# Cryptanalysis tasks , ADFGVX substitution and Transposition, assignment help

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Homework 3

Cryptanalysis

Please submit a DOC file. Do the best you can. Cheating (not Safe Assign, but other methods) will be

considered an HCV. Do not help others with this assignment.

Fractionation Systems

In fractionation systems, letters are both substituted and transposed yielding the superencryption. First, the plain

letters are substituted by selected letters (commonly pairs of letters are used, in which case the cipher is called a

"biliteral cipher"). Secondly, such letters are then superencrypted by the transposition.

Example:

Let’s superencrypt "Probability" by using keywords "cyber" for the ADFGVX substitution and "crime" for the

transposition matrix.

Step 1 - ADFGVX substitution:

One of the most famous field ciphers ever was a fractionation system - the ADFGVX Cipher which was

employed by the German Army during the First World War. This system was so named because it used a 6 by 6

matrix to substitution-encrypt the 26 letters of the alphabet and 10 digits into pairs of the symbols A, D, F, G, V

and X. The variable setup of the matrix is guaranteed through the choice of the keyword (here “cyber”) that

precedes the remaining letters and digits. The resulting biliteral cipher is only the intermediate cipher; it is then

written into the rectangular matrix and transposed to produce the final cipher that is the one that was

transmitted.

A

D

F

G

V

X

A

c

y

b

e

r

a

D

d

f

g

h

i

j

F

k

l

m

n

o

p

G

q

s

t

u

v

w

V

x

z

0

1

2

3

X

4

5

6

7

8

9

Let's encrypt "probability" using the key word "cyber". The first letter "p" becomes "FX" as the starting letters

of the row and the column in which "p" appears. Similarly, the next letter "r" turns into "AV", etc.

Plaintext

p

r

o

b

a

b

i

l

i

t

y

Ciphertext

FX

AV

FV

AF

AX

AF

DV

PD

DV

GF

AD

Step 2 – Transposition:

This intermediate ciphertext then fills the columns (left to right) of a transposition matrix using the keyword

"crime". Since "crime"consists of 5 letters the matrix contains 5 rows. Note that the matrix is filled up with

AAA at the bottom right.

C

1

F

V

A

D

A

R

5

X

A

F

D

D

I

3

A

F

D

V

A

M

4

V

A

V

G

A

E

2

F

X

P

F

A

The final cipher is read as rows based on alphabetical order of letters of the key "crime":

FVADA FXPFA AFDVA VAVGA XAFDD

To decode, the recipient sets up two matrices based on two keywords, first to undo the transposition and finally

to undo the ADFGVX-substitution. Although this superencryption offers more security, it can be broken in

steps. First, the ADFGVX-substitution cipher has to be deciphered. Secondly, the remaining transpositions can

be undone by testing many possible transpositions.

Reference:

ADFGVX Cipher - https://en.wikipedia.org/wiki/ADFGVX_cipher

http://www.ti89.com/cryptotut/transposition.htm

TASK 1 (15 points)

Superencrypt "Abstractionism" by using keywords "Painter" for the ADFGVX substitution and "Kandinsky"

for the transposition matrix.

Substitution

A

D

F

G

V

X

A

p

a

i

n

...

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