1. You need to apply RSA algorithm for given prime numbers p=17 and q=19. Calcul

Question

1. You need to apply RSA algorithm for given prime numbers p=17 and q=19. Calculate private and public key. Encrypt and decrypt message m=219 to prove that the private and public numbers you calculated are accurate.

2. You need to apply RSA algorithm for given prime numbers p=17 and q=11. Calculate private and public key. Encrypt and decrypt message m=88 to prove that the private and public numbers you calculated are accurate.

3. Alice and Bob want to communicate over an insecure medium. Design, on the basis of a shared secret key KAB, a protocol, which enables Alice and Bob to authenticate each other. Assume that the shared secret key KAB is known in advance to both partners. b.) What are the disadvantages related to the use of a shared secret key?

4.  Alice and Bob want to communicate over an insecure medium. Design, on the basis of a shared secret key KAB, a protocol, which enables Alice and Bob to authenticate each other. Assume that the shared secret key KAB is not known in advance to both partners

Explanation / Answer

Answer 1:

Given: p=17, q=19

Modulus n = p * q = 323

Totient (phi) = (p-1)*(q-1) = 16* 18 = 288

Choose 'e' (encryption key ) such that GCD(e, phi) == 1

e = 5 satisfies the equation

Choose 'd' (decryption key) such that (d * e) mod phi == 1

d = 173 satisfies the equation

Public key = (n,e) = (323, 5)

Private Key = (n,d) = (323, 173)

M (message) = 219

C (cipher text) = Me mod n = 2195 mod 323 = 155

P (plain text) = Cd mod n = 155173 mod 323 = 219

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