- 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 3201 mod 11; and 2341 mod 341
- Determine the multiplicative inverse of x3 + x + 1 in GF(24) with m(x) = x4+ x + 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?
- 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 XA = 5, what is A’s public key YA?
- If user B has a private key XB = 12, what is B’s public key YB?
- 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.
Please provide your solution with details.
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