Decrypt the message that was encrypted using RSA algorithm with
and
.
The modulus is (n=77=7\times 11), so (\varphi(n)=(7-1)(11-1)=60). The decryption exponent (d) satisfies ____ ____ _______ _________ _________.
_____ _________ ________ _________ ______ _____.
___ ________ ______ __________ __________ _________ _______ ________.
_____ _______ _______ _____ _____.
___ ____ ________ ____ _________ _______ _________ __________.
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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.
Find a recurrence that generates the sequence 110110110110110.
Explain how Bob will decrypt the message.
9) a) Solve the discrete logarithm problem using Baby-Step, Giant-Step algorithm.
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.
Alice wants to send Bob the message . She chooses
. How will she compute the cipher text? What information does she send to Bob?
Use Miller-Rabin test to check whether 75521 is a strong pseuodprime to the base 2.
Find the inverse of 13 (mod 51) using extended euclidean algorithm.