# Function to perform the Diffie-Hellman key exchange
def diffie_hellman(P, G, a, b):
    # Calculate public keys
    A = (G ** a) % P
    B = (G ** b) % P

    # Calculate shared secret
    S1 = (B ** a) % P
    S2 = (A ** b) % P

    # Ensure shared secrets match
    assert S1 == S2, "Shared secrets do not match!"

    return S1

# Parameters
P = 33
G = 8
a = 3  # User 1's private key
b = 2  # User 2's private key

# Perform Diffie-Hellman key exchange
shared_secret = diffie_hellman(P, G, a, b)

# Function to decode hash using shared secret
def decode_hash(hash_value, shared_secret):
    decoded_hash = int(hash_value, 16) ^ shared_secret  # Convert hash to integer and perform XOR
    return decoded_hash

# Provided hash value
hash_value = "cd7760167c59fa13ddc180e7ce78c5e7e23eb54dc2e38bd2a0022058b16a5de98b2d579e680a4caa3b8b507dba9c1944"

# Decode hash using shared secret
decoded_hash = decode_hash(hash_value, shared_secret)

print("Shared Secret:", shared_secret)
print("Decoded Hash:", hex(decoded_hash)[2:])  # Convert decoded hash back to hexadecimal and remove the '0x' prefix