Prehistory of Cryptography - A Classical Introduction to Cryptography: Applications for Communications Security - page 5

Letter Probability Letter Probability Letter Probability
A

0.082 0.002 0.063

J S

B 0.015 K 0.008 T 0.091

0.028 0.040 0.028

C L U

0.043 0.024 0.010

D M V

E 0.127 N 0.067 W 0.023

0.022 0.075 0.001

F O X

G 0.020 P 0.019 Y 0.020

0.061 0.001 0.001

H Q Z

0.070 0.060

I R

Figure 1.1. Frequencies of characters in english texts.

are the 30 most frequent digrams in decreasing order of likelihood:

TH , HE , IN , ER , AN , RE , ED , ON , ES , ST , EN , AT ,

TO , NT , HA , ND , OU , EA , NG , AS , OR , TI , IS , ET ,

IT , AR , TE , SE , HI ,

and

OF .

Here are the 12 most frequent trigrams:

THE , ING , AND , HER , ERE , ENT , THA , NTH , WAS , ETH ,

FOR ,

and

DTH .

Transposition and substitution are the two elementary operations which can be
used to build up a cipher. Another important concept is the notion of key.

The Caesar Cipher was improved in the sixteenth century by Blaise de Vigenere.
Here we consider every character as an integral residue modulo the size of the alphabet.
This way, the Caesar Cipher can be considered as adding 3 to every characters. The
Vigenere Cipher consists of using a word as a secret key K , splitting the messages into
blocks of the the same length of the key, and adding characterwise the key onto every
block.

As an example we encrypt this is a dummy message with the key ABC .
Here we need to compute

thi sis adu mmy mes sag e

+

ABC ABC ABC ABC ABC ABC A

=

TIK SJU AEW MNA MFU SBI E

and we obtain TIKSJUAEWMNAMFUSBIE . Note that adding A , B , and C corresponds
to a translation by 0, 1, and 2 positions respectively in the alphabet. Translations are
cyclic, e.g. y + C = A .