# Cryptography | Traditional Symmetric Ciphers

The two types of traditional symmetric ciphers are **Substitution Cipher** and **Transposition Cipher**. The following flowchart categories the the traditional ciphers:

**1. Substitution Cipher:**

Substitution Ciphers are further divided into **Mono-alphabetic Cipher** and **Poly-alphabetic Cipher**.

First, let’s study about mono-alphabetic cipher.

**Mono-alphabetic Cipher –**

In mono-alphabetic ciphers, each symbol in plain-text (eg; ‘o’ in ‘follow’) is mapped to one cipher-text symbol. No matter how many times a symbol occurs in the plain-text, it will correspond to the same cipher-text symbol. For example, if the plain-text is ‘follow’ and the mapping is :

- f -> g
- o -> p
- l -> m
- w -> x

The cipher-text is ‘gpmmpx’.

Types of mono-alphabetic ciphers are:

**(a). Additive Cipher (Shift Cipher / Caesar Cipher) –**

The simplest mono-alphabetic cipher is additive cipher. It is also referred to as ‘Shift Cipher’ or ‘Caesar Cipher’. As the name suggests, ‘addition modulus 2’ operation is performed on the plain-text to obtain a cipher-text.C = (M + k) mod n

M = (C – k) mod nwhere,

C -> cipher-text

M -> message/plain-text

k -> keyThe key space is 26. Thus, it is not very secure. It can be broken by brute-force attack.

For more information and implementation see Caesar Cipher**(b). Multiplicative Cipher –**

The multiplicative cipher is similar to additive cipher except the fact that the key bit is multiplied to the plain-text symbol during encryption. Likewise, the cipher-text is multiplied by the multiplicative inverse of key for decryption to obtain back the plain-text.C = (M * k) mod n

M = (C * k^{-1}) mod nwhere,

k^{-1}-> multiplicative inverse of k (key)

The key space of multiplicative cipher is 12. Thus, it is also not very secure.

**(c). Affine Cipher –**

The affine cipher is a combination of additive cipher and multiplicative cipher. The key space is 26 * 12 (key space of additive * key space of multiplicative) i.e. 312. It is relatively secure than the above two as the key space is larger.

Here two keys k_{1}and k_{2}are used.C = [(M * k

_{1}) + k_{2}] mod n

M = [(C – k_{2}) * k_{1}^{-1}] mod nFor more information and implementation, see Affine Cipher

Now, let’s study about poly-alphabetic cipher.

**Poly-alphabetic Cipher –**

In poly-alphabetic ciphers, every symbol in plain-text is mapped to a different cipher-text symbol regardless of its occurrence. Every different occurrence of a symbol has different mapping to a cipher-text. For example, in the plain-text ‘follow’, the mapping is :f -> q

o -> w

l -> e

l -> r

o -> t

w -> yThus, the cipher text is ‘qwerty’.

Types of poly-alphabetic ciphers are:

**2. Transposition Cipher:**

The transposition cipher does not deal with substitution of one symbol with another. It focuses on changing the position of the symbol in the plain-text. A symbol in the first position in plain-text may occur in fifth position in cipher-text.

Two of the transposition ciphers are:

**Columnar Transposition Cipher –**

For information and implementation, see Columnar Transposition Cipher**Rail-Fence Cipher –**

For information and implementation, see Rail-Fence Cipher

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