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IT223 George Mason University Cryptanalysis & Fractionation Systems Paper 3

Please take a look at the attached file and help me complete this assignment asap.

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
FD
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
F
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.
TASK 2 (3 points) Please encrypt Claude Shannon’s quote
by using the given key:
“Information is the resolution of uncertainty”
Given key: n+2, n-1, n+1, n-2
Example:
You will encrypt the word “Hello” by using the given key above into “JDMJQ”.
TASK 3 (3 points each, total 6 points)
Here is another encryption/decryption exercise. For this exercise, I have provided a word that will serve as the
key. You must figure out the key in order to complete this section.
To get you started: Easy = GXTW (Once you figure out the pattern to this, you can do the following):
3a. Encrypt this plaintext:
Cryptography is the art of secret writing.
3b. Decrypt the following ciphertext:
ALVAC KPLNV GGIEU RJBXY AVPSR OBAVF DC
TASK 4 (7 points)
In 1759, Leonhard Euler, the famous mathematician, found the closed knight’s tour for traversing all the cells of
the chessboard only once. Read the text inscribed in the cells of the chessboard along this tour (see Figure 1).
The beginning of the text is at A8.
Please, look through these resources:
Knight’s tour – > https://en.wikipedia.org/wiki/Knight’s_tour
2 -> http://www.t-bag.org/KTour/voyager0/magicsqr.gif
A
8
B
1T
C
D
E
F
G
H
D
S
E
S
U
I
R
7
R
U
A
E
E
R
Y
C
P
H
O
S
S
E
C
S
C
U
N
A
Y
T
O
N
A
A
R
T
O
R
Y
6
5
I
C
E
M
T
A
O
G
T
4
3
I
E
T
R
2
I
N
N
U
1
I
B
N
S
T
P
E
F
Figure 1 – Chessboard with inscribed text
TASK 5 (4 points)
To encrypt messages, John and Jane used Scytale.
“Scytale is a tool used to perform a transposition cipher, consisting of a cylinder with a strip of parchment
wound around it on which is written a message. The ancient Greeks, and the Spartans in particular, are said to
have used this cipher to communicate during military campaigns. The recipient uses a cylinder of the same
diameter on which the parchment is wrapped to read the message. It has the advantage of being fast and not
prone to mistakes—a necessary property when on the battlefield’ (read more here:
https://en.wikipedia.org/wiki/Scytale).
John handed Jane a tape on which was written:
Unfortunately, Jane lost her cylinder, but she sees that the tape is full, and knows that while winding the tape,
the entire number of turnovers was made. Help her to recover the message. (Hint: there are 81 characters)

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