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Solve the the congruence 11x 4 (mod 26) Use the Lucas-Lehmer Test to show that 127...

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Advance Math

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?

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