## IT6010 – Mathematics for Computing

Q1) Design a Knapsack public key cryptosystem, using this system, encrypt the plaintext “BHP”. Show the details of the design process (give the selected values with explanation why selected them) and encryption process. Include in your answer Octave codes used. Use the ASCII or Unicode code to convert the plaintext characters to numbers. Finally, show how to decrypt the obtained cipher values to get the plaintext character back. (LOs 2,4) [6 Marks]

Q2) Answer each of the following:

- Explain why the security of the Monoalphabetic ciphers is easy to compromise?
- Define the “hashing”, then explain why hashing is used creating a digital signature.
- Distinguish between the Stream Cipher System and Block Cipher Systems, name one example for each system. (LO 4) [3 Marks]

Q3) Affine Cipher is an example of a Monoalphabetic substitution cipher. The encryption process is substantially mathematical done by using the following formula:

C = (P ∗ 𝑘1 + 𝑘2) mod 26.

Where *k1, k2* are two integers representing the key (selected randomly), C is the ciphertext value, and P is the plaintext value. Where C and P integers with values between 0 and 25.

- Write an Octave programme to implement this system, run your programme using the Plaintext: “the quick brown fox jumped over the lazy dog”. Show the obtained ciphertext with the selected values of the keys
*k1*&*k2*. [4 Marks] - Given that the plaintext “s” mapped to ciphertext “W”, plaintext “x” mapped to ciphertext “Z” when encrypted with Affine Cipher. Determine, mathematically, the values for the two keys
*K1 and K2*. [4 Marks]

(LOs 2,4) [8 Marks]

Q4) Given the following cipher text which has been ciphered with Mixed Alphabet Monoalphabetic Cipher:

UZQSOVUOHXMOPVGPOZPEVSGZWSZOPFPESXUDBMET SXAIZVUEPHZHMDZSHZOWSFPAPPDTSVPQUZWYMXUZU HSXEPYEPOPDZSZUFPOMBZWPFUPZHMDJUDTMOHMQ

By using statistical method to exploit the weaknesses in this cipher, you can conclude that there are two plain text letters that correspond two letters in the above ciphertext. Give these letters justifying your conclusion in detail.

(LO1) [ 3 Marks]