Anul 3 Semestrul 1

Anul 3/Semestrul 1/Public Key Cryptography/Crypto4.py

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+import random
+from sympy import isprime, gcd
+
+# Define the 27-character alphabet mapping
+ALPHABET = " ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+ALPHABET_MAP = {char: idx for idx, char in enumerate(ALPHABET)}
+REVERSE_ALPHABET_MAP = {idx: char for idx, char in enumerate(ALPHABET)}
+
+
+# Extended Euclidean Algorithm to find modular inverse
+def modular_inverse(a, m):
+    """Returns the modular inverse of a under modulo m, or None if it doesn't exist."""
+    m0, x0, x1 = m, 0, 1
+    while a > 1:
+        q = a // m
+        a, m = m, a % m
+        x0, x1 = x1 - q * x0, x0
+    if x1 < 0:
+        x1 += m0
+    return x1
+
+
+# RSA key generation function
+def generate_rsa_keys(bit_length=512):
+    p = generate_large_prime(bit_length)
+    q = generate_large_prime(bit_length)
+
+    n = p * q
+    phi = (p - 1) * (q - 1) # euler's function
+
+    e = 65537
+    while gcd(e, phi) != 1:
+        e = random.randint(2, phi - 1)
+
+    d = modular_inverse(e, phi)
+    if d is None:
+        raise ValueError("Modular inverse for the chosen e does not exist.")
+
+    return (n, e), (n, d)
+
+
+def generate_large_prime(bit_length):
+    """Generates a random prime number of approximately bit_length bits."""
+    while True:
+        candidate = random.getrandbits(bit_length)
+        if isprime(candidate):
+            return candidate
+
+
+# RSA encryption
+def rsa_encrypt(plaintext, public_key):
+    n, e = public_key
+    # Convert plaintext to numeric format using the alphabet map
+    numeric_plaintext = [ALPHABET_MAP[char] for char in plaintext if char in ALPHABET_MAP]
+    # Encrypt each character in the numeric plaintext
+    ciphertext = [pow(char, e, n) for char in numeric_plaintext]
+    return ciphertext
+
+
+# RSA decryption
+def rsa_decrypt(ciphertext, private_key):
+    n, d = private_key
+    # Decrypt each character in the ciphertext
+    decrypted_numbers = [pow(char, d, n) for char in ciphertext]
+    # Convert decrypted numbers back to characters
+    plaintext = ''.join(REVERSE_ALPHABET_MAP[num] for num in decrypted_numbers)
+    return plaintext
+
+
+# Validation functions
+def validate_plaintext(plaintext):
+    """Validates that the plaintext contains only characters from the 27-character alphabet."""
+    for char in plaintext:
+        if char not in ALPHABET_MAP:
+            raise ValueError(f"Invalid character in plaintext: {char}")
+
+
+def validate_ciphertext(ciphertext, n):
+    """Validates that each part of the ciphertext is a number less than n."""
+    for part in ciphertext:
+        if not (0 <= part < n):
+            raise ValueError(f"Invalid ciphertext value: {part}")
+
+
+# Example usage
+if __name__ == "__main__":
+    # Generate keys
+    public_key, private_key = generate_rsa_keys()
+
+    # Plaintext to encrypt
+    plaintext = "HELLO WORLD"
+    validate_plaintext(plaintext)
+
+    # Encrypt the plaintext
+    ciphertext = rsa_encrypt(plaintext, public_key)
+    print("Ciphertext:", ciphertext)
+
+    # Validate ciphertext and decrypt
+    validate_ciphertext(ciphertext, public_key[0])
+    decrypted_text = rsa_decrypt(ciphertext, private_key)
+    print("Decrypted Text:", decrypted_text)