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Frequency Analysis

 

In a plaintext that is long enough, each character occurs with a characteristic frequency, depending on the language. The most frequently used character in English is the ‘E’ with a frequency of 12.7 % followed by ‘T’ with a frequency of 9.1 %.
A monoalphabetic substitution cipher can easily be cracked with a frequency analysis. Such a cipher can be identified if two plaintext characters are never mapped to the same encoded character. Each plaintext character is assigned to one or more encoded characters (the frequency analysis is much harder if one plaintext character is mapped to more than one encoded character). To crack such a cipher the frequency of the characters in the encoded text has to be compared to the frequency of the plaintext characters in the specific language.

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Fig. 1: Frequency Analysis of a German text.

 

German text


English text

Letter

Frequency in %

Letter

Frequency in %

 

Letter

Frequency in %

Letter

Frequency in %

A

6,51

N

9,78

 

A

8,2

N

6,7

B

1,89

O

2,51

 

B

1,5

O

7,5

C

3,06

P

0,79

 

C

2,8

P

1,9

D

5,08

Q

0,02

 

D

4,3

Q

0,1

E

17,40

R

7,00

 

E

12,7

R

6,0

F

1,66

S

7,27

 

F

2,2

S

6,3

G

3,01

T

6,15

 

G

2,0

T

9,1

H

4,76

U

4,35

 

H

6,1

U

2,8

I

7,55

V

0,67

 

I

7,0

V

1,0

J

0,27

W

1,89

 

J

0,2

W

2,4

K

1,21

X

0,03

 

K

0,8

X

0,2

L

3,44

Y

0,04

 

L

4,0

Y

2,0

M

2,53

Z

1,13

 

M

2,4

Z

0,1

Tab. 1: Frequency Analysis of the German and English alphabet.2

 

Weblinks

http://en.wikipedia.org/wiki/Frequency_analysis

 

References

1 Schmeh, Klaus: "Kryptografie", dpunkt.verlag, 2007, P.45
2 Beker, H.; Piper, F.: "Cipher Systems: The Protection of Communication", John Wiley & Sons, 1983
Beutelsbacher, Albrecht: "Kryptologie", Vieweg+Teubner, 1993
 
   
     
 
 
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