Introduction

• In previous examples , the one time pad had vulnerability if the key used for encryption , is used multiple times . The symmetric cipher algorithms provide an alternative algorithm , an alternative way to encrypt the useful information.

• Symmetric Encryption uses the same key to encrypt and decrypt data .

  

The Ancient Ciphers like Caesar Cipher , and the one time pad are famous examples of symmetric ciphers , these could further be classified into stream and block ciphers based on the way of processing the data i.e. processing the data in blocks or one character at a time.

Caesar Cipher

• It is one of the most primitive type of encryption algorithm

• It involves the basic shift of the alphabets , by a constant factor , all the letters are displaced , such that it forms a cycle.

  

• Algorithm :

  • Encryption
    • Each character in the Alphabet is mapped to an integer , say for lowercase letters a -> 0 , b-> 1 …… z-> 25 and similarly for uppercase letters, rest of the symbols aren't changed by the cipher algorithm.
    • Once this mapping is established , one could replace the alphabet mapped to some index i , with the one mapped with index ( i + K ) % 26
    • Note that one could introduce any such substitution scheme like lower_case_alphabets being mapped to upper_case_alphabets and vice versa or , like mentioned above , which depends on the implementation.
  • Decryption

    • One could simply see from the fact that , say we have j = ( i + K ) % 26 , therefore for some integer L and some key K of the cipher , we can say ,

      i + K = L*26 + j , or simply ,

      i = L*26 + j - K ,

      as i is in range of 0 - 25 ,

      i % 26 = i = 0 + ( j - k ) % 26

    • This cipher is easily breakable , as there are effectively only 26 keys [0-25] available for the Caesar cipher , as after performing the mod operation any random integer chosen as key falls into the range [0-25]. And hence , given the cipher text and the given message , one could simply generate the key for the given cipher system and hence , it doesn't provides for much of the protection.

    • Scope for improvement The number of possible keys that could be generated , could be increased from 26 to some large number , so that the key for the cipher isn't compromised easily.This could be achieved by using one or more of the following techniques :

      1. introducing mono alphabetic substitution : wherein one could define mapping such that any letter of the alphabet could be replaced by any other possible alphabet and hence there may exist up to 26! different keys ( or arrangements ) to be tried before cracking the key of the given cipher.

      crypto-mania-/Symmetric Ciphers at main · KarmanjyotSingh/crypto-mania-

      CAESAR CIPHER

XOR

XOR operation defined by the symbol ⊕ , that operates on single bits or boolean values. Which is

1 ⊕ 1 = 0

1 ⊕ 0 = 1

0 ⊕ 1 = 1

0 ⊕ 0 = 0

Following are the arithmetic properties of the XOR operator :

1. Associative : a⊕(b⊕c) = (a⊕b)⊕c

2. Commutative : a ⊕ b = b ⊕ a

3. Any bit XOR itself is 0: a ⊕ a = 0. If a is 0, then itʼs 0 ⊕ 0 = 0; if a is 1, then itʼs 1 ⊕ 1 = 0.

4. Any bit XOR 0 is that bit again: a ⊕ 0 = a. If a is 0, then itʼs 0 ⊕ 0 = 0; if a is 1, then itʼs 1 ⊕ 0 = 1

   

One-Time Pad

• O.T.P is a type of symmetric encryption
  • When used correctly, the One Time Pad is a very good example of symmetric encryption , as Alice encrypts a file with the same key that Bob uses to decrypt the file, and hence the same key being used for accessing the shared or the communicated information.
• O.T.P and the perfect secrecy
  • perfect secrecy gives the notion of complete randomness of the input ( or the plain text to the attacker ) , i.e. the cipher text looks completely random and the list of possible messages or plain text cover the entire message space .
  • In one time pad , we do the xor operation , thus say if the cipher bit is 1 , then both 1 or 0 could have been the possibility of the corresponding bit in the plain text , and hence generated complete randomness.
  • This also means the fact that , even if a part of key or message is leaked ( compromised ) the rest of it still remains secure.

• The simple looking XOR operation , could be used for developing secure encryption techniques like the one-time-pad that offer high degree of security , as we'll see ahead.