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?
Alice first fixes the public parameters (p=83), (q=41), (g=2). Her private signing key is (a=3). From this she computes the public verification key [ y=g^a \bmod p = 2^3 \bmod 83 = 8. ] To sign the message (\mathcal{M}=20), Alice chooses the secret random ____ ___ _____ _________ ___ ___.
_________ ________ ___ ______ __________.
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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.
Find a recurrence that generates the sequence 110110110110110.
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 . 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
Decrypt the message that was encrypted using RSA algorithm with
and
.
Apply the frequency test, serial test and autocorrelation test to the following sequence at level of significance :
011001110000110010011100.