Decrypt the ciphertext 101000111001 which was encrypted with the Toy block cipher once using the key 101010010. Show all the steps.
The Toy Block Cipher follows a Feistel-like structure with a simple key schedule. Since you haven't specified a precise Toy Block Cipher variant, I'll assume a basic Feistel structure with a 12-bit block and a 9-bit key. We'll proceed step by step. --- ### Step 1: Understand the Cipher Structure - _________ _____ _____ ______ _______ ____ ____ ________ ___ _________ _____ _____.
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i) Bob uses ElGamal cyrptosystem with parameters p = 47, g = 5 and the secret value x = 3. What values will he make public?
ii) 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?
iii) Explain how Bob will decrypt the message.
Solve the discrete logarithm problem 5x ≡ 22 (mod 47) using Baby-Step, Giant-Step algorithm.
b)
). The table of values is given below:
| i | γ | Vector | i | γ i | Vector |
| 0 | 1 | (0,0,0,1) | 8 | γ 2 +1 | (0,1,0,1) |
| 1 | γ | (0,0,1,0) | 9 | γ 3 +1 | (1,0,1,0) |
| 2 | γ 2 | (0,1,0,0) | 10 | γ 2 +γ +1 | (0,1,1,1) |
| 3 | γ 3 | (1,0,0,0) | 11 | γ 3 +γ 2 +γ | (1,1,1,0) |
| 4 | γ +1 | (0,0,1,1) | 12 | γ 3 +γ 2 +γ +1 | (1,1,1,1) |
| 5 | γ 2 +γ | (0,1,1,0 | 13 | γ 3 +γ 2 +1 | (1,1,0,1) |
| 6 | γ 3 +γ 2 | (1,1,0,0) | 14 | γ 3 +1 | (1,0,0,1) |
| 7 | γ 3 +γ +1 | (1,0,1,1) |
c) Alice wants to use the Digital Signature algorithm for signing messages. She chooses p = 83, q = 41, g = 2 and a = 3. Alice wants to sign the message M = 20. She chooses the secret value k = 8. Explain the procedure that Alice will use for computing the signature. What information will she send Bob?
Apply poker test to the following sequence with level of significane α = 0.05. (4) 1001101000010000101111011 01110100101101100100110.
Let f (x) = x3 − x − 1 ∈ Z5[x]. Find the product of x2 + 2x + 1 + ( f (x)) and x2 + 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.
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:
Next, we choose an inveritble 2×2 matrix with coefficients in Z26, for example, A = 
This matrix has determinant 
is a unit in Z26 with inverse 
We write each pair of elements in Z26 as a column vector and multiply it by A:
We then convert each pair of numbers to a pair of characters and write them down. In this example, we get the cipher text "LSPFYGXUEN" corresponding to the plain text "ALLWELL".
To decrypt, we convert pairs of characters to pairs of numbers and multiply by
Decrypt the text "TWDXHUJLUENN" which was encrypted using the Hill’s cipher with the matrix 
as the encryption matrix.