Solve the the congruence 11x 4 (mod 26)
Use the Lucas-Lehmer Test to show that 127 = 2^7-1 is prime.
Use the Lucas-Lehmer Test to show that 2047 = 2^11- 1 is notprime
Use the Lucas-Lehmer Test to show that 8191 = 2^13 - 1 isprime.
Assume Alice uses the following information to develop thepublic key, N, in an SS Cryptosystem: p = 23 and
q = 41 with N = p2q = 21689. Suppose Bob wants to encrypt themessage m = 143 what ciphertext c does he
send Alice? Show this message, c, decrypts into m.
Playing the role of Eve, suppose Alice published the public key,N = 21689, in an SS Cryptosystem and you
intercept the message c = 263 sent from Bob to Alice. What wasBob's original message?
