Original description:

My furrier friend tried to send me a morse code message about some new furs, but he was using a noisy connection. I think he repeated it a few times but I still can’t tell what he said, could you figure out what he was trying to tell me? Here’s the code he used. (the flag is not in the actf{} format)

Problem:

You get a morse-message of unknown length with a lot of noise, but the constant length message is repeated a lot.

Problem code

import numpy as np
from random import gauss
morse = REDACTED
repeats = REDACTED
pointed = []
for c in morse:
    if c == ".":
        pointed.extend([1 for x in range(10)])
    if c == "-":
        pointed.extend([1 for x in range(20)])
    if c == " ":
        pointed.extend([0 for x in range(20)])
    pointed.extend([0 for x in range(10)])

with open("points.txt", "w") as f:
    for _ in range(repeats):
        signal = pointed
        output = []
        for x, bit in enumerate(signal):
            output.append(bit + gauss(0,2))

        signal = list(np.array(output) - .5)
        f.write('\n'.join([str(x) for x in signal])+"\n")
f.close()

Solution

As the signal is repeated multiple times, we can find out the original flags length via autocorrelation (self-similarity, i.e. how similar chunks of length N are to following chunks of length N via plot_acf.

We also know from inspecting the input-code, that we can further group by 10 and the average of these values already gives us a good estimate.

The binary-to-morse and morse-decode is pretty standard.

Solution Code

import matplotlib.pyplot as plt
from statsmodels.graphics.tsaplots import plot_acf
import numpy as np
from functools import reduce
factors = lambda n: sorted(reduce(list.__add__, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0)))

# compressed version with only 2 sigificant digits to be embedded here
data = np.array([0.70, -0.80, 1.07, 2.02, 1.92, 3.10, 0.82, 0.00, -0.11, -0.61, -0.74, -1.34, -0.23, -0.60, -1.71, -0.36, -0.80, 0.17, 0.40, -1.44, 0.26, -0.73, 0.64, -1.02, 0.69, -1.17, -0.78, -0.15, 0.17, 0.10, 0.30, 0.62, 2.40, 0.88, 1.31, 0.83, -0.15, -0.33, 0.37, 0.87, -0.21, 0.59, -0.32, 0.22, -0.14, -0.19, 1.22, -1.74, -0.61, -1.31, -1.05, 0.11, -0.48, -2.10, -0.42, -1.86, -1.18, -1.28, -2.68, -1.23, 1.76, 1.00, -0.17, -0.77, -0.00, 0.23, -1.21, 1.20, 0.10, -0.04, 0.25, 0.98, 0.84, -1.01, 0.32, 1.04, -0.89, -0.76, -1.27, -1.63, 0.09, -1.72, 0.34, 0.19, -0.16, -0.97, -0.70, 0.10, 2.60, 0.25, 1.43, 1.05, 0.96, 0.34, -1.03, 0.03, 1.23, 2.38, 2.94, 1.24, 0.10, -0.56, -1.32, -1.59, -0.46, 0.34, -0.27, 0.76, -1.01, -1.15, -0.01, 0.29, 1.01, -0.52, 2.19, 1.91, 0.22, -0.15, 0.64, 1.17, 0.95, -0.22, -0.10, -1.50, 0.31, 0.19, -0.39, -0.27, -0.39, -1.22, -1.24, -0.79, -0.45, 0.93, -1.45, -0.37, -0.41, -0.47, -1.93, 0.35, 0.09, -1.87, -1.18, -0.17, -0.35, -0.27, 0.27, -1.41, -0.14, 0.09, 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