- Encrypt the message “meet me at the usual place at ten rather than eight oclock” using the Hill Cipher with the key .

Show your calculations and the result.

- Show the calculations for corresponding decryption of the ciphertext to recover the original plaintext.

** **

- Determine the values of
*f*(27),*f*(49) and*f*(440), where*f*(*n*) is the Euler’s Totient Function.

C Find 3^{201 }mod 11; and 2^{341} mod 341

- Determine the multiplicative inverse of
*x*^{3}+*x*+ 1 in GF(2^{4}) with*m*(*x*) =*x*^{4}+*x*+ 1.

- Develop a table similar to Table 4.9 on page 121 of the textbook for GF(2
^{8}), with*m*(*x*) =*x*^{8 }_{+ }*x*^{4}+*x*^{3 + }*x*^{2 }+ 1 (from 0 to g^{14})

F The Miller-Rabin test can determine if a number is not prime but cannot determine if a number is prime. How can such an algorithm be used to test for primality?

- Given
*x*º 2 (mod 3),*x*º 2 (mod 7), and*x*º 3 (mod 5), please solve the*x*by using Chinese Remainder Theorem.

- Given
*p*= 17;*q*= 31;*e*= 7;*C*= 128, please calculate the*d*value for private key and recover the original plain text message*M*. (Need to show the details of the calculation in details)

* *

* *

* *

* *

* *

* *

- User A and B use the Diffie-Hellman key exchange technique with a common prime
*q*= 71 and a primitive root*a*= 7.

- If user A has a private key
*X*= 5, what is_{A}*A*’s public key*Y*?_{A} - If user B has a private key
*X*= 12, what is_{B}*B*’s public key*Y*?_{B} - What is the shared security key?

- Using the extended Euclidean algorithm, find the multiplicative inverses of

- 13 mod 2436 (10 points)
- 144 mod 233 (10 points)

- Draw a matrix similar to Table 1.4 (on page 21 of the textbook) that shows the relationship between security mechanisms and attacks.

Note:

Please provide your solution with details.

p(2)

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