L6 Classical ciphers cryptanalysis

2.4 CLASSICAL CIPHERS CRYPTANALYSIS:
Most of classical cipher cryptanalysis methods make use of the statistical properties of the natural languages. Among these properties is the letter frequency distribution, which gives the percentage frequency of the characters in the given text. Another property of natural language is the frequency of pairs and triples of letters in the target language. After encryption, some information will remain in the cipher text, especially for simple cipher systems. Cryptanalysis will rely heavily on such information to analyze the cipher text.
The knowledge of the above mentioned properties is quite sufficient for simple substitution ciphers and monoalphabetic ciphers, because the cipher text alphabet is a rotation of the plaintext alphabet and not an arbitrary permutation. Therefore the statistical information unchanged during the encryption process. Homophonic substitution ciphers do not obscure all of the statistical properties of the plaintext, hence it is slightly harder than simple substitution ciphers to break. In polyalphabetic ciphers, if the key length (period) is equal to one (d - 7), then polyalphabetic ciphers become monoalphabetic (simple substitution), and hence, it is as easy as its equivalent to break. However, as period increased, it becomes harder and harder.
To solve a periodic substitution cipher, the cryptanalyst must determine the period of the cipher. Two earlier methods of classical ciphers cryptanalysis have been used, Index of Coincidence (IC), and Kasiski method, which help to determine the period.

2.4.1 STATISTICAL CRYPTANALYSIS.
All natural languages have statistical characteristics, which means that each character in the alphabet has its own frequency in any text of 1000 characters or more. Since these frequencies are so consistent, then an approximate probability can be attached to letter. For example p(e) is much greater than every other probability, we would deduce that the most significant letter in a monoalphabetic cipher is equivalent for (e). However, English characters can be grouped into five sets according to their frequencies:
group letters frequency
I e 9.614
II t , a ,o , i ,n , s , h, r 6.855 - 4.532
III d , l 3.219 - 3.047
IV c, u , m , w , f, g , y , p , b 2.106 - 1.129
V v, k , j , x , q , z 0.741 - 0.056

Digrams, trigrams, also have consistent frequencies.
Example: in a given ciphertext, after calculating characters frequency, tlie following results are obtained:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z .
5 24 19 23 12 7 0 24 21 29 6 21 1 3 0 3 1 11 14 8 0 27 5 17 12 45