Find a recurrence that generates the sequence 110110110110110.
To find a recurrence that generates the sequence 110110110110110, let's first examine its structure. The sequence appears to alternate between "11" and "0" every two terms, so it can be expressed as: \[ 1, 1, 0, 1, 1, 0, 1, _________ __________ _________ ________ ____ __________ ______ ____ __________ __________.
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Apply runs test to the following sequence:
1001101000010000101111011
0111010010110110010011010
0110011100001100100111000
1100001101010111101001110
0010001111000001101010010
1000110100000110100101101
1110001001
i) Prepare logarithm and antilogarithm tables as given in page 23 of block 1
b) i) Bob uses ElGamal cyrptosystem with parametersand the secret value x = 3. What values will he make public?
ii) Alice wants to send Bob the messageShe 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
Apply poker test to the following sequence with level of significane α = 0.05. (4) 1001101000010000101111011 01110100101101100100110.
c) Apply runs test to the following sequence
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"
a) 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 726-
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.This matrix has determinant
5 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
Find a recurrence that generates the sequence 110110110110110.