Simple Geometry

Platform: duckerz | Category: Reversing | Type: Challenge | Difficulty: Medium | OS: NA | Author: XESXOR | Date: 2026-01-09 | Status: Solved Techniques: geometry_constraints, static_analysis, vector_math

Summary

The simple_geo program (64-bit ELF, stripped) requests coordinates of 6 points on a plane (12 double values) and validates them against a set of geometric constraints. Upon passing all checks, the server returns the flag.

Simple Geometry — duckerz

Description

The simple_geo program (64-bit ELF, stripped) requests coordinates of 6 points on a plane (12 double values) and validates them against a set of geometric constraints. Upon passing all checks, the server returns the flag.

Analysis

Static analysis revealed that the program reads 12 floating-point numbers that form three line segments:

• s1: from $P_1$ to $P_2$
• s2: from $P_3$ to $P_4$
• s3: from $P_5$ to $P_6$

Validation conditions:

1. Length of s1: $4.0 \le \text{dist}(P_1, P_2) < 5.0$
2. Length of s2: $5.0 \le \text{dist}(P_3, P_4) < 6.0$
3. Length of s3: $\text{dist}(P_5, P_6) \approx 4.0$ (absolute difference from 4.0 must be $< 10^{-5}$)
4. Relationship between s1 and s2: $|\cos(s_1, s_2)| < 1.0$. This means segments $s_1$ and $s_2$ must not be parallel.
5. Relationship between s1 and s3: $0.5 \le |\cos(s_1, s_3)| \le 1.0$. This corresponds to an angle between segments in the range from 0° to 60°. ‍​‌‌​​​​‌​‌‌​​‌‌​​‌‌​​‌‌​​‌‌​​‌​​​​‌‌​​​​​‌‌​​‌‌​​‌‌​​‌​‌​‌‌​​‌​‌‍

The program uses standard formulas:

• Distance: $\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
• Cosine of angle: $\frac{|\vec{v_1} \cdot \vec{v_2}|}{|\vec{v_1}| \cdot |\vec{v_2}|}$

Solution

To satisfy all conditions, we choose the simplest possible coordinates using coordinate axes:

1. For s1: $P_1=(0,0), P_2=(4,0)$.
   • Length = 4.0 (falls within $[4.0, 5.0)$).
2. For s2: $P_3=(0,0), P_4=(0,5)$.
   • Length = 5.0 (falls within $[5.0, 6.0)$).
   • Vector $s_1 = (4, 0)$, vector $s_2 = (0, 5)$.
   • $\cos(s_1, s_2) = 0$ (perpendicular, $0 < 1.0$, condition satisfied).
3. For s3: $P_5=(0,0), P_6=(4,0)$.
   • Length = 4.0 (difference from 4.0 equals 0, which is $< 10^{-5}$).
   • Vector $s_3 = (4, 0)$.
   • $\cos(s_1, s_3) = 1.0$ (parallel, $0.5 \le 1.0 \le 1.0$, condition satisfied). ‍​‌‌​​​​‌​‌‌​​‌‌​​‌‌​​‌‌​​‌‌​​‌​​​​‌‌​​​​​‌‌​​‌‌​​‌‌​​‌​‌​‌‌​​‌​‌‍

Script to obtain the flag:

 python read-only • copy allowed Copy
#!/usr/bin/env python3
from pwn import *

# Connection configuration
host = 'tasks.duckerz.ru'
port = 30005

# Point coordinates (x1, y1, x2, y2, ...)
# p1=(0,0), p2=(4,0) -> s1
# p3=(0,0), p4=(0,5) -> s2
# p5=(0,0), p6=(4,0) -> s3
coords = [
    0, 0, 4, 0,
    0, 0, 0, 5,
    0, 0, 4, 0
]

payload = " ".join(map(str, coords))

try:
    r = remote(host, port)
    r.sendline(payload.encode())
    response = r.recvall(timeout=5).decode()
    print(response)
except Exception as e:
    print(f"Error: {e}")

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