Added new algo for RSA

*  Used in cryptography, the RSA algorithm is known for its complexity
   in terms of factoring large prime numbers

Author: rishabhkemni

other/RSA_Algo/rsa_algo.py

@@ -0,0 +1,120 @@
+import random
+from sympy import isprime, mod_inverse
+import sys
+
+def generate_prime_candidate(length):
+    """
+    Generate a large prime number candidate.
+    
+    >>> p = generate_prime_candidate(16)
+    >>> isprime(p)
+    True
+    """
+    p = random.getrandbits(length)
+    while not isprime(p):
+        p = random.getrandbits(length)
+    return p
+
+def generate_keys(keysize):
+    """
+    Generate RSA keys.
+    
+    >>> public, private = generate_keys(16)
+    >>> len(bin(public)) - 2  # Check bit length of n
+    32
+    >>> len(bin(private)) - 2  # Check bit length of n
+    32
+    """
+    try:
+        e = d = n = 0
+
+        p = generate_prime_candidate(keysize)
+        q = generate_prime_candidate(keysize)
+        
+        n = p * q
+        phi = (p - 1) * (q - 1)
+
+        e = random.randrange(1, phi)
+        g = gcd(e, phi)
+        while g != 1:
+            e = random.randrange(1, phi)
+            g = gcd(e, phi)
+
+        d = mod_inverse(e, phi)
+
+        return ((e, n), (d, n))
+    except Exception as ex:
+        print(f"Error generating keys: {ex}", file=sys.stderr)
+        sys.exit(1)
+
+def gcd(a, b):
+    """
+    Compute the greatest common divisor of a and b.
+    
+    >>> gcd(48, 18)
+    6
+    """
+    while b != 0:
+        a, b = b, a % b
+    return a
+
+def encrypt(pk, plaintext):
+    """
+    Encrypt a message with a public key.
+    
+    >>> public, private = generate_keys(16)
+    >>> encrypted = encrypt(public, "test")
+    >>> isinstance(encrypted, list)
+    True
+    """
+    try:
+        key, n = pk
+        cipher = [(ord(char) ** key) % n for char in plaintext]
+        return cipher
+    except Exception as ex:
+        print(f"Error during encryption: {ex}", file=sys.stderr)
+        return None
+
+def decrypt(pk, ciphertext):
+    """
+    Decrypt a message with a private key.
+    
+    >>> public, private = generate_keys(16)
+    >>> encrypted = encrypt(public, "test")
+    >>> decrypted = decrypt(private, encrypted)
+    >>> decrypted == "test"
+    True
+    """
+    try:
+        key, n = pk
+        plain = [chr((char ** key) % n) for char in ciphertext]
+        return ''.join(plain)
+    except Exception as ex:
+        print(f"Error during decryption: {ex}", file=sys.stderr)
+        return None
+
+if __name__ == '__main__':
+    import doctest
+    doctest.testmod()
+
+    try:
+        keysize = 1024
+        public, private = generate_keys(keysize)
+
+        message = "Hello, RSA!"
+        print("Original message:", message)
+
+        encrypted_msg = encrypt(public, message)
+        if encrypted_msg:
+            print("Encrypted message:", encrypted_msg)
+
+            decrypted_msg = decrypt(private, encrypted_msg)
+            if decrypted_msg:
+                print("Decrypted message:", decrypted_msg)
+            else:
+                print("Decryption failed.", file=sys.stderr)
+        else:
+            print("Encryption failed.", file=sys.stderr)
+    except Exception as ex:
+        print(f"An error occurred: {ex}", file=sys.stderr)
+        sys.exit(1)