def paillier_demo(p: int, q: int, m: int, g: int, r: int):
"""Dems encryption and decryption with the given arguments."""
print("Paillier")
# find public key param n
n = p * q
print("Message m:", m)
print("Primes p & q:", p, q)
print("Public key parameter n:", n)
print("Public key parameter g:", g)
# find private key params (ƛ, μ)
ƛ = cf.lcm(p - 1, q - 1)
k = cf.L((g**ƛ) % (n**2), n)
μ = cf.inverse_mod(k, n)
print("Private key parameter ƛ:", ƛ)
print("Pre-parameter k:", k)
print("Private key parameter μ:", μ, "\n")
# keys
print("Public key (n, g):", n, g)
print("Private key (ƛ, μ):", ƛ, μ, "\n")
# find ciphertext c = g**m r**n mod n**2
c = g**m * r**n % n**2
print("Ciphertext:", c)
# decrpyt c to verify the plaintext m
p = cf.L(c**ƛ % n**2, n) * μ % n
print("Decrypted plaintext:", p)
def generate_keys(p: int, q: int, g: int):
""" Return a dict containing private and public key parameters."""
n = p * q
ƛ = cf.lcm(p - 1, q - 1)
k = cf.L((g**ƛ) % (n**2), n)
μ = cf.inverse_mod(k, n)
return {"n": n, "g": g, "ƛ": ƛ, "μ": μ}
def decrypt(ƛ: int, μ: int, n: int, c: int):
""" Return decrypted plaintext."""
return cf.L(c**ƛ % n**2, n) * μ % n