Consider the RSA public key cryptosystem. Table 1 ( figure 1 ) contains the plain text that will be encrypted.

If the prime numbers p=3 and q=11 are used to encrypt the plain text:

a. Compute n and z.

b. Is d=5 a number relatively prime to the number obtained for z previously? If d is not a number relatively prime to z, propose a legal number for d.

c. If e=3, use the information calculated in items a,b and table 1 to encrypt the following words (IF POSSIBLE):

"COOL" and "FUN"

d. List the public key pair and the private key pair used during the previous problem.

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Symbolic Numeric 40 10 12 13 14 15 16 17 18 19 20 21 23 24 25