7. The following ciphertext 261 163 196 172 217 172 89 142 76 217 209 172 7 was produced using the Merkle-Hellman Knapsack cryptosystem for a user with a private key that consists of the sequence (5,8,17, 36, 71}, modulus m = message." 145, and multiplier a = 82. Obtain the plaintext 8. The Rabin public-key encryption scheme is similar to RSA. Research this cryptosystem and decrypt the following ciphertext: 25292168 which was encrypted for a user with public key n = 27219809. 9. Prove that 9un+24 if and only if 9 un. Hìnt: Use identity (1) on page 288. 10. Establish the following Fibonacci identity: (mod 3) "n 8+4n 11. Establish the following relation between Fibonacci and Lucas numbers: 11/19/2 百/08 67 prt sc delete insert f12 OL! V/ [オ backspace P. home enter 7

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