Mohammad Hajjat
20010171102

Review Questions:

Question 2.3)

It depends on type of Encryption technique used.

·  Symmetric / single-key / secret-key / Conventional Encryption è one key for both sender and receive.

·  Asymmetric / two-key / public-key è two keys; one for sender and one for receive.

Question 2.7)

Unconditionally Secure / No matter how much Cipher text is available and no matter time is available we can't get the corresponding Plaintext.
Computationally Secure / We can decrypt the data BUT it will not be useful because
·  The cost of deciphering the data > value of encrypted data
·  Time required to decipher the data > useful lifetime of the data.

Question 2.11)

Mono-alphabetic cipher / The mapping used for single characters. Each plaintext letter maps to a different ciphertext letter.
Key is 26 letters long è 26! Possible keys.
Letter frequency is used to cryptanalysis hacks.
Poly-alphabetic cipher / Uses multiple cipher alphabets. For eg. the Vigenere cipher maps the same plain-text letter to multiple ciphertext letters.
Letter frequency is hard to implement here.

Problems:

Question 2.4)

This question is not clear and mixes the two versions together.

It was disclosed yesterday that several informal but direct contacts have been made with political representatives of the viet cong in Moscow.

A / B / C / D / E / F / G / H / I / J / K / L / M / N / O / P / Q / R / S / T / U / V / W / X / Y / Z
S / A / H / V / P / B / W / U / C / X / T / D / M / Y / E / O / Z / I / F / Q / G

We can formulate it like thisè

------

S P U T ? I G (? Chars = J K L N R)

A B C D E F ?

H ? ? M O Q

V W X Y Z ?

Or

------

S A H V

P B J W

U C K X

T D M Y

N E O Z

I F Q ?

G ?

And then stretching it out è

SPUTING - ABCDEF –HJKMOQ- VWXYZ

So the keyword would be Sputing.

Question 2.6)

We first write each letter with its corresponding numerical value

A / B / C / D / E / F / G / H / I / J / K / L / M
0 / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12
N / O / P / Q / R / S / T / U / V / W / X / Y / Z
13 / 14 / 15 / 16 / 17 / 18 / 19 / 20 / 21 / 22 / 23 / 24 / 25

The plaintext:

"Meet me at the usual place at then rather than eight oclock"

Corresponding Values:

M / E / E / T / M / E / A / T / T / H / E / U / S / U / A / L
12 / 4 / 4 / 19 / 12 / 4 / 0 / 19 / 19 / 7 / 4 / 20 / 18 / 20 / 0 / 11
P / L / A / C / E / A / T / T / H / E / N / R / A / T / H / E / R
15 / 11 / 0 / 2 / 4 / 0 / 19 / 19 / 7 / 4 / 13 / 17 / 0 / 19 / 7 / 4 / 17
T / H / A / N / E / I / G / H / T / O / C / L / O / C / K
19 / 7 / 0 / 13 / 4 / 8 / 6 / 7 / 19 / 14 / 2 / 11 / 14 / 2 / 10

