Find the inverse of 13 (mod 51) using extended euclidean algorithm

Considering the bytes 10001001 and 10101010 as elements of the field F2[X]/hg(X)i, where g(X) is the polynomial X 8 +X 4 +X 3 +X +1, find their product and quotient .

Let f(x) = x ⁴ +x+1 ∈ F2[x]. We represent the field F_{2 4} by F2[x]/(f(x)). Let us write γ = x+ (f(x)). The table of values is given below:

i ) Prepare logarithm and antilogarithm tables as given in page 23 of block 1.

Process Skills

In this exercise, we introduce you to Hill cipher. In this cipher, we convert our message to
numbers, just as in affine cipher. However, instead of encrypting character by character, we
encrypt pairs of characters by multiplying them with an invertible matrix with co-efficients in
Z26.
Here is an example: Suppose we want to ENCRYPT "ALLISWELL". Since we require the
plaintext to have even number of characters, we pad the message with the character ‘X’. We
break up the message into pairs of characters AL, LI, SW, EL and LX. We convert each pair of
characters into a pair elements in Z26 as follows:

Decrypt the ciphertext 101000111001 which was encrypted with the Toy block cipher once using the key 101010010. Show all the steps.

 Decrypt each of the following cipher texts:
i) Text: "CBBGYAEBBFZCFEPXYAEBB", encrypted with affine cipher
with key (7,2).
ii) Text:"KSTYZKESLNZUV", encrypted with Vigenère cipher with key "RESULT"

Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.