Signal Sur Chat

Link to the challenge

This challenge was one of the most challenging as my loudspeakers distorted the og cat’s sound, the cat command was just hanging instead of printing stuff as it used to and I am not fluent in cat.

Nevertheless after calling my own cat and asking him to type what he heard I got the flag F…C…:mouse:…C. The problem is, it was not so sure of how it continued so I had to figure out another method.

This challenge’s instructions were fairly straightforward and the principal difficulty I met in its resolution was not botching the implementation of Gold and LFSR… which I did many times. Resigned I went on github cloned a repo that did it flawlessly and now things were going.

Once this was done the script basically just :

reads the audio file
enumerated the different phases specified in the instructions, and for each of them
- calculated the correlation between the Gold code step and the audio data
- determined for each bit if the data were positively correlated then the bit was 1 else 0
- translated the binary to ASCII
enjoyed

This is the script

import os

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

# Thanks to https://github.com/chrinels/sequences


LFSR_LEN = 15
SEQ_LEN = (1 << LFSR_LEN) - 1  # 32767
INIT_STATE = [int(x) for x in format(0x7FFF, f'0{LFSR_LEN}b')]
TAPS1 = [15, 7, 0]  # x^15 + x^7 + 1
TAPS2 = [15, 10, 5, 4, 0]  # x^15 + x^10 + x^5 + x^4 + 1
PHASES = [4, 7, 8, 24, 27, 31, 39, 42, 43, 49, 53, 54, 59, 62, 65, 73, 93, 99, 118, 119, 120, 128]
BITS_PER_CHAR = 8
AUDIO_FILE = 'signal-sur-chat.wav'
PLOT = False


def transform_gold_code(gold_code: np.ndarray) -> np.ndarray:
    return np.where(gold_code == 1, -0.5, 0.5)


def decode_signal(audio_data: np.ndarray, phases: list[int]) -> str:
    flag = ''
    samples_per_bit = SEQ_LEN

    for idx, phase in enumerate(phases):
        gold_generator = Gold(TAPS1, INIT_STATE, TAPS2, INIT_STATE, index=phase)
        gold_code = gold_generator.step()

        gold_code_corr = transform_gold_code(np.array(gold_code))

        bits = []
        for bit_index in range(BITS_PER_CHAR):
            start = bit_index * samples_per_bit
            end = start + samples_per_bit
            segment = audio_data[start:end]

            correlation = float(np.sum(segment * gold_code_corr[: len(segment)]))

            bit = '1' if correlation > 0 else '0'
            bits.append(bit)

        char_val = int(''.join(bits), 2)
        try:
            char = chr(char_val)
            flag += char
        except Exception:
            flag += '?'

        print(
            f"Char {idx+1:2d} (phase={phase:3d}): bits={''.join(bits)} -> {char if 32 <= char_val < 127 else '?'}",
        )

    return flag


if __name__ == '__main__':
    gold_generator = Gold(TAPS1, INIT_STATE, TAPS2, INIT_STATE, index=128)

    if not os.path.exists(AUDIO_FILE):
        print(f"Error: Audio file '{AUDIO_FILE}' not found.")
        exit(1)

    print(f'Reading audio file: {AUDIO_FILE}...')
    sample_rate, audio_data_raw = wavfile.read(AUDIO_FILE)
    audio_data = audio_data_raw.astype(np.float64)
    if audio_data.ndim > 1:
        audio_data = audio_data[:, 0]

    print(f'Audio read: {len(audio_data)} samples, Sample rate: {sample_rate} Hz')
    if len(audio_data) != BITS_PER_CHAR * SEQ_LEN:
        print(f'Warning: audio length {len(audio_data)} != expected {BITS_PER_CHAR * SEQ_LEN}')

    flag = decode_signal(audio_data, PHASES)
    print(f'\nFlag: {flag}')