Apply runs test to the following sequence:
1001101000010000101111011 0111010010110110010011010
0110011100001100100111000
1100001101010111101001110
0010001111000001101010010
1000110100000110100101101
1110001001
First, combine all the given sequences into a single binary sequence: 1001101000010000101111011 0111010010110110010011010 0110011100001100100111000 1100001101010111101001110 0010001111000001101010010 1000110100000110100101101 1110001001 Count the total number of 1’s and 0’s: * Count of 1’s ((n_1)) = 81 * Count of 0’s ((n_0)) = 79 Next, identify the runs. A run is a __________ ________ _________ _______ _______ __________ ____.
________ _________ _______ ____ ___ _________ _________ ______ _______.
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Decrypt the ciphertext 101000111001 which was encrypted with the Toy block cipher once using the key 101010010. Show all the steps.
b) A 64 bit key for the DES is given below 11000111
10000101
11110111
11000001
11111011
10101011
10011101
10010001
i) Check whether the key is error free using the parity bits.
Alice wants to send Bob the message . She chooses
. How will she compute the cipher text? What information does she send to Bob?
Let . 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.
Apply runs test to the following sequence:
1001101000010000101111011 0111010010110110010011010
0110011100001100100111000
1100001101010111101001110
0010001111000001101010010
1000110100000110100101101
1110001001
) Let . We represent the field
by
. Let us write
. The table of values is given below:
|
|
| Vector |
|
| Vector |
| 0 |
|
| 8 |
|
|
| 1 |
|
| 9 |
|
|
| 2 |
|
| 10 |
|
|
| 3 |
|
| 11 |
|
|
| 4 |
|
| 12 |
|
|
| 5 |
|
| 13 |
|
|
| 6 |
|
| 14 |
|
|
| 7 |
|
|
i) Prepare logarithm and antilogarithm tables as given in page 23 of block 1.
ii) Compute and
using the logarithm and antilogarithm tables
Explain how Bob will decrypt the message.
9) a) Solve the discrete logarithm problem using Baby-Step, Giant-Step algorithm.
Find the inverse of 13 (mod 51) using extended euclidean algorithm.