Find the inverse of 13 (mod 51) using extended euclidean algorithm.
To find the inverse of 13 modulo 51 using the Extended Euclidean Algorithm, we need to solve for \( x \) in the equation:
\[
13x \equiv 1 \mod 51
\]
This is equivalent to finding \( x \) such that \( 13x - 51k = _________ _______ ________ ______ _______ ________ ______ __________ _____ _______ ____.
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Solve the discrete logarithm problem 5x ≡ 22 (mod 47) using Baby-Step, Giant-Step algorithm.
a) Find the product of
using the algorithm in page 23, block 1. You should show all the steps as in example 11, pag 22, 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
a) Decrypt the ciphertext 101000111001 which was encrypted with the Toy block cipher once using the key 101010010. Show all the steps
a) Apply the frequency test, serial test and autocorrelation test to the following sequence at level of significance α = 0.05: 011001110000110010011100
a) Decrypt the message c = 23 that was encrypted using RSA algorithm with e = 43 and n = 77.
Let f (x) = x3 − x − 1 ∈ Z5[x]. 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.