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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.
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

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

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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Anonymous
Tutor went the extra mile to help me with this essay. Citations were a bit shaky but I appreciated how well he handled APA styles and how ok he was to change them even though I didnt specify. Got a B+ which is believable and acceptable.

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