c) Alice wants to use the Digital Signature algorithm for signing messages. She chooses p = 83, q = 41, g = 2 and a = 3. Alice wants to sign the message M = 20. She chooses the secret value k = 8. Explain the procedure that Alice will use for computing the signature. What information will she send Bob?
We are given the following parameters for the Digital Signature Algorithm (DSA): * $p = 83$ (a prime number) * $q = 41$ (a prime divisor of $p - 1 = 82$) * $g = 2$ (generator of order $q$ mod $p$) * $a = 3$ (private key of Alice) * $M = 20$ (message to sign) * $k = 8$ (random secret per-signature integer) We will now follow the DSA signature generation ______ _______ __________ _______ ___ _______ _______ ____.
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b) A 64 bit key for the DES is given below
i) Check whether the key is error free using the parity bits.
ii) Find the keys for the second round.
i) Prepare logarithm and antilogarithm tables as given in page 23 of block 1
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.
ii) Find the keys for the second round
ii) Compute using the logarithm an antilogarithm tables
b) 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"
Considering the bytes 10001001 and 10101010 as elements of the field F2[X]/hg(X)i, where g(X) is the polynomial X 8 +X 4 +X 3 +X +1, find their product and quotient.