## Calculations

Calculations. Calculations.

1. 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.

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

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

C  Find 3201 mod 11; and 2341 mod 341

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

1. 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?

1. 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.

1. 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)

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

1. If user A has a private key XA = 5, what is A’s public key YA?
2. If user B has a private key XB = 12, what is B’s public key YB?
3. What is the shared security key?

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

1. 13 mod 2436   (10 points)
2. 144 mod 233   (10 points)

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

Note:

p(2)

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