Assuming that p = 7 q = 11 (n == 77) then possible values for e == 91 and d =31 since the values satisfy the equation: n = p*q e*d - 1 == k*(p-1)*(q-1) for k = 1,2,3,

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Assuming that p = 7 q = 11 (n == 77) then possible values for e == 91 and d =31 since the values satisfy the equation:

n = p*q

e*d - 1 == k*(p-1)*(q-1) for k = 1,2,3,....

91*31 - 1 == 47*(11-1)*(7-1)

2820 == 47*10*6 

Given the message m == 2 then encryption of m results in 2 since

m^emod n = 2⁹¹ mod 77 == 2

The decryption calculation also results in 2:

2^d mod n == 2³¹ mod 77 == 2

In fact, for any message m = 2, 3, 4, 5 .. < n, the encoding of the message m using e

results in the message m and using d to decode the message again results in the original

message m 

 m^emod n == m and m^d mod n == m 

This should not happen Explain the error :