Complete the following exercises.

Question Description

1. List all multiplicative inverse pairs in modulus 20.

2.Find the multiplicative inverse of each of the following integers in Z₁₈₀ using the extended Euclidean algorithm.

a.38

b.7

c.132

3. Encrypt the message “this is an exercise” using one of the following ciphers. Ignore the space between words. Decrypt the message to get the original plaintext.

a. Additive cipher with key = 20

b. Multiplicative cipher with key = 15

c. Affine cipher with key = (15,20)

4.Use a brute-force attack to decipher the following message enciphered by Alice using an additive cipher. Suppose that Alice always uses a key that is close to her birthday, which is on the 13th of the month:

NCJAEZRCLASJLYODEPRLYZRCLASJLCPEHZDTOPDZQLNZTY

5.Use a brute-force attack to decipher the following message. Assume that you know it is an affine cipher and that the plaintext “ab” is enciphered to “GL”.

XPALASXYFGFUKPXUSOGEUTKCDGFXANMGNVS

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