Anul 3 Semestrul 1

Anul 3/Semestrul 1/Public Key Cryptography/Crypto5.py

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+#2. Paillier cryptosystem
+
+import random
+from math import gcd, lcm
+from sympy import isprime, public
+
+ALPHABET = " ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ALPHABET_MAP = {char: idx for idx, char in enumerate(ALPHABET)}
+REVERSE_ALPHABET_MAP = {idx: char for idx, char in enumerate(ALPHABET)}
+
+def text_to_numeric(plaintext):
+    return [ALPHABET_MAP[char] for char in plaintext if char in ALPHABET_MAP]
+
+def numeric_to_text(numeric_plaintext):
+    return "".join([REVERSE_ALPHABET_MAP[idx] for idx in numeric_plaintext])
+
+
+def generate_paillier_keypair(bit_length=512):
+    p = generate_large_prime(bit_length)
+    q = generate_large_prime(bit_length)
+    n = p * q
+    n_squared = n * n
+
+    lambda_n = lcm(p - 1, q - 1)
+
+    mmi = 0
+
+    while True:
+        g = random.randint(1, n_squared-1)
+        if g // n == g / n:
+            continue
+        mmi = pow(L(pow(g, lambda_n, n_squared), n),-1,n)
+        break
+
+    public_key = (n, g)
+    private_key = (lambda_n, mmi)
+    return public_key, private_key
+
+def L(x, n):
+    return (x - 1) // n
+
+def generate_large_prime(bit_length):
+    while True:
+        candidate = random.getrandbits(bit_length)
+        if isprime(candidate):
+            return candidate
+    
+def paillier_encrypt(plaintext, public_key):
+    n, g = public_key
+    r = random.randint(1, n-1)
+    while gcd(r, n) != 1:
+        # Extremly unlikely to happen
+        r = random.randint(1, n-1)
+    ciphertext = []
+    for int_letter in text_to_numeric(plaintext):
+        c = (pow(g, int_letter, n*n) * pow(r, n, n*n)) % (n*n)
+        ciphertext.append(c)
+    return ciphertext
+
+
+def paillier_decrypt(ciphertext, private_key, public_key):
+    lambda_n, mmi = private_key
+    n, g = public_key
+    plaintext = []
+    for c in ciphertext:
+        l = L(pow(c, lambda_n, n*n), n)
+        m = (l * mmi) % n
+        plaintext.append(m)
+    return numeric_to_text(plaintext)
+    
+
+if __name__ == "__main__":
+    public_key, private_key = generate_paillier_keypair()
+    plaintext = "HELLO WORLD"
+    print("Plaintext:", plaintext)
+    ciphertext = paillier_encrypt(plaintext, public_key)
+    print("Ciphertext:", ciphertext)
+    decrypted = paillier_decrypt(ciphertext, private_key, public_key)
+    print("Decrypted:", decrypted)