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
68 lines
1.6 KiB
Markdown
68 lines
1.6 KiB
Markdown
---
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title: "Slopped — RSA Small Factors"
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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/ch13-slopped.md"
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created_at: "2026-08-21T07:26:21.304Z"
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updated_at: "2026-08-21T07:26:21.304Z"
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category: "crypto"
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challenge: "Slopped"
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difficulty: "medium"
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event: "GEMASTIK 2026 Warmup"
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flag: "GEMASTIK19{qu4ntum_c0mput3r_br0k3_rs4_y0u_sh0uld_us3_p4p3r_s34rch_mcp_sk1ll}"
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points: 500
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---
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# Slopped (500 pts) — Crypto / RSA small factors
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**File:** `chall.py`
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```python
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import random
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p = random.randint(1, 10**4) # tiny prime candidates
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q = random.randint(1, 10**4)
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# ... find small primes, multiply
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n = p * q * (big prime)
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e = 0x10001
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c = pow(flag, e, n)
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```
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## Analisis
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RSA dengan `e = 0x10001`, `n` 2048-bit, `c = pow(flag, e, n)`.
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`n` dibangun dari **faktor prima kecil** (sloppy primes — "my AI broke RSA with
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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)`.
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## Solusi
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```python
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from Crypto.Util.number import long_to_bytes
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from sympy import factorint
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e = 0x10001
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n = 0xdb... # 2048-bit modulus
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c = 0x...
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factors = factorint(n)
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print(factors)
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# {83: 1, 233: 1, 9679: 1, <big_prime>: 1}
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phi = 1
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for p, exp in factors.items():
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phi *= (p - 1) * p**(exp - 1)
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d = pow(e, -1, phi)
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m = pow(c, d, n)
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print(long_to_bytes(m))
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# GEMASTIK19{qu4ntum_c0mput3r_br0k3_rs4_y0u_sh0uld_us3_p4p3r_s34rch_mcp_sk1ll}
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```
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## Flag
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`GEMASTIK19{qu4ntum_c0mput3r_br0k3_rs4_y0u_sh0uld_us3_p4p3r_s34rch_mcp_sk1ll}`
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> Flag ini adalah petunjuk untuk ch14 (paper search).
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