Noisy — HackTheBox

Description

"Encrypting data with discrete values is all very well and good, but there'll always be a finite number of outputs, and I hate anything you can brute force. That's why I use continuous values to store my flags! It's just... quite hard to get them back again..."

Files: encrypt.py, encrypted.wav

Analysis

The encrypt.py script encodes each flag character as a sine wave and sums them into a single WAV file:

import numpy as np
from scipy.io.wavfile import write

from secret import flag

N = 1_000_000
T = .0001

x = np.linspace(0.0, N*T, N, endpoint=False)
final_waveform = 0

count_used = dict()

for i, c in enumerate(flag):
    count_used[c] = count_used.get(c, 0) + 1
    multiplier = .1 * c * (4**(count_used[c]-1))
    final_waveform += (i+1) * np.sin(2 * np.pi * x * multiplier)

write("encrypted.wav", 20_000_000, final_waveform)

Encoding Parameters

For each character c at position i:

Parameter	Formula	Purpose
Frequency	0.1 * ASCII(c) * 4^(occurrence - 1)	Unique frequency for each character; repeated characters get exponentially higher frequencies (x4 each time)
Amplitude	i + 1	Character position in the flag (1-indexed)
Signal	amplitude * sin(2*pi*freq*x)	Standard sine wave

The resulting WAV = sum of 39 sine waves (one per flag character).

Key Observation

This is a classic inverse Fourier transform problem: sum of sine waves -> FFT -> individual frequency components with amplitudes. FFT is the exact mathematical inverse of the encoding process.

Solution

Step 1: FFT Decomposition

Apply Fast Fourier Transform to the WAV file to decompose the summed signal into individual sinusoidal components:

fft_result = np.fft.rfft(data)
freqs = np.fft.rfftfreq(N, d=T)
magnitudes = np.abs(fft_result)

Step 2: Peak Detection

...