The key =

Then using Matlabè

> mod([9 4 ; 5 7]*[12;4],26)
ans =
20
10
> mod([9 4 ; 5 7]*[4;19],26)
ans =
8
23
> mod([9 4 ; 5 7]*[0;19],26)
ans =
24
3
> mod([9 4 ; 5 7]*[19;7],26)
ans =
17
14
> mod([9 4 ; 5 7]*[4;20],26)
ans =
12
4
> mod([9 4 ; 5 7]*[18;20],26)
ans =
8
22
> mod([9 4 ; 5 7]*[0;11],26)
ans =
18
25
> mod([9 4 ; 5 7]*[15;11],26)
ans =
23
22
> mod([9 4 ; 5 7]*[0;2],26)
ans =
8
14
> mod([9 4 ; 5 7]*[4;0],26)
ans =
10
20
> mod([9 4 ; 5 7]*[19;19],26)
ans =
13
20
> mod([9 4 ; 5 7]*[7;4],26)
ans =
1
11
> mod([9 4 ; 5 7]*[13;17],26)
ans =
3
2
> mod([9 4 ; 5 7]*[0;19],26)
ans =
24
3
> mod([9 4 ; 5 7]*[7;4],26)
ans =
1
11
> mod([9 4 ; 5 7]*[17;19],26)
ans =
21
10
> mod([9 4 ; 5 7]*[7;0],26)
ans =
11
9
> mod([9 4 ; 5 7]*[13;4],26)
ans =
3
15
> mod([9 4 ; 5 7]*[8;6],26)
ans =
18
4
> mod([9 4 ; 5 7]*[7;19],26)
ans =
9
12
> mod([9 4 ; 5 7]*[14;2],26)
ans =
4
6
> mod([9 4 ; 5 7]*[11;14],26)
ans =
25
23
> mod([9 4 ; 5 7]*[2;10],26)
ans =
6
2

Corresponding Cipher:

M / E / E / T / M / E / A / T / T / H / E / U / S / U / A / L
20 / 10 / 8 / 23 / 20 / 10 / 24 / 3 / 17 / 14 / 12 / 4 / 8 / 22 / 18 / 25
U / K / I / X / U / K / Y / D / R / O / M / E / I / W / S / Z
P / L / A / C / E / A / T / T / H / E / N / R / A / T / H / E / R
23 / 22 / 8 / 14 / 10 / 20 / 13 / 20 / 1 / 11 / 3 / 2 / 24 / 3 / 1 / 11 / 21
X / W / I / O / K / U / N / U / B / L / D / C / Y / D / B / L / V
T / H / A / N / E / I / G / H / T / O / C / L / O / C / K
10 / 11 / 9 / 3 / 15 / 18 / 4 / 9 / 12 / 4 / 6 / 25 / 23 / 6 / 2
K / L / J / D / P / S / E / J / M / E / G / Z / X / G / C


Decryption:

Decryption requires the inverse of K.

K K-1 = I

K =

K-1 =

We get the P vector as the followingè

P = K-1 C mod 26 = K-1 KP = P

1/43 = 0.023256 so we can use 23

20 / 10 / / è / 12 / 4
U / K / M / E
8 / 23 / / è / 4 / 19
I / X / E / T
20 / 10 / / è / 12 / 4
U / K / M / E
24 / 3 / / è / 0 / 19
Y / D / A / T
17 / 14 / / è / 19 / 7
R / O / T / H
12 / 4 / / è / 4 / 20
M / E / E / U
8 / 22 / / è / 18 / 20
I / W / S / U
18 / 25 / / è / 0 / 11
S / Z / A / L
23 / 22 / / è / 15 / 11
X / W / P / L
8 / 14 / / è / 0 / 2
I / O / A / C
10 / 20 / / è / 4 / 0
K / U / E / A
13 / 20 / / è / 19 / 19
N / U / T / T
1 / 11 / / è / 7 / 4
B / L / H / E
3 / 2 / / è / 13 / 17
D / C / N / R
24 / 3 / / è / 0 / 19
Y / D / A / T
1 / 11 / / è / 7 / 4
B / L / H / E
21 / 10 / / è / 17 / 19
V / K / R / T
11 / 9 / / è / 7 / 0
L / J / H / A
3 / 15 / / è / 13 / 4
D / P / N / E
18 / 4 / / è / 8 / 6
S / E / I / G
9 / 12 / / è / 7 / 19
J / M / H / T
4 / 6 / / è / 14 / 2
E / G / O / C
25 / 23 / / è / 11 / 14
Z / X / L / O
6 / 2 / / è / 2 / 10
G / C / C / K

Question 2.10)

By reading the last word of each line we get the following messageè

George, your package should be ready by Friday 21st, room three. Please destroy this immediately.

7