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?
To solve this problem, Alice will use the Digital Signature Algorithm (DSA), which involves signing the message \(M = 20\) using the given parameters: - \(p = 83\) (prime modulus) - \(q = 41\) (a divisor of \(p-1\)) - \(g = 2\) (generator of a subgroup of order \(q\)) - \(a = 3\) (Alice's private key) - \(k = 8\) (Alice's secret nonce) ### ___ __________ __________ ___ ______.
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Text: "CBBGYAEBBFZCFEPXYAEBB", encrypted with affine cipher with key (7,2)
Solve the discrete logarithm problem (mod 47) using Baby-Step, Giant-Step algorithm.
Text:"KSTYZKESLNZUV", encrypted with Vigenère cipher with key "RESULT"
a) Considering the bytes 10001001 and 10101010 as elements of the field where
is the polynomial
find their product and quotient.
b) Find a recurrence that generates the sequence 110110110110110.
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 .
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 as follows:
Next, we choose an inveritble 2×2 matrix with coefficients in , for example,
This matrix has determinant and 5 is a unit in
with inverse
We write each pair of elements in
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
and we have
Decrypt the text "TWDXHUJLUENN" which was encrypted using the Hill’s cipher with the matrix as the encryption matrix
a) Apply the frequency test, serial test and autocorrelation test to the following sequence at level of significance :
011001110000110010011100.
b) Apply poker test to the following sequence with level of significane
1001101000010000101111011
01110100101101100100110.
c) Apply runs test to the following sequence:
1001101000010000101111011
0111010010110110010011010
0110011100001100100111000
1100001101010111101001110
0010001111000001101010010
1000110100000110100101101
1110001001
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 |