Challenge description: Convert the provided series of transmit bits into in-phase quadrature (I/Q) samples.

The challenge is available at this address.

Let's connect to the challenge instance:

We are asked to convert a series of bits into an I/Q sample using QPSK (Quadrature Phase Shift Keying) modulation.

QPSK Modulation

QPSK modulation is a digital phase modulation technique where the phase of the carrier is altered to transmit data. You can review a lesson on modulation [here](just here) and on phase [here](right here).

Specifically, with this modulation, bits are grouped in pairs giving 4 possible combinations: 00, 01, 10, and 11, resulting in 4 distinct phases. Typically, each phase is separated by 90°. For example, one might assign 00 to 0°, 01 to 90°, 11 to 180°, and 10 to 270°.
This can also be seen in the following diagram with alternative values, but still separated by 90°:

I/Q Sample

I (In-phase) and Q (Quadrature) are the two orthogonal components of the modulated signal. They represent the cosine and sine parts of the modulated carrier wave, respectively.
An I/Q sample represents the numerical values of these two components, allowing us to depict the phase modulation used in QPSK on a two-dimensional plane (the constellation diagram).

Solution

To solve the challenge, we’ll write a script in Python. Since in QPSK the bits are encoded in pairs, we begin with the following step:

bits = "01000011 01110010 01101111 01101101 01110101 01101100 01100101 01101110 01110100 00001010"

bits_pair = []
i = 0
while i < len(bits):
    if bits[i] == " ": # Skip spaces (they could have been removed manually, but this keeps it neat)
        i += 1
    pair = bits[i:i+2]
    bits_pair.append(pair)
    i += 2

print(bits_pair) # ['01', '00', '00', '11', '01', '11', '00', '10', '01', '10', '11', '11', '01', '10', '11', '01', '01', '11', '01', '01', '01', '10', '11', '00', '01', '10', '01', '01', '01', '10', '11', '10', '01', '11', '01', '00', '00', '00', '10', '10']

Each bit pair is mapped to a specific point in the I/Q plane where I (In-phase) is the horizontal axis and Q (Quadrature) is the vertical axis. Based on the provided diagram, we can deduce our bit mapping scheme:

bits_map = {
    "00": "-1.0 -1.0",
    "01": "-1.0 1.0",
    "10": "1.0 -1.0",
    "11": "1.0 1.0"
}

iq_samples = []
for pair in bits_pair:
    iq_value = bits_map.get(pair)
    iq_samples.append(iq_value)

print(iq_samples) # ['-1.0 1.0', '-1.0 -1.0', '-1.0 -1.0', '1.0 1.0', '-1.0 1.0', '1.0 1.0', '-1.0 -1.0', '1.0 -1.0', '-1.0 1.0', '1.0 -1.0', '1.0 1.0', '1.0 1.0', '-1.0 1.0', '1.0 -1.0', '1.0 1.0', '-1.0 1.0', '-1.0 1.0', '1.0 1.0', '-1.0 1.0', '-1.0 1.0', '-1.0 1.0', '1.0 -1.0', '1.0 1.0', '-1.0 -1.0', '-1.0 1.0', '1.0 -1.0', '-1.0 1.0', '-1.0 1.0', '-1.0 1.0', '1.0 -1.0', '1.0 1.0', '1.0 -1.0', '-1.0 1.0', '1.0 1.0', '-1.0 1.0', '-1.0 -1.0', '-1.0 -1.0', '-1.0 -1.0', '1.0 -1.0', '1.0 -1.0']

Finally, we construct our QPSK sample:

qpsk = ' '.join(iq_samples)
print(qpsk)

Just run the entire script and you'll see output like:

python .\iq.py
-1.0 1.0 -1.0 -1.0 -1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 1.0 -1.0 -1.0 1.0 -1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 1.0 1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 -1.0 -1.0 -1.0 1.0 1.0 -1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 1.0 -1.0 -1.0 1.0 1.0 1.0 -1.0 1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 1.0 -1.0 1.0 -1.0

Copy and paste the output and you’ll receive the flag :)

> docker run --rm -i -e FLAG=pouet iq:challenge
[...]
Input samples: -1.0 1.0 -1.0 -1.0 -1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 1.0 -1.0 -1.0 1.0 -1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 1.0 1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 -1.0 -1.0 -1.0 1.0 1.0 -1.0 -1.0 1.0 -1.0 1.0 -1.0 1.0 1.0 -1.0 1.0 1.0 1.0 -1.0 -1.0 1.0 1.0 1.0 -1.0 1.0 -1.0 -1.0 -1.0 -1.0 -1.0 -1.0 1.0 -1.0 1.0 -1.0
You got it! Here's your flag:
pouet

Writeup Hack-A-Sat: IQ

QPSK Modulation

I/Q Sample

Solution