Determine the frequencies of the various transitions between the primitive patterns, find frequently repeated sequences (relation-seeking), compare the time intervals on which these sequences are based (inverse comparison)

Which security mechanism(s) are provided in each of the following cases?A school server disconnects a student if she is logged into the system for more than two hours.

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Show that with Diffie-Hellman key establishment, we have c ^{x}_{2} mod p equal to c^{y}_{1} mod p. Diffie-Hellman and PKI are computationally expensive because they make use of the exponentiation operation. How can complexity of the computation of exponentiation be reduced?

1. 2521 2 1 is a Mersenne prime. Find the perfect number associated with this number. Write your answer using exponents with a base of 2.

2. In RSA encryption, if the public key is 35, what is the private key?

3. In RSA encryption, if the public key is 51, what is the private key?

4. In RSA encryption, if the public key is 143, what is the private key?

5. In RSA encryption, if the public key is 221, what is the private key?

6. a. Rewrite the first four perfect numbers with the binary system.

b. Describe the pattern or patterns you see in the result of part (a).

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