Alice wants to use the ElGamal digital signature scheme with public parameters p = 47, α = 2, secret value a = 7 and β = 34. She wants to sign the message M = 20 and send it to Bob. She chooses k = 5 as the secret value. Explain the procedure that Alice will use for computing the signature of the message. What information will she send Bob?
To solve the problem of signing the message \( M = 20 \) using the ElGamal digital signature scheme, Alice will follow these steps: ### Given Parameters: - Public parameters: \( p = 47 \), \( \alpha = 2 \) - Alice's secret key: \( a = 7 \) - Public key: \( \beta = 34 \) - Message to sign: \( M = 20 \) - Random secret value: \( k = 5 \) ### Step 1: Compute \( r \) The first part of the signature is \( r \), which is computed as: \[ r = \alpha^k \mod p \] Substitute the given values: \[ r = 2^5 \mod 47 \] Calculate \( 2^5 _________ _______ ____ ________ _____.
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b) A 64 bit key for the DES is given below
i) Check whether the key is error free using the parity bits.
ii) Find the keys for the second round.
a) Find the product of
using the algorithm in page 23, block 1. You should show all the steps as in example 11, pag 22, block 1.
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) |
Decrypt the message c = 23 that was encrypted using RSA algorithm with e = 43 and n = 77.
Alice wants to use the ElGamal digital signature scheme with public parameters p = 47, α = 2, secret value a = 7 and β = 34. She wants to sign the message M = 20 and send it to Bob. She chooses k = 5 as the secret value. Explain the procedure that Alice will use for computing the signature of the message. What information will she send Bob?
Apply poker test to the following sequence with level of significane α = 0.05. (4) 1001101000010000101111011 01110100101101100100110.
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:
| S | E | C | R | T |
| A | T | T | A | C |
| K | A | T | D | A |
| W | N | X | X | X |