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?
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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.
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?
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
Find a recurrence that generates the sequence 110110110110110.
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.
Bob uses ElGamal cryptosystem with parameters ,
and the secret value
. What values will he make public?