Added hill_cipher.py (#696)

A python class that implements the Hill cipher algorithm.

Author: JekyllAndHyde8999

ciphers/hill_cipher.py

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+"""
+
+Hill Cipher:
+The below defined class 'HillCipher' implements the Hill Cipher algorithm.
+The Hill Cipher is an algorithm that implements modern linear algebra techniques
+In this algortihm, you have an encryption key matrix. This is what will be used
+in encoding and decoding your text.
+
+Algortihm:
+Let the order of the encryption key be N (as it is a square matrix).
+Your text is divided into batches of length N and converted to numerical vectors
+by a simple mapping starting with A=0 and so on.
+
+The key is then mulitplied with the newly created batch vector to obtain the
+encoded vector. After each multiplication modular 36 calculations are performed
+on the vectors so as to bring the numbers between 0 and 36 and then mapped with
+their corresponding alphanumerics.
+
+While decrypting, the decrypting key is found which is the inverse of the
+encrypting key modular 36. The same process is repeated for decrypting to get
+the original message back.
+
+Constraints:
+The determinant of the encryption key matrix must be relatively prime w.r.t 36.
+
+Note:
+The algorithm implemented in this code considers only alphanumerics in the text.
+If the length of the text to be encrypted is not a multiple of the
+break key(the length of one batch of letters),the last character of the text
+is added to the text until the length of the text reaches a multiple of
+the break_key. So the text after decrypting might be a little different than
+the original text.
+
+References:
+https://apprendre-en-ligne.net/crypto/hill/Hillciph.pdf
+https://www.youtube.com/watch?v=kfmNeskzs2o
+https://www.youtube.com/watch?v=4RhLNDqcjpA
+
+"""
+
+import numpy
+
+
+def gcd(a, b):
+    if a == 0:
+        return b
+    return gcd(b%a, a)
+
+
+class HillCipher:
+    key_string = "ABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789"
+    # This cipher takes alphanumerics into account
+    # i.e. a total of 36 characters
+
+    replaceLetters = lambda self, letter: self.key_string.index(letter)
+    replaceNumbers = lambda self, num: self.key_string[round(num)]
+
+    # take x and return x % len(key_string)
+    modulus = numpy.vectorize(lambda x: x % 36)
+
+    toInt = numpy.vectorize(lambda x: round(x))
+    
+    def __init__(self, encrypt_key):
+        """
+        encrypt_key is an NxN numpy matrix
+        """
+        self.encrypt_key = self.modulus(encrypt_key) # mod36 calc's on the encrypt key
+        self.checkDeterminant() # validate the determinant of the encryption key
+        self.decrypt_key = None
+        self.break_key = encrypt_key.shape[0]
+
+    def checkDeterminant(self):
+        det = round(numpy.linalg.det(self.encrypt_key))
+        
+        if det < 0:
+            det = det % len(self.key_string)
+
+        req_l = len(self.key_string)
+        if gcd(det, len(self.key_string)) != 1:
+            raise ValueError("discriminant modular {0} of encryption key({1}) is not co prime w.r.t {2}.\nTry another key.".format(req_l, det, req_l))
+
+    def processText(self, text):
+        text = list(text.upper())
+        text = [char for char in text if char in self.key_string]
+
+        last = text[-1]
+        while len(text) % self.break_key != 0:
+            text.append(last)
+
+        return ''.join(text)
+    
+    def encrypt(self, text):
+        text = self.processText(text.upper())
+        encrypted = ''
+
+        for i in range(0, len(text) - self.break_key + 1, self.break_key):
+            batch = text[i:i+self.break_key]
+            batch_vec = list(map(self.replaceLetters, batch))
+            batch_vec = numpy.matrix([batch_vec]).T
+            batch_encrypted = self.modulus(self.encrypt_key.dot(batch_vec)).T.tolist()[0]
+            encrypted_batch = ''.join(list(map(self.replaceNumbers, batch_encrypted)))
+            encrypted += encrypted_batch
+
+        return encrypted
+
+    def makeDecryptKey(self):
+        det = round(numpy.linalg.det(self.encrypt_key))
+        
+        if det < 0:
+            det = det % len(self.key_string)
+        det_inv = None
+        for i in range(len(self.key_string)):
+            if (det * i) % len(self.key_string) == 1:
+                det_inv = i
+                break
+
+        inv_key = det_inv * numpy.linalg.det(self.encrypt_key) *\
+                  numpy.linalg.inv(self.encrypt_key)
+
+        return self.toInt(self.modulus(inv_key))
+    
+    def decrypt(self, text):
+        self.decrypt_key = self.makeDecryptKey()
+        text = self.processText(text.upper())
+        decrypted = ''
+
+        for i in range(0, len(text) - self.break_key + 1, self.break_key):
+            batch = text[i:i+self.break_key]
+            batch_vec = list(map(self.replaceLetters, batch))
+            batch_vec = numpy.matrix([batch_vec]).T
+            batch_decrypted = self.modulus(self.decrypt_key.dot(batch_vec)).T.tolist()[0]
+            decrypted_batch = ''.join(list(map(self.replaceNumbers, batch_decrypted)))
+            decrypted += decrypted_batch
+
+        return decrypted
+
+
+def main():
+    N = int(input("Enter the order of the encryption key: "))
+    hill_matrix = []
+
+    print("Enter each row of the encryption key with space separated integers")
+    for i in range(N):
+        row = list(map(int, input().split()))
+        hill_matrix.append(row)
+
+    hc = HillCipher(numpy.matrix(hill_matrix))
+
+    print("Would you like to encrypt or decrypt some text? (1 or 2)")
+    option = input("""
+1. Encrypt
+2. Decrypt
+"""
+                   )
+
+    if option == '1':
+        text_e = input("What text would you like to encrypt?: ")
+        print("Your encrypted text is:")
+        print(hc.encrypt(text_e))
+    elif option == '2':
+        text_d = input("What text would you like to decrypt?: ")
+        print("Your decrypted text is:")
+        print(hc.decrypt(text_d))
+    
+
+if __name__ == "__main__":
+    main()