Explain how Bob will decrypt the message.

Alice wants to send Bob the message M = 15. She chooses k = 5. How will she compute the cipher text? What information does she send to Bob?

Bob uses ElGamal cyrptosystem with parameters p = 47, g = 5 and the secret value x = 3. What values will he make public?

Decrypt the message c = 23 that was encrypted using RSA algorithm with e = 43 and n = 77.

Apply runs test to the following sequence:
1001101000010000101111011
0111010010110110010011010
0110011100001100100111000
1100001101010111101001110
0010001111000001101010010
1000110100000110100101101
1110001001

Apply poker test to the following sequence with level of significane α = 0.05. (4) 1001101000010000101111011 01110100101101100100110.

Apply the frequency test, serial test and autocorrelation test to the following sequence at level of significance α = 0.05: 011001110000110010011100.

Find a recurrence that generates the sequence 110110110110110.

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 .

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

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:

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

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

Another version of the columnar transposition cipher is the cipher using a key word. In this cipher, we encrypt as follows: Given a key word, we remove all the duplicate characters in the key word. For example, if the key word is ‘SECRET’, we remove the second ‘E’ and use ‘SECRT’ as the key word. To encrypt, we form a table as follows: In the first row, we write down the key word. In the following rows, we write the plaintext. Suppose we want to encrypt the text ‘ATTACKATDAWN’. We make a table as follows

Then we read off the columns in alphabetical order. We first read the column under ‘C’, followed by the columns under ‘E’, ‘R’, ‘S’ and ‘T’. We get the cipher text TTX TAN ADX AKW CAX. To decrypt, we reverse the process. Note that, since we know the length of the keyword, we can find the length of the columns by dividing the length of the message by the length of the keyword. Given the ciphertext ‘HNDWUEOESSRORUTXLARFASUXTINOOGFNEGASTORX’ and the key word ‘LANCE’, find the plaintext

 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"

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.

Let f(x) = x ³ −x−1 ∈ Z₅[x]. Find the product of x ² +2x+1+ (f(x)) and x ² +3x−1+ (f(x)) using the algorithm in page 23, block 1. You should show all the steps as in example 11, page 22, block 1.

Unit Plan

BICS and CALP