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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print("data length", len(data))
print("factors", factors(len(data)))

# plot autocorrelation
plot_acf(data, lags=1500)
plt.show()

plot_acf(data, lags=range(950, 1000))
plt.show()
data length 28800
factors [1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 36, 40, 45, 48, 50, 60, 64, 72, 75, 80, 90, 96, 100, 120, 128, 144, 150, 160, 180, 192, 200, 225, 240, 288, 300, 320, 360, 384, 400, 450, 480, 576, 600, 640, 720, 800, 900, 960, 1152, 1200, 1440, 1600, 1800, 1920, 2400, 2880, 3200, 3600, 4800, 5760, 7200, 9600, 14400, 28800]

png

png

Solution description

As the sequence is repeated, the autocorrelation gives us possible repeat-sites. The repeat-number also has to be a multiple of x10 as the internal-repeat factor is 10.

You can find the highest autocorrelation in the plot at at 960, which also matches our x10 requirement.

# Re-order the array to be (size/96/10) x (96) x (10), so we can take a mean over the axis to get a resulting 96-long flag (axis 0 and 2)
d = data.reshape((-1, 96, 10)).mean((0, 2)) > 0
# Convert bool np array to 10101010-string
d = "".join(d.astype(int).astype(str))
# Transform bool to morse
d = d.replace("110", "-").replace("10", ".").replace("000", " ")
print(d)
.- -. --- .. ... -.-- -. --- .. ... .
encode = { 'A':'.-', 'B':'-...', 'C':'-.-.', 'D':'-..', 'E':'.', 
            'F':'..-.', 'G':'--.', 'H':'....', 'I':'..', 'J':'.---', 'K':'-.-', 
            'L':'.-..', 'M':'--', 'N':'-.', 'O':'---', 'P':'.--.', 'Q':'--.-', 
            'R':'.-.', 'S':'...', 'T':'-', 'U':'..-', 'V':'...-', 'W':'.--', 
            'X':'-..-', 'Y':'-.--', 'Z':'--..', '1':'.----', '2':'..---', '3':'...--', 
            '4':'....-', '5':'.....', '6':'-....', '7':'--...', '8':'---..', '9':'----.', 
            '0':'-----', ', ':'--..--', '.':'.-.-.-', '?':'..--..', '/':'-..-.', '-':'-....-', 
            '(':'-.--.', ')':'-.--.-'} 
decode = dict((v,k) for (k,v) in encode.items())

#Then we backwards-replace the morse code.
text = "".join(decode[letter] for letter in d.split())
print(text)

Prints: ANOISYNOISE