Fractionation (cryptology)

from Wikipedia, the free encyclopedia

Under fractionation (of Latin fractio , "Breaking", English fractionation ) means in cryptology the decomposition of each character of the plaintext into two or more components and then "tearing" of the components prior to encryption . Fractionation is also understood and designated as a tomographic process .

Procedure

The French scholar Honoré Gabriel Victor de Riqueti, Marquis de Mirabeau , (1749–1791) had the idea of ​​fractionating texts as early as the 18th century. It was used, for example, in 1918 by the German army during World War I as part of the ADFGX encryption process . These, advanced for their time German hand key method used substitution , ie the replacement of plaintext character by ciphertext characters , here in more detail by ciphertext character pairs ( bigrams ), then the rupture of the bigrams and finally the transposition , so the offsetting of the components.

example

In the ADFGX process, the first step is to replace the plaintext letters with secret character bigrams that only consist of the letters A, D, F, G or X. A Polybios square is used for this , which was generated in the following example using the secret password “wikipedia”. So you get an intermediate text, which is now fractionated. To do this, the two halves of each pair are torn apart. This is done here by separate and different offsetting of each individual pair half, i.e. each individual letter of the intermediate text.

A. D. F. G X
A. w i k p e
D. d a z y x
F. v u t s r
G q O n m l
X H G f c b

The plain text is replaced letter by letter by the pairs of characters on the edge of the Polybios square. A typical text would be, for example, " Accelerate ammunition point, if not seen also during the day ". The first letter “M” of the message becomes “GG”, “u” becomes “FD”, and so on. Overall, the plain text (top line in each case) results in the following "intermediate text" (bottom line in each case):

M. u n i t i O n i e r u n G b e s c H l e
GG FD GF AD FF AD GD GF AD AX FX FD GF XD XX AX FG XG XA GX AX
u n i G e n P u n k t S. O w e i t n i c H
FD GF AD XD AX GF AG FD GF AF FF FG GD AA AX AD FF GF AD XG XA
t e i n G e s e H e n a u c H b e i T a G
FF AX AD GF XD AX FG AX XA AX GF DD FD XG XA XX AX AD FF DD XD

The intermediate text is entered line by line in a matrix . The width of the matrix results from the length of a second password, for example "OBSERVATION LIST", which is written over the matrix. The letters of this password are numbered in alphabetical order. The "A" gets the number 1, the "B" at the beginning the number 2, the second "B" the number 3 and so on until finally the "U", which gets the number 17.

B. E. O B. A. C. H T U N G S. L. I. S. T E.
2 5 12 3 1 4th 8th 15th 17th 11 7th 13 10 9 14th 16 6th
G
D
X
X
A
F
A
D 		G
A
G
G
A
A
X
F 		F
X
X
F
A
X
G
F 		D
F
A
A
X
A
F
D 		G
X
G
G
A
D
D
D 		F
F
X
F
D
G
D
X 		A
D
A
D
F
F
F
D 		D
G
X
G
F
X
D
 F
F
F
F
G
D
X
 F
X
D
A
F
A
G
 A
D
G
F
A
X
X
 D
X
F
F
D
F
A
 G
X
A
F
X
G
X
 D
A
D
F
G
A
X
 G
X
X
G
X
X
A
 F
F
D
G
A
X
X
 A
G
A
D
F
A
A

After the intermediate text has been entered line by line in the matrix, it is now read out again column by column . The order of the columns is determined by the alphabetical order of the individual letters of the password, which is noted below the password for the sake of clarity. Reading therefore begins with the fifth column (password letter "A") and the ciphertext piece "GXGGADDD" and ends with the ninth column (password letter "U") and the text fragment "FFFFGDX". The complete ciphertext is: 

GXGGA DDDGD XXAFA DDFAA XAFDF FXFDG DXGAG GAAXF AGADF AAADG
FAXXA DADFF FDDAD FGAXG XAFXG XFXDA FAGFX XFAXG FDXFF DFAGX
XGXXA DGXGF XDFFD GAXXF FFFGD X

It is cryptographically important that the letter pairs are fractionated in this way. The two halves of a bigram, which corresponds to one plaintext letter in monoalphabetics, are torn apart. This fractionation achieves a considerably improved security against unauthorized decipherment .

literature

Individual evidence

  1. ↑ Friedrich L. Bauer : Deciphered secrets - methods and maxims of cryptology . Springer, Berlin 2000 (3rd edition), p. 68, ISBN 3-540-67931-6 .
  2. ↑ Friedrich L. Bauer : Deciphered secrets - methods and maxims of cryptology . Springer, Berlin 2000 (3rd edition), p. 175, ISBN 3-540-67931-6 .
  3. ^ George Lasry et al .: Deciphering ADFGVX messages from the Eastern Front of World War I, Cryptologia , p. 1, doi: 10.1080 / 01611194.2016.1169461