8. Radio Polybius Square

8.1. Polybius cipher

The Polybius Cipher, also known as the Polybius Square, is a substitution cipher that maps each letter of the alphabet to a pair of coordinates in a grid.

Grid Creation: A 5x5 grid is created, and each cell is filled with a letter of the alphabet. To fit the 26 letters of the alphabet into the 25 cells created by the table, the letters I and J are usually combined into a single cell.

Encryption: Each letter in the plaintext is replaced by its corresponding coordinates on the grid. For example, if B is in the cell at row 0 column 1. An image with the LED turned on at position (0, 1) represents the B.

Decryption: The process is reversed to decrypt the message. The LED turned on at position (0, 1) is converted to a B.

---

8.2. Break the code

This script uses radio communication for sending and receiving encrypted messages.

The script sets up a radio group, defines a list of secret phrases, and implements a polybius square function for encryption.

When the A-button is pressed, it selects a random secret message, applies the polybius square, sends the image strings via radio for display on the receiver’s microbit, and starts a timer.

If button B is pressed, it stops the timer and displays the elapsed time.

For the receiver, the script also checks for incoming radio messages and displays them on the microbit’s LED display.

from microbit import *
import radio
import random


# Turn on the radio
radio.on()
# Choose own group in pairs 0-255
radio.config(group=8)

# polybius cipher letters
ALPHABET = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"

# secrets to be chosen from
SECRETS = [
    "MEET AT DAWN",
    "THE BIRD HAS FLOWN",
    "TRUST NO ONE",
    "SEEK THE TRUTH",
    "SECURE THE ASSET",
    "AVOID DETECTION",
    "KEEP MOVING",
    "STAY HIDDEN",
    "WATCH YOUR BACK",
    "TIME IS KEY",
]


# Define the Polybius square
# I and J now share the same grid cell
polybius_square = {
    "A": (0, 0),
    "B": (1, 0),
    "C": (2, 0),
    "D": (3, 0),
    "E": (4, 0),
    "F": (0, 1),
    "G": (1, 1),
    "H": (2, 1),
    "I": (3, 1),
    "J": (3, 1),
    "K": (4, 1),
    "L": (0, 2),
    "M": (1, 2),
    "N": (2, 2),
    "O": (3, 2),
    "P": (4, 2),
    "Q": (0, 3),
    "R": (1, 3),
    "S": (2, 3),
    "T": (3, 3),
    "U": (4, 3),
    "V": (0, 4),
    "W": (1, 4),
    "X": (2, 4),
    "Y": (3, 4),
    "Z": (4, 4),
}



# Function to extract numbers from the image string
def extract_image_string(image):
    # Convert the image to a string
    full_image_string = str(image)
    # Replace the colon and newline characters with an empty string
    image_string = full_image_string.replace("'", "").replace("\n", "").replace(" ", "").replace("(", "").replace(")", "").replace("Image", "")
    return image_string


def polybius_cipher(message):
    cipher_imgstring_list = []
    for char in message:
        if char in ALPHABET:
            # Get the coordinates for the letter
            x, y = polybius_square[char.upper()]
            # Create an empty image
            img = Image("00000:" * 5)
            # Set the pixel at the coordinates to 9
            img.set_pixel(x, y, 9)
            cipher_imgstring_list.append(extract_image_string(img))
        else:
            img = Image("00000:" * 5)
            cipher_imgstring_list.append(extract_image_string(img))
    return cipher_imgstring_list


def receive_image():
    # Receive a message from the radio
    incoming = radio.receive()
    if incoming:
        try:
            display.show(Image(incoming))
        except:
            display.show(incoming)


# Initialize timer
timer = 0

while True:
    # Check button presses to send a secret message
    if button_a.was_pressed():
        # Select a random secret message and add a space so the final dot is cleared automatically
        secret = random.choice(SECRETS) + " "
        # Display the secret message on the sender's microbit
        display.scroll(secret, delay=100, wait=False)
        cipher_texts = polybius_cipher(secret)
        for cipher_text in cipher_texts:
            radio.send(cipher_text)
            sleep(1000)
        # Start the timer
        timer = running_time()
    elif button_b.was_pressed() and timer:
        # time must be not 0; so A-button must be pressed first
        # Stop the timer and display the elapsed time in seconds
        elapsed_time = int((running_time() - timer) / 1000)
        display.scroll(str(elapsed_time))
        timer = 0
    # Check for incoming messages
    receive_image()

---

Exercises

1. Challenge your partner to crack the code. Use a polybius grid on paper to help decryption. Press A, read the message sent, and then press B when your partner has worked out the message correctly. Write down the time and reverse rolls to see who has the best time.