Find a recurrence that generates the sequence 110110110110110.
Let's denote the sequence as (a_n), where (n \ge 0) and the sequence is (1, 1, 0, 1, 1, ______ _________ ________ _________ ____ _________ __________ ____ ________ _______ ___ ________.
_____ _________ __________ _______ _________ ________ ________ _______ __________ ___ ___ _____.
_______ ___ ___ __________ _______.
________ __________ _______ ________ ________ ______ _________ ___.
__________ _____ ______ ________ __________ ________ ___ _____ ____ ___ ______.
________ __________ _____ ________ ___ _____ _________ ________ ____ ____ ________.
____ _________ ________ ________ ___ ____ _________ _________ _______ ___ _____.
_____ ___ _____ ____ _______ _____ ___ _______ _____ ______.
________ _____ ____ ____ _______ _______ _______.
_________ __________ ________ _____ _______ _____ ____ ________ _________.
_________ ____ ___.
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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.
Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.
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.
Find the keys for the second round.
6) a) Considering the bytes 10001001 and 10101010 as elements of the field , where g(X) is the polynomial X8 + X4 + X3 + X + 1, find their product and quotient.
Alice wants to send Bob the message . She chooses
. How will she compute the cipher text? What information does she send to Bob?
Apply poker test to the following sequence with level of significance .
1001101000010000101111011
01110100101101100100110.
) 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