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, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0). ______ _____ _______ _________ ________ ___ ______ _______ _________ ___.
_________ ____ _______ ___ __________ ___ ________ _____ _____ __________.
__________ ___ ____ ____ ______ _______.
_________ _______ ___ _________ ____ _____ _____.
_______ __________ ______ _____ ________ ________ ______ ____ _________.
_______ _____ _______ ______ ______ ____ _________ _________ _________ _______ ____.
______ ________ __________ _____ ______ ______ ___ _________ _______ _____.
___ ___ _____ __________ ____.
______ _________ ___ ____ _______ _________ _________ ___ _____ __________ ________.
________ ______ ________ ________ _____ ______ ________ ______.
____ _________.
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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 use the ElGamal digital signature scheme with public parameters ,
, secret value
and
. She wants to sign the message
and send it to Bob. She chooses
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 the frequency test, serial test and autocorrelation test to the following sequence at level of significance :
011001110000110010011100.
Alice wants to use the Digital Signature algorithm for signing messages. She chooses ,
,
and
. Alice wants to sign the message
. She chooses the secret value
. Explain the procedure that Alice will use for computing the signature. What information will she send Bob?
Bob uses ElGamal cryptosystem with parameters ,
and the secret value
. What values will he make public?
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.
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".
b) 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 |