Consider a network the uses TCP transport protocol Assume th

Consider a network the uses TCP transport protocol. Assume that the slow-start threshold (ssthresh) is set at 8 after which the congestion avoidance protocol is used. Assume that acknowledgements are expected to arrive one time unit after a window of segments is transmitted. Assume also that the timer for the third window expired with no ACK received. Trace the behavior of the system as progresses through 7 transmission cycles. This problem is on the RSA algorithm. Specifically, we consider 2 prime numbers p = 7 and q = 13 so that their product is n = p times q = 91. What is the Euler\'s phi function (or totient function) phi(91)? Try different small prime numbers d and find another number e such that phi(91)|(de-1); that is, try different values of small primes d and multiply it by a number e such that de - 1 is divisible by phi(91). What are the values of d and e? Assume that the message M = 9 is to be encrypted with the key d. What is the encrypted value of 9? Show how we can recover the message M = 9 at the receiver. If we encrypt M = 9 with the key e, what is the encrypted message?

Solution

for question 4 steps and logic:

now if to encrypt

c = m^e mod n =>

now to decrypt

m\' = c^d mod n =>

if in question given

m=9 encrypted with d

e)

c = m^e mod n => 9^5 mod 91 =(59049,91)=81

for part c and d

c = m^d mod n 9^2 mod 91

m\' = c^e mod n