L5 Substitution cipher systems

2.3 SUBTITUTION CIPHERS.
2.3.1 SIMPLE SUBTTTUION CIPHERS:
In simple substitution (or monoalphabetic) ciphers, each character of the plaintext is replaced with a corresponding character of ciphertext. A single one-to-one mapping function (ƒ) from plaintext to ciphertext character is used to encrypt the entire message using the same key (k); such that
Ek(M)=f(m1)f(m2)….. f(mN)=C
Where N: is the length of the message.
M: is plaintext message given by M= (m 1, m2 ...... mN).
C: is ciphertext message given by C=(c1, c2,….,cN)
Simple substitution ciphers are often called monoalphabetic ciphers, figure (2-2) represents two concentric rings of which the outer is free to rotate and represent the ciphertext while the inner one represent the plaintext. If the outer one is moved to a certain position then the plaintext letters could be enciphered by replacing each letter by the one out side it. The letter frequency distribution is preserved in the ciphertext. Several forms of f can be used in simple substitution, such as:

• Shifted alphabet (Caesar cipher):
f(mi) - (mi + k) mod n
Where k is the number of positions to be shifted, mi is a single character of the
alphabet, and n is the size of the alphabet.
If k = 3 then we can encrypt the following message as:


M: R E N A I S S A N C E
Ek(M): U H Q D L V V D Q F H

• Multiplication based (decimation):
f(mi) = mi * k mod n
where k and n are relatively prime in order to produce a complete set of residues.
Example: k = 9; then the above message can encrypted as:
M: R E N A I S S A N C E
Ek(M): X K N A U G G A N S K
If k and n are not prime, several letters will encipher to the same ciphertext letter, and not all letters will appear in the ciphertext.
Home work: try it when k = 13

• Addition and multiplication (affine) :
f(mi)= (mi * k1+k0) mod n
Where k1 and n are relatively prime.
Simple substitution ciphers does not hide the underlying frequencies of the different letters of the plaintext, and hence it can be easily broken.