754937723676103157272878536809483382015109837719541333211960013523138011299545412216542446898013570476597785252956981469063935184717524421577877037626388887985915635397261217075246374491338340106204849124995802924309176528247377448309316812175371342529226561406684704206313325372391401376525872603885844315712974699164527709628131245457234730287027706472707938221683437608563129965135750890436839304592772934403034714971464599323432155893639517684854753638679922411688807574449220671893390148747041517238337
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e = 0x10001
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c = 0x... # dari challenge
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# Dari appendix paper: 10 contoh, setiap contoh punya p & q
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paper_examples = [
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# (p_i, q_i) — faktor dari 10 contoh paper
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...
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]
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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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print(f"Found factor via GCD with paper prime!")
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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}`
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