Length 1 2 Pages Excluding The Title Page And Reference Pages And D ✓ Solved

Length: 1-2 pages (excluding the title page and reference pages) and double-spaced 1. Construct a Playfair matrix with the key largest . 2. Construct a Playfair matrix with the key occurrence . 3. Using this Playfair matrix: Encrypt this message: Must see you over Cadogan West Coming at once

Paper for above instructions

Introduction

The Playfair cipher is a technique for encrypting alphabetic text by using a matrix of letters. The algorithm was devised by Charles Wheatstone in 1854, but it was named after Lord Playfair, who promoted its use. This encryption method uses digraphs (pairs of letters) instead of single letters, which provides a significant security improvement over simple substitution ciphers. In this assignment, we will construct two Playfair matrices with the keys "largest" and "occurrence," and we will use these matrices to encrypt the message "Must see you over Cadogan West Coming at once."

Part 1: Constructing the Playfair Matrix with Key "largest"

To construct the Playfair matrix, we follow these steps:
1. Remove duplicate letters: The letters in the key should be distinct. For "largest", the unique letters in order are: L, A, R, G, E, S, T.
2. Complete the matrix: After the key, we fill the rest of the matrix with the remaining letters of the alphabet (I/J share a cell), ensuring only letters A-Z are included.
The resulting matrix with the key "largest" will look like this:
```
L A R G E
S T B C D
F H I/J K M
N O P Q U
V W X Y Z
```

Part 2: Constructing the Playfair Matrix with Key "occurrence"

Similarly, we compute the matrix for the key "occurrence":
1. Remove duplicate letters: The unique letters in "occurrence" are O, C, U, R, E, N, and A.
2. Complete the matrix: We will fill the remainder of the matrix with remaining letters.
The resulting matrix with the key "occurrence" will look like this:
```
O C U R E
N A B D F
G H I/J K L
M P Q S T
V W X Y Z
```

Part 3: Encrypting the Message

We will use the Playfair matrix created from the key "largest" to encrypt the message, "Must see you over Cadogan West Coming at once."

Step 1: Prepare the Message

First, we must format the message:
- Remove spaces and punctuation: The message becomes "mustseeyouovercadoganwestcomingatonce".
- Split into digraphs: If there are duplicate letters in a pair, replace them with an 'X'. Thus, the digraphs are:
```
MU ST SE EY OU OV ER CA DO GA NW ES TC OM IN GA TO NC EX
```

Step 2: Encrypt the Digraphs Using the Matrix

Using the Playfair matrix for the key "largest", we can apply the following rules for encryption:
1. If both letters of the digraph are in the same row, replace them with letters to their immediate right (wrap if needed).
2. If both letters are in the same column, replace them with the letters immediately below (wrap if needed).
3. If they form a rectangle, replace them with letters on the same row but at the opposite corners of the rectangle.
Now let's encrypt each digraph:
- MU: M (3,4), U (4,4): Rectangle → (3,4) and (4,4) yields "NF"
- ST: S (2,1), T (2,2): Same row → "TB"
- SE: S (2,1), E (1,5): Rectangle → "LA"
- EY: E (1,5), Y (5,5): Same column → "E"
- OU: O (4,1), U (4,4): Same row → "NP"
- OV: O (4,1), V (5,1): Rectangle → "CW"
- ER: E (1,5), R (1,3): Same row → "GA"
- CA: C (2,4), A (1,2): Rectangle → "L"
- DO: D (2,3), O (4,1): Rectangle → "NI"
- GA: G (1,4), A (1,2): Same row → "RE"
- NW: N (3,3), W (5,2): Rectangle → "XL"
- ES: E (1,5), S (2,1): Rectangle → "RT"
- TC: T (1,4), C (2,3): Rectangle → "BR"
- OM: O (4,1), M(3,4): Rectangle → "FA"
- IN: I (3,6), N (4,1): Rectangle → "PO"
- GA: G (1,4), A (1,2): Same row → "RX"
- TO: T (2,2), O (1,4): Rectangle → "SV"
- NC: N (3,3), C (2,4): Rectangle → "QP"
- EX: E (1,5), X (5,3): Rectangle → "AY"

Final Encrypted Message

Combining all the resultant digraphs, we get the encrypted text: "NF TB LA E NP CW GA L NI RE XL RT BR FA PO RX SV QP AY".

Conclusion

The Playfair cipher demonstrates the principles of cryptography by using digraphs rather than monoalphabetic substitutions, making it a more complex encryption technique. The matrices constructed using the given keys further illustrate how the Playfair cipher leverages the arrangement of letters in a matrix format for encryption.

References

1. Gollmann, D. (2011). Computer Security. Wiley.
2. Stallings, W. (2018). Cryptography and Network Security: Principles and Practice. Pearson.
3. Kahn, D. (1996). The Codebreakers: The Story of Secret Writing. Simon & Schuster.
4. Diffie, W., & Landau, S. (2007). Privacy on the Line: The Politics of Wiretapping and Encryption. MIT Press.
5. Anderson, R. (2001). Security Engineering: A Guide to Building Dependable Distributed Systems. Wiley.
6. Schneier, B. (1996). Secrets and Lies: Digital Security in a Networked World. Wiley.
7. Katz, J., & Lindell, Y. (2014). Introduction to Modern Cryptography: Principles and Protocols. Chapman & Hall.
8. Menscher, M. (1988). Introduction to Cryptography. CRC Press.
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