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 ___ ____ _________ _____ __________ _____ _________ ____ _________.
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Alice wants to send Bob the message . She chooses
. How will she compute the cipher text? What information does she send to Bob?
Apply runs test to the following sequence:
1001101000010000101111011 0111010010110110010011010
0110011100001100100111000
1100001101010111101001110
0010001111000001101010010
1000110100000110100101101
1110001001
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.
Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.
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 |
In this exercise, we introduce you to Hill cipher. In this cipher, we convert our message to numbers, just as in affine cipher. However, instead of encrypting character by character, we encrypt pairs of characters by multiplying them with an invertible matrix with co-efficients in Z26.
Here is an example: Suppose we want to ENCRYPT "ALLISWELL". Since we require the plaintext to have even number of characters, we pad the message with the character ‘X’. We break up the message into pairs of characters AL, LI, SW, EL and LX. We convert each pair of characters into a pair elements in Z26 as follows:
">
Next, we choose an invertible matrix with coefficients in
, for example,
.
This matrix has determinant and
is a unit in
with inverse
. We write each pair of elements in
as a column vector and multiply it by A:
We then convert each pair of numbers to a pair of characters and write them down. In this example, we get the cipher text "LSPFYGXUEN" corresponding to the plain text "ALLWELL". To decrypt, we convert pairs of characters to pairs of numbers and multiply by and we have
Decrypt the text "TWDXHUJLUENN" which was encrypted using the Hill’s cipher with the matrix as the encryption matrix.
Bob uses ElGamal cryptosystem with parameters ,
and the secret value
. What values will he make public?