Draw a matrix similar that shows the relationship between

Question

A.

a. 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.

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

B. Determine the values of Φ(27), Φ(49) and Φ(440), where Φ(n) is the Euler's Totient Function.

C Find 3²⁰¹ mod 11; and 2³⁴¹ mod 341

D. Determine the multiplicative inverse of x³ + x + 1 in GF(2⁴) with m(x) = x⁴ + x + 1.

E. Develop a table similar to Table 4.9 on page 121 of the textbook for GF(2⁸), with m(x) = x⁸ + x⁴ + x³ + x² + 1 (from 0 to g¹⁴)

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?

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

H. 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)

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

a. If user A has a private key X_A= 5, what is A's public key Y_A?

b. If user B has a private key X_B= 12, what is B's public key Y_B?

c. What is the shared security key?

J. Using the extended Euclidean algorithm, find the multiplicative inverses of

a. 13 mod 2436

b. 144 mod 233

K. Draw a matrix similar that shows the relationship between security mechanisms and attacks.

Answer 1

For the following mathematics problem, carry on step by step method and show all in a word document file. Q1. Find out the values of F(27), F(49) and F(440), in which F(n) is the Euler's Totient Function. Q2. Determine 3201 mod 11; and 2341 mod 341. Q3. Find out the multiplicative inverse of x3 + x + 1 in GF(24) having m(x) = x4 + x + 1. Q4. Build up a table identical to the of the textbook for GF(28), having m(x) = x8 + x4 + x3 + x2 + 1 (from 0 to g14) Q5. The Miller-Rabin test can find out if a number is not prime however can’t find out if a number is prime. Explain how can such an algorithm be employed to test for the primality? Q6. Provided x = 2 (mod 3), x = 2 (mod 7), and x = 3 (mod 5), please resolve the x by employing Chinese Remainder Theorem. Q7. Provided p = 17; q = 31; e = 7; C = 128, please compute the d value for the private key and improve the original plain text message M.