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
60 lines
1.4 KiB
Markdown
60 lines
1.4 KiB
Markdown
---
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title: "Slopped — RSA Small Factors"
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event: "GEMASTIK 2026 Warmup"
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challenge: "Slopped"
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category: "crypto"
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points: 500
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difficulty: "medium"
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flag: "GEMASTIK19{qu4ntum_c0mput3r_br0k3_rs4_y0u_sh0uld_us3_p4p3r_s34rch_mcp_sk1ll}"
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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 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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# Trial division menemukan faktor kecil
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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 ("you should use paper search").
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